Major General Edward O. Ord - American Civil War

Major General Edward O. Ord - American Civil War Edward O. Ord - Early Life Career: Born October 18, 1818 at Cumberland, MD, Edward Otho Cresap Ord was the son of James and Rebecca Ord.  His father briefly served in the US Navy as a midshipman but transferred to the US Army and saw action during the War of 1812.  A year after Edwards birth, the family moved to Washington, DC.  Educated in the nations capital, Ord quickly showed an aptitude for mathematics.  To further these skills, he obtained an appointment to the US Military Academy in 1835.  Arriving at West Point, Ords classmates included Henry Halleck, Henry J. Hunt, and Edward Canby.  Graduating in 1839, he ranked seventeenth in a class of thirty-one and received a commission as a second lieutenant in the 3rd US Artillery. Edward O. Ord - To California: Ordered south, Ord immediate saw combat in the Second Seminole War.  Promoted to first lieutenant in 1841, he next moved to garrison duty at several forts along the Atlantic coast.  With the beginning of the Mexican-American War and swift capture of California in 1846, Ord was dispatched to the West Coast to aid in occupying the newly-captured territory.  Sailing in January 1847, he was accompanied by Halleck and Lieutenant William T. Sherman.  Arriving in Monterey, Ord took command of  Battery F, 3rd US Artillery with orders to complete the construction of Fort Mervine.  With Shermans assistance, this task was soon completed.  With the beginning of the Gold Rush in 1848, prices for goods and living expenses began to outpace the officers salaries.  As a result, Ord and Sherman were permitted to take side jobs to make extra money.   This saw them conduct a survey of Sacramento for John Augustus Sutter, Jr. which established much of the layout for the citys central areas.  In 1849, Ord accepted a commission to survey Los Angeles.  Aided by William Rich Hutton, he completed this task and their work continues to provide insight in the citys earliest days.  A year later, Ord was ordered north to the Pacific Northwest where he commenced surveying the coast.  Promoted to captain that September, he returned to California in 1852.  While on garrison duty at Benicia, Ord married  Mary Mercer Thompson on October 14, 1854.  Over the next five years, he remained on the West Coast and took part in various expeditions against the Native American in the region. Edward O. Ord - The Civil War Begins: Returning east in 1859, Ord arrived at Fortress Monroe for service with the artillery school.  That fall, his men were directed to move north to aid in suppressing John Browns attack on Harpers Ferry but were not needed as Lieutenant Colonel Robert E. Lee was able to deal with the situation.  Sent back to the West Coast the following year, Ord was there when the Confederates attacked Fort Sumter and opened the Civil War in April 1861.  Returning east, he received a commission as a brigadier general of volunteers on September 14 and assumed command of a brigade in the Pennsylvania Reserves.  On December 20, Ord led this force as it won a skirmish with Brigadier General J.E.B. Stuarts Confederate cavalry near Dranesville, VA.  Ã‚  Ã‚  Ã‚  Ã‚   On May 2, 1862, Ord received a promotion to major general.  Following brief service in the Department of the Rappahannock, he was transferred west to lead a division in Major General Ulysses S. Grants Army of the Tennessee.  That fall, Grant ordered Ord to direct part of the army against Confederate forces led by Major General Sterling Price.  This action was to be coordinated with Major General William S. Rosecrans Army of the Mississippi.  On September 19, Rosecrans engaged Price at the Battle of Iuka.  In the fighting, Rosecrans won a victory, but Ord, with Grant at his headquarters, failed to attack due to an apparent acoustic shadow.  A month later, Ord won a victory over Price and Major General Earl Van Dorn at Hatchies Bridge as the Confederates retreated after being repulsed at Corinth. Edward O. Ord - Vicksburg the Gulf: Wounded at Hatchies Bridge, Ord returned to active duty in November and held a series of administrative posts.  While Ord recovered, Grant embarked on a series of campaigns to capture Vicksburg, MS.  Laying siege to the city in May, the Union leader relieved the troublesome Major General John McClernand from command of XIII Corps the following month.  To replace him, Grant selected Ord.  Taking over on June 19, Ord led the corps for the remainder of the siege which ended on July 4.  In the weeks after the fall of Vicksburg, XIII Corps took part in Shermans march against Jackson.  Serving in Louisiana as part of the Department of Gulf for much of the latter part of 1863, Ord left XIII Corps in January 1864.  Returning east, he briefly held posts in the Shenandoah Valley. Edward O. Ord - Virginia:  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   On July 21, Grant, now leading all Union armies, directed Ord to assume command of XVIII Corps from the ill Major General William Baldy Smith.  Though part of Major General Benjamin Butlers Army of the James, XVIII Corps operated with Grant and the Army of the Potomac as they besieged Petersburg.  In later September, Ords men crossed the James River and took part in the Battle of Chaffins Farm.  After his men succeeded in capturing Fort Harrison, Ord fell badly wounded as he attempted to organize them to exploit the victory.  