A fraction shows a part in proportion to a whole. If you have two buttons and one button is yellow, you would write that fraction as ½. The numerator (1 in this case) is located on the top and the denominator (2 in this case) is located on the bottom.
A mixed number is a combination that includes a whole number and a fraction. An example of a mixed number is 4½. If you had 5 apples and you ate half of one, you would have 4½ apples.
Converting Mixed Numbers to Improper Fractions
It is likely that you will need to convert mixed numbers to improper fractions on the Mathematics section of the test. An improper fraction contains a numerator that is greater than its denominator.
Let’s practice with our leftover apples: 4½
Step 1: Multiply the denominator and the whole number. (4 x 2 = 8)
Step 2: Add the answer from the first step to the numerator. (8 + 1 = 9)
Step 3: Write answer from the second step over the denominator. (9 / 2)
So, 4½ is the same as 9 / 2. We just converted a mixed number to an improper fraction – 9 apple halves are left!
Sometimes on the SSAT, you may need to compare fractions. For example, you may be given a list of fractions and be asked to order them from least to greatest. Usually, these fractions will have different denominators.
Take a look at the list below.
In order to order this list from least to greatest, all of the fractions must have the same denominator. We must find the LCD, or least common denominator, by determining the lowest number that each of the denominators can divide without remainders.
The least common denominator for these fractions is 24; 2 x 12 = 24, 3 x 8 = 24, 6 x 4 = 24, and so on.
In order to compare the fractions, we must multiply each numerator by the same number that the denominator must be multiplied by for a result of 24.
For example, take a look at the first fraction. Since 2 x 12 = 24, we must multiply 3 x 12 to get 36. Now, we write our new numerator over 24: (36 / 24).
So, let’s review adding fractions next. This is another important concept to know on the SSAT. Take a look at the following problem:
Penelope has a jar full of candy. She gives ¼ of the total number of candies to Jason, and she gives ⅙ of the total number of candies to Emani. What fraction of her candies does Penelope give away?
The question is basically asking us to add ¼ and ⅙. First, we need to find the LCD, which is 12.
Since 4 x 3 = 12 and 6 x 2 = 12, we need to multiply the first numerator by 3 and the second numerator by 2. Then, our problem looks like this:
(3 / 12) + (2 / 12) = 5 / 12
Penelope gave away 5 / 12 of her candies.
Next, we will practice doing the opposite of adding fractions; we will review subtracting them. Here’s another sample problem:
Alicia has has 3¼ cups of blueberries. If she uses ⅔ of a cup of her blueberries in a pancake recipe, how many blueberries does she have left?
The question is asking us to subtract ⅔ from 3¼.
In order to solve this problem, we will complete many of the same steps that we did in earlier examples.
So, let’s start by converting 3¼ to an improper fraction. Since 3 x 4 = 12 and 12 + 1 = 13, Alicia started with 13 / 4 cups of blueberries.
Now, we must subtract ⅔ from 13 / 4. Our LCD is 12 and by multiplying our numerators by the same number that we multiply our denominators by to get 12, we find that the problem is (39 / 12) – (4 / 12).
Because this is a subtraction problem, we will subtract 4 from 12. Alicia now has 35 / 12 cups of blueberries. The number 12 goes into 35 twice.
12 x 2 = 24
So, we know that we have 2 full cups of blueberries left, but we have a remainder of 11 (35 – 24 = 11).
So, Alicia is left with 2 11/12 cups of blueberries.
Next, let’s take a look at a multiplication problem using fractions.
Margaret has a large bag of rocks. She pours ¼ of the bag around her pond on Tuesday. On Wednesday, she pours twice that amount around a statue in her garden. What fraction of the original full bag of rocks does Margaret pour on Wednesday?
In order to solve this problem, we need to multiply ¼ by 2. Since 2 is the same as 2/1, our problem looks like this:
¼ x 2/1 =
We can solve the problem by multiplying the two numerators together and the two denominators together:
¼ x 2/1 = 2/4
Since both 2 and 4 can be evenly divided by two, we can simplify our answer to ½.
On Wednesday, Margaret used half of the original amount of rocks.
Dividing fractions is just like multiplying fractions, except we take the inverse of one of the fractions. In other words, we turn it upside down, so that the numerator and denominator switch places. Here’s an example question:
What is ¼ divided by ½?
¼ ÷ ½ = ¼ x 2/1
Notice that we flip one of the fractions and change the division sign to an addition sign.
¼ x 2/4= 2
The answer is 2.
That was pretty simple, right? Now, let’s review another concept.