General Fractions - PSAT Math

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Going from 48 cookies to 12 cookies is a scaling factor of 1/4, so all the ingredients get multiplied by 1/4. In order to make 12 cookies you will need 1/4 c white sugar, 1/4 c packed brown sugar, and 3/4 c flour. Added all together you get 5/4 or 1 1/4 c.

How many times does 12 go into 17? Once with a remainder of 5.

So becomes

First, you must solve the equation for . Then, you must convert the answer's improper fraction to a mixed fraction.

Solve for .

Now, to convert an improper fraction, you must see how many times the denominator goes into the numerator, and then leave the remainder as a fraction. Example below:

Find out how many times the denominator goes into the numerator:

Therefore,

becomes

The greatest common divisor is 4. This means that both numbers must be divisible by 4. Furthermore, the least common multiple is 40, so both must divide 40.

The prime factorization of 40 is . For a number to divide 40, it must therefore be composed of (at most) three 2's and one 5. Because divides both numbers, we also know that they must both have at least two 2's.

Now each number will have either two or three 2's and zero or one 5's. However, we also know that they can't both have three 2's, (since then the greatest common divisor would have three 2's as well). Similarly, only one can have a 5.

In essence, our problem becomes one of choice. We have 2 places with value 4. We choose to give a 5 to one of the two. We then give a 2 to one of the two. If we give a 5 and a 2 to the same side, we end up with and 4. If we give a 5 to one and a 2 to the other, we end up with and .

Thus our two pairs are:

4,40 and 8,20

We need to find a common denominator to add and subtract these fractions. Let's do the addition first. The lowest common denominator of 5 and 7 is 5 * 7 = 35, so 3/5 + 4/7 = 21/35 + 20/35 = 41/35.

Now to the subtraction. The lowest common denominator of 35 and 3 is 35 * 3 = 105, so altogether, 3/5 + 4/7 – 1/3 = 41/35 – 1/3 = 123/105 – 35/105 = 88/105. This does not simplify and is therefore the correct answer.

We need to find a common denominator to add and subtract these fractions. Let's do the addition first. The lowest common denominator of 5 and 7 is 5 * 7 = 35, so 3/5 + 4/7 = 21/35 + 20/35 = 41/35.

Now to the subtraction. The lowest common denominator of 35 and 3 is 35 * 3 = 105, so altogether, 3/5 + 4/7 – 1/3 = 41/35 – 1/3 = 123/105 – 35/105 = 88/105. This does not simplify and is therefore the correct answer.

First, find the common denominator of the fractions in order to add them together. Looking at the first two fractions, we can see that the common denominator is 15 because 3 times five is 15. We can now change both fractions to have a denominator of 15 so that we can add them together:

Now, find a common denominator for the remaining fractions. This can be done by listing multiples of 15 and 20 and finding the lowest common multiple:

15: 15, 30, 45, 60, 75

20: 20, 40, 60, 80

60 is the lowest common multiple, so it is our least common denominator.

A fraction multiplied by its reciprocal will equal 1. To find the reciprocal of a fraction, switch the denominator and numerator. The reciprocal of 18/27 is 27/18.

There are two ways to deal with fractions. One way is to convert them all to decimals. (By using your calculator, divide the numerator by the denominator). Using this method all you would need to do is to see which is greater than 0.5. Otherwise to see which is greater than 1/2, double the numerator and see if the result is greater than the denominator. In B, the correct answer, doubling the numerator gives us 12, which is bigger than 11.

If all are converted to decimals, 0.65 is the biggest.

The easiest method is to put each of these fractions into a calculator, and then place them in order on a number line to see which value falls in between 1/2 = 0.5 and ¾ = 0.75. Without a calculator you must do long division to find the value of the numerator (top number) divided by the denominator (bottom number) for each fraction. You can actually eliminate answers b. and d. because they are equal to 1/2 and ¾ respectively. 4/5= 0.80, 3/6 = 0.5, 5/8= 0.625, 6/8 = 0.75.

Using math symbols to dictate height we find that Ben>Jaime, Mary>Ben, Chris>Mary. Putting these in order we have Chris>Mary, Mary>Ben, Ben>Jaime. This shows that Mary is the second tallest.