Out of action for the remainder of the fall, he saw his corps and the Army of the James completely reorganized in his absence.  Resuming active duty in January 1865, Ord found himself in temporary command of the Army of the James. In this post for the remainder of the conflict, Ord directed the armys operations during the latter stages of the Petersburg Campaign including the final assault on the city on April 2.  With Petersburgs fall, his troops were among the first to advance into the Confederate capital of Richmond.  As Lees Army of Northern Virginia retreated west, Ords troops joined in the pursuit and ultimately played a key role in blocking the Confederate escape from Appomattox Court House.  He was present at Lees surrender on April 9 and later purchased the table at which Lee had sat. Edward O. Ord - Later Career: Following President Abraham Lincolns assassination on April 14, Grant ordered Ord north to investigate and ascertain if the Confederate government had played a role.  His determination that John Wilkes Booth and his conspirators had acted alone helped calm demands that the newly-defeated South be punished.  That June, Ord assumed command of the Department of the Ohio.  Promoted to brigadier general in the regular army on July 26, 1866, he later oversaw the Department of Arkansas (1866-1867), Fourth Military District (Arkansas Mississippi, 1867-68), and Department of California (1868-1871).   Ord spent the first half of the 1870s commanding the Department of the Platte before moving south to lead the Department of Texas from 1875 to 1880.  Retiring from the US Army on December 6, 1880, he received a final promotion to major general a month later.  Accepting a civil engineering position with the Mexican Southern Railroad, Ord worked to build a line from Texas to Mexico City.  While in Mexico in 1883, he contracted yellow fever prior to departing on business for New York.  Falling severely ill while at sea, Ord was landed at Havana, Cuba where he died on July 22.  He remains were brought north and interred at Arlington National Cemetery.   Selected Sources Civil War Trust: Edward O. OrdTSHA: Edward O. OrdOhio Civil War Central: Edward O. Ord

Complete Guide to Fractions and Ratios on SAT Math

Complete Guide to Fractions and Ratios on SAT Math SAT / ACT Prep Online Guides and Tips You likely had your first taste of working with fractions sometime in elementary school, though it's probably been a while since you've had to deal with how they shift, change, and interact with one another. To refresh, fractions and ratios are both used to represent pieces of a whole. Fractions tell you how many pieces you have compared to a potential whole amount (3 red marbles in a bag of 5, for example), while ratios compare pieces to each other (3 red marbles to 2 blue marbles) or, more rarely, pieces to the whole amount (again, 3 red marbles in 5 total). If this sounds complicated to you right now, don’t worry! We will go through all the principles behind fractions and ratios in this guide. If this seems easy to you right now, definitely check out the practice problems at the end of the guide to make sure you have mastered all the different kinds of fraction and ratio problems you’ll see on the test. The SAT likes to present familiar concepts in unfamiliar ways, so don’t let your mastery of fractions lead you to make assumptions about how you’ll see fractions and ratios on the test. No matter how comfortable you are (or are not) with fractions and ratios right now, this guide is for you. Here, we will go through the complete breakdown of fractions and ratios on the SAT- what they mean, how to manipulate them, and how to answer the most difficult fraction and ratio problems on the SAT. This Guide This guide is seperated into two distinct categories- everything you need to know about fractions and everything you need to know about ratios. For each section, we will go through the ins and outs of what fractions and ratios mean as well as how to manipulate and solve the different kinds of fraction and ratio problems you'll see on the SAT. We will also breakdown how you can tell when an SAT problem requires a ratio or a fraction and how to set up your approach these kinds of problems. At the end, you will be able to test your knowledge on real SAT math questions. The more you prep for the SAT, the more your brain can be Swiss-army-knife-ready for any question the test can throw at you. What are Fractions? $${\a \piece}/{\the \whole}$$ Fractions are pieces of a whole. They are expressed as the amount you have (the numerator) over the whole (the denominator). A pizza is divided into 8 pieces. Kyle ate 3 pieces. What fraction of the pizza did he eat? He ate $3/8$ths of the pizza. 