SSAT Upper Level

Fraction Operations

Adding, subtracting, multiplying, and dividing fractions and mixed numbers — excludes percent calculations (see percent-calculations) and ratio/proportion problems (see ratios-proportions-solving)

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Have you ever tried to share a pizza with friends, but someone ate a slice before you even started? 🍕 Welcome to the world of fractions! Fractions are just math's way of talking about pieces of a whole. Whether you are slicing up a giant chocolate cake or figuring out how much of your video game download is finished, you are using fractions!

On the SSAT, you will need to know how to add, subtract, multiply, and divide these pieces. Think of adding and subtracting fractions like organizing a messy toy box. You can only combine things that are exactly the same size! That is why we need a "common denominator" (the bottom number). You wouldn't mix your LEGO bricks with your puzzle pieces, right? Once the bottom numbers match, you just add or subtract the top numbers (the numerators) and keep the bottom the same.

Multiplying and dividing are even easier! For multiplication, you just multiply straight across the top and straight across the bottom. No matching needed! 🚀 And for dividing? Just flip the second fraction upside down and multiply. It is like a fun skateboard trick for numbers!

Mixed numbers (like $1 \frac{1}{2}$ ) are just whole numbers with a fraction sidekick. If they give you trouble, turn them into "improper fractions" first. Master these fraction moves, and you will be a fraction ninja on the SSAT! 🥷

Key Formula

To add or subtract fractions, you MUST find a common denominator first!

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

Practice Questions

4 practice questions for SSAT Upper Level

Q1 Hard

Evaluate

\frac{3}{4} \div (\frac{1}{2} - \frac{1}{6})

\frac{1}{4}

\frac{3}{8}

\frac{9}{4}

\frac{5}{2}

3

Show Solution

First, simplify the expression inside the parentheses by finding a common denominator, which is 6. $\frac{1}{2}$ becomes $\frac{3}{6}$ . Subtracting $\frac{1}{6}$ gives $\frac{3}{6} - \frac{1}{6} = \frac{2}{6}$ , which simplifies to $\frac{1}{3}$ . Now substitute this back into the original expression: $\frac{3}{4} \div \frac{1}{3}$ . To divide by a fraction, multiply by its reciprocal: $\frac{3}{4} \times \frac{3}{1} = \frac{9}{4}$ .

Answer: C

Q2 Hard

A library has 120 fiction books and 80 nonfiction books on a return cart. If

\frac{3}{4}

of the fiction books are hardcovers and 40% of the nonfiction books are hardcovers, how many more fiction hardcovers are there than nonfiction hardcovers?

A 26

B 42

C 50

D 58

E 64

Show Solution

First, find the number of fiction hardcovers: $\frac{3}{4} \times 120 = 90$ . Next, find the number of nonfiction hardcovers: 40% of 80 is $0.40 \times 80 = 32$ . Finally, subtract to find the difference: 90 - 32 = 58.

Answer: D

Q3 Hard

A baker makes 4 identical batches of cookies. One fourth of the flour needed for a single batch is 1.5 cups. The total amount of flour needed for all 4 batches can be determined by multiplying 1.5 by which of the following numbers?

\frac{1}{4}

B 1

C 4

D 8

E 16

Show Solution

If $\frac{1}{4}$ of the flour for a single batch is 1.5 cups, then the flour needed for one whole batch is $4 \times 1.5$ cups. Since the baker is making 4 batches, the total flour needed is $4 \times (4 \times 1.5)$ , which equals $16 \times 1.5$ . Therefore, you multiply 1.5 by 16.

Answer: E

Q4 Hard

Sarah spent

\frac{1}{3}

of her weekly allowance on a movie ticket and

\frac{1}{4}

of the remaining money on snacks. If she has $15 left, what was her original allowance?

A $24

B $30

C $36

D $45

E $60

Show Solution

After spending $\frac{1}{3}$ of her allowance, Sarah has $1 - \frac{1}{3} = \frac{2}{3}$ of her allowance remaining. She then spends $\frac{1}{4}$ of that remainder on snacks: $\frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \frac{1}{6}$ of her original allowance. Her total fraction spent is $\frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$ . This means she has $\frac{1}{2}$ of her allowance left. If $\frac{1}{2}$ of her allowance equals $15, then her original allowance was $ $15 \times 2 = 30$ .

Answer: B

Tips & Strategies

Always check if you can simplify your final answer! The SSAT answer choices will almost always be in their simplest form. If you got $\frac{4}{8}$ , look for $\frac{1}{2}$ !
When multiplying or dividing mixed numbers, ALWAYS change them into improper fractions first (like turning $1 \frac{1}{2}$ into $\frac{3}{2}$ ). Do not try to multiply the whole numbers and fractions separately!

Common Mistakes

Watch out for adding straight across! A huge mistake is adding the top AND bottom numbers like $\frac{1}{2} + \frac{1}{2} = \frac{2}{4}$ . Remember, the bottom number stays the same once they match!
Don't forget to flip the SECOND fraction when dividing. If you are solving $\frac{1}{2} \div \frac{3}{4}$ , keep the $\frac{1}{2}$ , change to multiplication, and flip the $\frac{3}{4}$ to $\frac{4}{3}$ .

Frequently Asked Questions

Do I always need a common denominator?

Nope! You ONLY need a common denominator for adding and subtracting. For multiplying and dividing, you can jump right in and work with the numbers as they are! 🚀

What is an improper fraction?

It is a fraction where the top number (numerator) is bigger than the bottom number (denominator), like $\frac{5}{3}$ . They are super helpful for multiplying and dividing mixed numbers!

Will I get points off if I don't simplify my fraction on the SSAT?

The SSAT is multiple choice, so you won't lose points, but you probably won't find your unsimplified answer in the choices! Always simplify so you can match your answer to the test's options. 🕵️‍♂️

How do I turn a mixed number into an improper fraction?

Multiply the big whole number by the bottom number, then add the top number. Put that new number on top, and keep the bottom the same! For $2 \frac{1}{4}$ , do $2 \cdot 4 + 1 = 9$ , so it becomes $\frac{9}{4}$ .

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