3 is the numerator (top number) because he ate that many pieces of the whole, and 8 is the denominator (bottom number) because there are 8 pieces total (the whole). Math is always more fun when it's delicious. Special Fractions A number over itself equals 1 $3/3=1$ $10/10=1$ $(a+b)/(a+b)=1$ A whole number can be expressed as itself over 1 $5=5/1$ $22/1=22$ $(a+b)/1=a+b$ 0 divided by any number is 0 $0/17=0$ $0/(a+b)=0$ There is one exception to this rule: $0/0=\undefined$. The reason for this lies in the next rule. Any number divided by 0 is undefined Zero cannot act as a denominator. For more information on this check out our guide to advanced integers. But for now all that matters is that you know that 0 cannot act as a denominator. Reducing Fractions If both the numerator and the denominator have a common factor (a number they can both be divided by), then the fraction can be reduced. For the purposes of the SAT, you will need to reduce your fractions to get to your final answer. To reduce a fraction, you must divide both the numerator and the denominator by the same amount. This keeps the fraction consistent and maintains the proper relationship between numerator and denominator. If your fraction is $3/12$, then it can be written as $1/4$. Why? Because both 3 and 12 are divisible by 3. $3/3=1$ and $12/3=4$. So your final fraction is $1/4$ Now let's figure out how to perform the four basic math functions on fractions. Adding or Subtracting Fractions You can add or subtract fractions as long as their denominators are the same. To do so, you keep the denominator consistent and simply add the numerators. $4/15+2/15=6/15$ But you CANNOT add or subtract fractions if your denominators are unequal. $4/15+2/5=?$ So what can you do when your denominators are unequal? You must make them equal by finding a common multiple (number they can both multiply evenly into) of their denominators. In the case of $4/15+2/5$, a common multiple of the denominators 15 5 is 15. When you find a common multiple of the denominators, you must multiply both the numerator and the denominator by the amount it took to achieve that number. Again, this keeps the fraction (the relationship between numerator and denominator) consistent. Think of it as the opposite of reducing a fraction. To get to the common denominator of 15, $4/15$ must be multiplied by $1/1$ Why? Because 15*1=15. $(4/15)(1/1)=4/15$. The fraction remains unchanged. To get to the common denominator of 15, $2/5$ must be multiplied by $3/3$. Why? Because 5*3=15. $(2/5)(3/5)=6/15$. Now we can add them, as they have the same denominator. $4/15+6/15=10/15$ We can further reduce $10/15$ into $2/3$ because both 10 and 15 are divisible by 5. So our final answer is $2/3$. Multiplying Fractions Multiplying fractions is a bit simpler than adding or dividing fractions. There is no need to find a common denominator- you can just multiply the fractions straight across. To multiply a fraction, first multiply the numerators. This product becomes your new numerator. Next, multiply your two denominators. This product becomes your new denominator. $1/4*2/3=(1*2)/(4*3)=2/12$ And again, we reduce our fraction. Both the numerator and the denominator are divisible by 2, so our final answer becomes: $1/6$ Special note: you can speed up the multiplication and reduction process by finding a common factor of your cross multiples before you multiply. $1/4*2/3$ = $1/2*1/3$. Why? Because both 4 and 2 are divisible by 2, we were able to reduce the cross multiples before we even began. This saved us time in reducing the final fraction at the end. So now we can simply say: $1/2*1/3=1/6$. No need to further reduce- our answer is complete. Take note that reducing cross multiples can only be done when multiplying fractions, never while adding or subtracting them! It is also a completely optional step, so do not feel obligated to reduce your cross multiples- you can simply reduce your fraction at the end. Dividing Fractions In order to divide fractions, we must first take the reciprocal (the reversal) of one of the fractions. Afterwards, we simply multiply the two fractions together. Why do we do this? Because division is the opposite of multiplication, so we must reverse one of the fractions to turn it back into a multiplication question. ${2/3}à ·{3/4}$ = $2/3*4/3$ (we took the reciprocal of $3/4$, which means we flipped the fraction upside down to become $4/3$) $2/3*4/3=8/9$ But what happens if you need to divide a fraction by a whole number? If a cake is cut into thirds and each third is cut into fourths, how many pieces of cake are there? *** We start out with $1/3$ of a cake and we need to divide each third 4 more times. Because 4 is a whole number, it can be written as $4/1$. This means that its reciprocal is $1/4$. $1/3à ·4$ = $1/3*1/4=1/12$ Our denominator (the whole) is 12. This means there will be 12 pieces total in the cake. Decimal Points Because fractions are pieces of a whole, you can also express fractions as either a decimal point or a percentage. To convert a fraction into a decimal, simply divide the numerator by the denominator. (The / symbol also acts as a division sign.) $4/5$ = 4/5 = 0.8 Sometimes it is easier to convert a fraction to a decimal in order to work through a problem. This can save you time and effort trying to figure out how to divide or multiply fractions. If $j/k=32$ and $k=3/2$, what is the value of $1/2j$ ? *** As you can see, there are two ways to approach this problem- using fractions and using decimals. We’ll look at both ways. If you were to use fractions, you would set up the problem as a fraction division problem. $k=3/2$ So $j/k=j/{3/2}$ $j/{3/2}$ = $j*2/3$ (remember, we take the reciprocal when we divide) So our full problem looks like this: $2/3*j=32$ Now we must divide 32 by $2/3$ in order to bring it over to the other side and isolate j. This means we need to take the reciprocal yet again. So ${32}/{2/3}$ = $32*3/2=96/2=48$ $j=48$ Now, for the final step, we must take $1/2$ of j. (Note: to "take $1/2$" is the same thing as multiplying by $1/2$.) $48*{1/2}=48/2=24$ Our final answer is 24. Alternatively, we could save ourselves the headache of using fractions and reciprocals and simply use decimals instead. We know that $k=3/2$. Instead of keeping the fraction, let us convert it into a decimal. $3à ·2=1.5$ So $k=1.5$ $j/k=32$ $j/1.5=32$ When you multiply both sides by 1.5, you get: $j=(32)(1.5)=48$ $j=48$ And ${1/2}j={1/2}(48)=24$ So again, our final answer is 24. Percentages After you convert your fraction to a decimal, you can also turn it into a percentage (if needed). So 0.8 from can also be written as 80%, because 0.8*100=80. A pie chart is a useful way of showing relative sizes of fractions and percentages. This shows just how large a fraction $7/10$ (or 70%) truly is. Mixed Fractions Sometimes you may be given a mixed fraction on the SAT. A mixed fraction is a combination of a whole number and a fraction. For example, 7$3/4$ is a mixed fraction. We have a whole number, 7, and a fraction, $3/4$. You can turn a mixed fraction into an ordinary fraction by multiplying the whole number by the denominator and then adding that product to the numerator. The final answer will be ${\the \new \numerator}/{\the \original \denominator}$. 7$3/4$ (7)(4)=28 28+3=31 So your final answer = $31/4$ You must convert mixed fractions into fractions in order to multiply, divide, add, or subtract them with other fractions. In this problem, we began with 5 gallons of water and we ended with 2$1/3$. We must figure out how many gallons we used. 5−2 $5-2{1/3}$ First, let’s get our mixed fraction into a regular fraction. 2$1/3$ = ${[(2*3)+1]}/3={7/3}$ $5/1-7/3$ Now, we need to give each fraction the same denominator. We'll do this by converting $5/1$ into a new fraction with a denominator of 3. $5/1*3/3=15/3$ Finally, we can find the difference between the amounts. $15/3-7/3=8/3$ So we have used up $8/3$rds of the water. Now let’s count how many times the pail was emptied to use up that $8/3$rds of the total water. If you count the dots, the pail was emptied 8 times (the first dot does not count as a time it was emptied- that is merely our starting point). Because the same amount of water was removed each time, we must divide our emptied water by 8. ${8/3}à ·{8/1}$ = $8/3*1/8$ We can now either reduce the cross-multiples (because this is a multiplication problem), which would give us: $8/3*1/8$ = $1/3*1/1$ $1/3*1/1=1/3$ Or we can multiply through and then reduce afterwards: $8/3*1/8=8/24$ $8/12=1/3$ Either way, our final answer is $1/3$; each trip removed $1/3$ of a gallon of water from the tank. Now that we've broken down all there is to know about SAT fractions, let's take a look at their close cousin- the ratio. This shape is called the "golden ratio" and has been studied for thousands of years. It has applications in geometry, nature, and architecture. What are Ratios? Ratios are used as a way to compare one thing to another (or multiple things to one another). If Leslie has 5 white socks and 2 red socks, the white socks and the red socks have a ratio of 5 to 2. Expressing Ratios Ratios can be written in three different ways: A â€Å'to â€Å'B A:B $A/B$ No matter which way you write them, these are all ratios comparing A to B. Different Types of Ratios Just as a fraction represents a part of something out of a whole (written as: ${\a \part}/{\the \whole}$), a ratio can be expressed as either: aâ€Å'part:a â€Å'different â€Å'part OR aâ€Å'part:theâ€Å' whole Because ratios compare values, they can either compare individual pieces to one another or an individual piece to the whole. If Leslie has only 5 white socks and 2 red socks in a drawer, the ratio of white socks to all the socks in the drawer is 5 to 7. (Why 7? Because there are 5 white and 2 red socks, so together they make 5+2=7 socks total.) Some of the many uses of ratios in action (in this case, the ratios are- a part: a different part). Reducing Ratios Just as fractions can be reduced, so too can ratios. Kyle has a stamp collection. 45 of them have pictures of daisies and 30 of them have pictures of roses. What is the ratio of daisy stamps to rose stamps in his collection? *** Right now, the ratio is $45:30$. But they have a common denominator of 15, so this ratio can be reduced. $45/15=3$ $30/15=2$ So the stamps have a ratio of $3:2$ Increasing Ratios Because you can reduce ratios, you can also do the opposite and increase them. In order to do so, you must multiply each piece of the ratio by the same amount (just as you had to divide by the same amount on each side to reduce the ratio). So the ratio of 4:3 can also be $4(2):3(2)=8:6$ $4(3):3(3)=12:9$ And so on. Marbles are to be removed from a jar that contains 12 red marbles and 12 black marbles. What is the least number of marbles that could be removed so that the ratio of red marbles to black marbles left in the jar will be 4 to 3? *** Right now, there are an equal amount of marbles, so the ratio is 12:12 (or 1:1) We know that we have an end ratio of 4:3 that we want to achieve and that each side of the ratio has to be multiplied (or divided) by the same amount to keep the ratio consistent. We want to remove as few marbles as possible, so let us imagine that 4:3 is a reduced ratio. That means we need to see how many total marbles the reduced ratio of 4:3 could possibly be. So both 4 and 3 have to be multiplied by the same amount to maintain their ratio and yet achieve a higher number of total marbles than just their 7 (4+3=7). We can see that 12 is divisible by 4, so the red marbles could conceivably remain unchanged in order to get a new ratio of 4:3. $12/4=3$ Because 4 can go evenly into 12, this will give us the fewest amount of marbles taken away. Because the 4 is multiplied 3 times to get 12, we know that both 4 and 3 must be multiplied by 3 to keep a new ratio of 4:3 consistent. To find the new number of black marbles, we take 3*3=9. The new amount of black marbles has to be 9. And because our red marbles remain the same (12), we must take only 3 marbles away from the total number of marbles (Why? Because 12â€Å' blackâ€Å' marbles−3 â€Å'blackâ€Å' marbles=9â€Å' blackâ€Å' marbles) So our final answer is 3, we must take 3 black marbles away to get a new ratio of 4:3 of red marbles to black marbles. Finding the Whole If you are given a ratio comparing two parts (piece:anotherâ€Å'piece), and you are told to find the whole amount, simply add all the pieces together. It may help you to think of this like an algebra problem wherein each side of the ratio is a certain multiple of x. Because each side of the ratio must always be divided or multiplied by the same amount to keep the ratio consistent, we can think of each side as having the same variable attached to it. For example, a ratio of 4:5 can be: $4(1):5(1)=4:5$ $4(2):5(2)=8:10$ And so on, just as we did above. But this means we could also represent 4:5 as: $4x:5x$ Why? Because each side must change at the same rate. And in this case, our rate is $x$. So if you were asked to find the total amount, you would add the pieces together. $4x+5x=9x$. The total amount is 9x. In this case, we don’t have any more information, but we know that the total must be divisible by 9. So let’s take a look at another problem. Teyvon has a basket of eggs that he is going to sell. There are two different kinds of eggs in the basket- white and brown. The brown eggs are in a ratio of 2:3 to the white eggs. What is NOT a possible number of eggs that Teyvon can have in the basket? A) 5 B 10 C) 12 D) 30 E) 60 *** In order to find out how many eggs he has total, we must add the two pieces together. So 2+3=5 This means that the total number of eggs in the basket has to either be 5 or any multiple of 5. Why? Because 2:3 is the most reduced form of the ratio of eggs in the basket. This means he could have: $2(2):3(2)=4:6$ eggs in the basket (10 eggs total) $2(3):3(3)=6:9$ eggs in the basket (15 eggs total) And so forth. We don’t know exactly how many eggs he has, but we know that it must be a multiple of 5. This means our answer is C, 12. There is no possible way that he can have 12 eggs in the basket. Now that we are armed with knowledge of fractions and ratios, we must follow the right steps to solve our problems. How to Solve Fraction, Ratio, and Rational Number Questions Now that we have discussed how fractions and ratios work indivisually, let's look at how you'll see them on the test. When you are presented with a fraction or ratio problem, take note of these steps to find your solution: #1: Identify whether the problem involves fractions or ratios A fraction will involve the comparison of a $\piece/\whole$. A ratio will almost always involve the comparison of a piece:piece (or, very rarely, a piece:whole). You can tell when the problem is ratio specific as the question text will do one of three things: Use the : symbol, Use the phrase "___ to ___† Explicitly use the word "ratio† in the text. If the questions wants you to give an answer as a ratio comparing two pieces, make sure you don’t confuse it with a fraction comparing a piece to the whole! #2: If a ratio question asks you to change or identify values, first find the sum of your pieces In order to determine your total amount (or the non-reduced amount of your individual pieces), you must add all the parts of your ratio together. This sum will either be your complete whole or will be a factor of your whole, if your ratio has been reduced. A total of 120,000 votes were cast for 2 opposing candidates, Garcia and Pà ©rez. If Garcia won by a ratio of 5 to 3, what was the number of votes cast for Pà ©rez? (A) 15,000 (B) 30,000 (C) 45,000 D) 75,000 (E) 80,000 *** As you can see, our ratio of 5 to 3 has been greatly reduced (neither of those numbers is in the tens of thousands). We know that there are a total of 120,000 votes, so we need to determine the number of votes for each candidate. Let’s first add our ratio pieces together. 5:3 = 5+3=8 Because 8 is much (much) smaller than 120,000, we know that 8 is not our whole. But 8 is the factor of our whole. ${120,000}/8=15,000$ So if we think of 15,000 as one component (a replacement for our variable, $x$), and Garcia and Pà ©rez have a ratio of 5 components to 3 components, then we can find the total number of votes per candidate. G:P=5:3 = $5x:3x$ 5*15,000=75,000 3*15,000=45,000 So Garcia earned 75,000 votes and Pà ©rez earned 45,000 votes. (You can even confirm that this must be the correct number of votes each by making sure they add up to 120,000. 75,000+45,000=120,000. Success!) So our final answer is C, Pà ©rez earned 45,000 votes. #3: When in doubt, try to use decimals Decimals can make it much easier to work out problems (as opposed to using fractions). So do not be afraid to convert your fractions into decimals to make life easier. #4: Remember your special fractions Always remember that a number over 1 is the same thing as the original number, and that a number over itself = 1. If $h$ and $k$ are positive numbers and $h+k=7$ then ${7-k}/h=$ (A) 1 (B) 0 (C) -1 (D) $h$ (E) $k-1$ *** Here we have two equations: $h+k=7$ and ${7-k}/h$ So let us manipulate the first. $h+k=7$ can be re-written as: $h=7−k$ (Why? We simply subtracted $k$ from either side) So now we can replace the $(7−k)$ from the second equation with $h$, as the two terms are equal. This leaves us with: $h/h$ And we know that any number over itself = 1. So our final answer is A, 1. Now, let's put your knowledge to the test! Test Your Knowledge #1: Flour, water, and salt are mixed by weight in the ratio of 5:4:1, respectively, to produce a certain type of dough. In order to make 5 pounds of this dough, what weight of salt, in pounds, is required? (A) $1/4$ (B) $1/2$ (C) $3/4$ (D) 1 (E) 2 #2: #3: Which of the following answer choices presents the fractions $5/4$, $4/3$, $19/17$, $13/12$, and $7/6$ in order from least to greatest? (A) $19/17$, $7/6$, $13/12$, $4/3$, $7/6$, $5/4$ (B) $4/3$, $5/4$, $7/6$, $19/17$, $13/12$ (C) $13/12$, $7/6$, $19/17$, $5/4$, $4/3$ (D) $19/17$, $13/12$, $5/4$, $7/6$, $4/3$ (E) $13/12$, $19/17$, $7/6$, $5/4$, $4/3$ Answers: B, D, E Answer Explanations: #1: This question is a perfect example of when to find the whole of the pieces of the ratio. Flour, water, and salt are in a ratio of 5:4:1, which means that the whole is: $5x+4x+1x=10x$ So $10x$ is our whole. We want 5 pounds of the recipe, so we must convert $10x$ to 5. $10x=5$ $x=1/2$ Our variable is $1/2$ . Now, we are looking for the amount of salt to use when we started out with $1x$. So let us replace our $x$ with the value we found for it. $1x$ $1(1/2)$ $1/2$ This means we need $1/2$ a pound of salt to make 5 pounds of the mixture. Our final answer is B, $1/2#. #2: For this question, we must find a non-zero integer for t in which $x+{1/x}=t$, where $x$ is also an integer. We know, based on our special fractions, that the only possible way to get a whole number in fraction form is to have our demoninator equal 1 or -1. This means that x cannot possibly be anything other than 1 or negative 1. (Why? If x were anything else but 1, we would end up with a mixed fraction. For example, if x=2, then we would have: $2+{1/2}$. If $x=3$, we would have: $3+{1/3}. And so on. The only way to get an integer value for $t$ is when $x=1$.) So let us try replacing our $x$ value with 1. $x+{1/x}=t$ $1+{1/1}=2$ $t=2$ Well, $t$ could possibly equal 2, but this is not one of our answer choices. So now let us replace $x$ with -1 instead. $x+{1/x}=t$ $-1+{1/-1}=-2$ t=−2 Success! We have found a value for $t$ that matches one of our answer choices. Our final answer is D, $t=−2$ #3: For a problem like this (one that has you order fractions by size), it is usually a good idea to break out the decimals. But we will go through how to solve it using both methods of fractions and decimals. Solving with decimals: To solve with decimals, simply divide each numerator by its denominator to get the decimal. Then, order them in ascending order (as we are told). $5/4=1.25$ $4/3=1.333$ $19/17=1.12$ $13/12=1.08$ $7/6=1.16$ We can see here that the order from least to greatest is: 1.08, 1.12, 1.16, 1.25, 1.33 Which, converted back to their fraction form is: $13/12$, $19/17$, $7/6$, $5/4$, $4/3$ So our final answer is E. Alternatively, we can solve using fractions. Solve using fractions: Let us find a common denominator between all the numerators. A quick way to do this is by multiplying the two largest numerators together. (It may not be the least common denominator, but it'll do for our purposes.) $17*12=204$ Now let's make sure that the other denominators can go evenly into 204 as well. $204/6=34$ $204/4=51$ $204/3=68$ Perfect! Now let us convert all of our fractions. $5/4={5(51)}/{4(51)}=255/204$ $4/3={4(68)}/{3(68)}=272/204$ $19/17={19(12)}/{17(12)}=228/204$ $13/12={13(17)}/{12(17)}=221/204$ $7/6={7(34)}/{6(34)}$ Now that they all share a common denominator, we can compare and order their numerators. So, in ascending order, they would be: $221/204$, $228/204$, $238/204$, $255/204$, $272/204$ Which, when converted back to their original form, is: $13/12$, $19/17$, $7/6$, $5/4$, $4/3$ So again, our final answer is E. I think a nap is in order- don't you? Take-Aways Fractions and ratios may look tricky, but they are merely ways to represent the relationships between pieces of a whole and the whole itself. Once you know what they mean and how they can be manipulated, you’ll find that you can tackle most any fraction or ratio problem the SAT can throw at you. But always remember- though ratios and fractions are related, do not get them mixed up on the SAT! The vast majority of the time, the ratios they give you will compare parts to parts and the fractions will compare parts to the whole. It can be easy to make a mistake during the test, so don’t let yourself lose a point due to careless error. What’s Next? You've conquered fractions and you've decimated ratios and now you're eager for more, right? Well look no further! We have guides aplenty for the many math topics covered on the SAT, including probability, integers, and solid geometry. Feel like you're running out of time on the SAT? Check out our article on how to finish your math sections before time's up. Don't know what score to aim for? Make sure you have a good grasp of what kind of score would best suit your goals and current skill level, and how to improve it from there. Angling to get an 800 on SAT Math? Look to our guide on how to get a perfect score, written by a perfect SAT scorer. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

A comparison between two different proteomic approaches used to Essay

A comparison between two different proteomic approaches used to investigate cancer system - Essay Example Also contacts and communication between the proteins that make up a specific proteome under investigation is significant in proteomics. Nowadays doctors adopt proteomic approaches in the diagnosis of cancers avoiding the pre existing diagnose techniques like Immunohistochemistry, ELISA (Enzyme-Linked ImmunoSorbant Assays), Immunoblots etc. The proteomic approaches adopted for cancer diagnosis by medical field are mainly based on electrophoresis and spectrometry. Proteomes exhibit varied characters at various instances of simulations especially due to hormones. This is due to the variations in proteins composing those proteomes. Both approaches employed in proteomics try to dig out those characteristics making up variations in human cells. There are many approaches using both electrophoresis as well as spectrometry techniques. 2D-PAGE, MALDI-MS, SELDI-TOF-MS, Antibody arrays etc. are some specific approaches of proteomics. In this paper, the comparative proteomic approaches of 2D- PAGE and MALDI-MS in Human Lung Squamous Carcinoma and functional proteomic approach in Breast cancer. The detailing on diagnostic functional proteomic approach used in breast cancer can be initiated with identifying basic facts on it. â€Å"Functional proteomics approaches that comprehensively evaluate the biological activities of human cDNAs may provide novel insights into disease pathogenesis.† (Witt, et al., 2005, p.1). The analysis on cDNAs is taken up through thorough investigation about their response to various stimulations especially those expected during initial stages of breast cancer. To analytically examine the practical response of cDNAs especially those involved in breast carcinogenesis, first a collection of such cDNAs are made named as Breast Cancer 1000 (BC1000). Again stimulations similar to tumour instigation and development are imposed on those cDNAs create response, but it is clear that each response corresponds to a rearrangement of proteins composing the

Corporate social responsibility in Asia Essay Example | Topics and Well Written Essays - 2500 words

Corporate social responsibility in Asia - Essay Example By initiating education, environment and health care programs, the government has established an avenue that firms are now adopting. For example, in 2009 the Chinese government launched an expansive tree planting program and in response Chinese based firms established tree planting as part of their CSR initiatives. Another notable aspect that makes China maintain a strong business to business relationship is the support among various organizations that operate in China. For example, based on its effort to support small enterprises and conserve the environment, Wokai benefits from the support of Cathay Pacific Airways and Morrison & Foerster that provides financial and legal support respectively (Chen and Dean, 2007). One of the major challenges that faced China is the earlier cases of violation of human rights that created a negative image of the country business atmosphere. Major cases that created a negative image for the government was the use of prison labor in order to produce p rofitable products in the international market. In the area culture, Alan (2003) argues that the government has been noted to violate human rights by persecution of individuals who engaged in activities that threatened the control of the government. However, in its effort to create investors confidence, the Chinese government has engaged in dialogue with foreign countries on the matters of human rights. For example, in the past 5 years, the government has invited delegations from Britain, France, Australia and France to access the human right situation. The major country that has led in the ending of human rights violation in China is US. In their studies on the impact of human rights on business investors in china,... One of the major aspects that make Japan a country with business opportunities is the extensive use of CSR in the Japanese corporate management. As compared to Europe and the US where firms aims at attaining short-term returns for their shareholders, Japanese companies place high value to all the stakeholders including the customers, employees, shareholders and members of the community (Waldenberger, 2007). In this regard, majority of companies in Japan have established departments that deal with corporate social responsibilities. Yamaha Company, a Japanese based firm is one of the key companies that have initiated a strong CSR department. Through this department, the company initiated Yamaha Forest reforestation program in 2010. During the first phase of the program that took place in Sukabumi Regency, Yamaha Motor Company in collaboration with Yamaha Corporation planted approximately 115,110 trees. Other organizations that are engaged in the environmental conservation in Japan incl ude Japan International Cooperation Agency (JICA) and University of Kuningan among others.

The Way to Improve Social Inequality Essay Example | Topics and Well Written Essays - 750 words

The Way to Improve Social Inequality - Essay Example The common racial problem exists between the ‘white’ and the ‘black’ people. This emanated from the fact that long time ago African people were slaves in the United States. In the old times, African people could not go to the same schools with the white people and everything had to be separated between the two races. Although slavery was abolished, the issues that developed from it still exist in today’s society. Bearing in mind that the skin color is still different, the problem persists. This is because there are some white people who still hold the belief that they are better as compared to the black people. There are good examples from the video that we watched in class; one of them is about the demonstration of racism. The purpose of this demonstration was to let people understand the feeling of being racially profiled and being treated unequally. We all live in the same planet. People should therefore respect each other regardless of place of or igin or skin color. The problem of racism also leads to violence in various societal settings such as schools and homes. In recent years, cases related to violence at home or in school have increased significantly. Why is violence increasing each year? The main reason is that people have different cultures and backgrounds. Some examples include that conservative traditionalists may think they have the right to control women and that women are not equal to men. Children may be influenced by their parents. Here, children who witness or are victims of violence may learn to believe that violence is the only way to resolve conflicts between people. The video that we watched in class was about Cape Town; in this town, there are many gangsters mostly comprised of teenagers. One of the people interviewed in the video was a victim of violence. Due to family issues, the victim ran away from home and joined the clan to

Gender Policy Review Essay Example | Topics and Well Written Essays - 2000 words

Gender Policy Review - Essay Example Violence against women and girls is a prevalent and systematic infringement of elementary human rights and a pervasive form of gender-based discrimination (United Nations 2006, p.7). Statistics indicate that one in every three women has suffered the wrath of violence; physically, sexually, or some other way- most prevalently by someone she knows, inclusive of the intimate partner or another male family member. Violence against women and girls (VAWG) takes diverse forms and comprises of such acts as physical, psychological, sexual, and emotional abuse. Every day, worldwide, women confront gender-based discrimination including acts such as genital mutilation, forced prostitution, sexual slavery, and domestic violence. The analysis of oppression of women demands analysis of conditioning and socialization of individuals as the nature of economic and social utilization influences the phenomenon of violence against women (Heise 1994, p.8). In fact, women with disabilities remain predispose d to experience violence compared to other women and girls. Violence against women is degrading, humiliating, and belittling. Violence against women mainly provokes fear and insecurity, especially among the subjects and curtails women from leading independent lives (United Nations 2006, 28). Violence against women also increases their vulnerability and dependence. ... It is frequently argued that state and civil society institutions must recognize and accept responsibility for female subordination and desist from encouraging acts of violence against women. While the certain forms of violence against women (such as rape) can be regarded as widespread, other forms of abuse against women are specific to certain regions or countries (Leicht and Jenkins 2010, p.280). Thus, policy makers must understand the processes that propel women violence if those policies were to be effective. One of the historical power relations blamed for propagating violence against women encompass economic and social forces that propel exploitation of female labour and the female body. Economically disadvantaged women are highly susceptible to sexual harassment, trafficking, and sexual slavery. Furthermore, the denial of women economic power and economic independence is a significant cause of violence against women and lengthens their vulnerability and dependence. Within the family institution, historical power relations often play out (Leicht and Jenkins 2010, p.284). The family is a critical source of positive fostering and caring of values, and also plays out as a social institution where labour is exploited, and male sexual power is aggressively expressed. The family also sums up as a place where socialization that frequently disempowers women frequently features. In certain cases, familial expectations may camouflage or yield negative images of self that constrain the ability of women to realize their full potential (Leicht and Jenkins 2010, p.286). Gender- based violence can be regarded as flowing from the failure of governments and society to honour and protect the human rights of women; thus, policy makers

International Relations Essay Example | Topics and Well Written Essays - 1000 words - 2

International Relations - Essay Example We may often wonder why some nations cooperate with each other while other nations go to war. The answer lies in analysis and the application of theories of political science and international relations. In this manner, theory can guide in the analysis and application of a basis for explaining current scenarios and unfolding realities. The present political scenario in Egypt and other parts of the Middle East is rather fluid and in a state of flux. As long established autocratic regimes break up and expose the cruel games of their despotic rulers, the era of the political strongman seems to be at a close. Saddam has already met his end. America cannot afford to look the other way any longer. The time is right for change and the writing is on the wall for Tunisia, Egypt, Yemen, Jordan, Libya and a slew of other Axis of Evil nations that seek to perpetuate their regimes through suppression of dissent and oppression of the native people, many of whom do not even know their political rig hts- and are much less allowed to express their true feelings. Change took thirty years to come about in Egypt, but the people paid the price for their freedom. The Structural Theorist Perspective & Core Assumptions Supporters of the structural theorist perspective are of the view that changes and political upheaval is brought on by the structures or institutions that are in place in a particular region. A structural theorist like Mary would seek to explain the recent changes in Egypt by using as her basis of argument characteristics associated with the system. She would be inclined to discount the value of state players. The structural theorist believes that the inherent nature of the international system is hierarchical or anarchical. Power distribution between states might be uni-polar, bi-polar or multi-polar. The system structure determines the goal of states whether it is security or wealth accumulation. At any given time there is a certain degree of uncertainty surrounding re lations between states. Comments about what should happen in Egypt now have come from Barrack Obama of the USA, David Cameron of the UK (he even made a visit to Egypt after Mubarak’s ouster and mingled with people at Tahrir Square after talking to the key general of the Armed Forces to bring about a change according to people’s expectations) and Germany’s Angela Merkel- so clearly these G20 leaders are keenly interested in Egypt’s fortunes and its implications for the future international relations and policy. The Social Theorist Perspective & Core Assumptions Supporters of the social theorist perspective are of the view that changes and political upheaval is brought on by the different classes of society or institutions that are in place in a particular region. A social theorist like Tom would point out to the rot in the system initiated and maintained by Hosni Mubarak for thirty years- and the creation of different classes of people in society that foug ht each other as they vied for power, wealth and prosperity. So here we would have the grounds for debate between the structural theorist and the social theorist. Mary would point out that the final impetus for change was pushed through by comments from Obama, Cameron and other world leaders. It was only