SSAT Middle 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

5 practice questions for SSAT Middle Level

Q1 Medium

Compute:

\frac{5}{6} - \frac{1}{4} + \frac{2}{3}

\frac{5}{12}

\frac{3}{4}

\frac{11}{12}

\frac{7}{6}

\frac{5}{4}

Show Solution

To add and subtract these fractions, find the least common multiple of the denominators 6, 4, and 3, which is 12. Convert each fraction to have a denominator of 12: $\frac{5}{6} = \frac{10}{12}$ , $\frac{1}{4} = \frac{3}{12}$ , and $\frac{2}{3} = \frac{8}{12}$ . Then, compute the numerators: $\frac{10}{12} - \frac{3}{12} + \frac{8}{12} = \frac{15}{12}$ . Finally, simplify the fraction by dividing the numerator and denominator by 3 to get $\frac{5}{4}$ .

Answer: E

Q2 Medium

What is the value of

\frac{3}{5} \div \frac{9}{10} \times \frac{1}{2}

\frac{1}{6}

\frac{2}{5}

\frac{1}{3}

\frac{27}{100}

\frac{3}{10}

Show Solution

Following the order of operations, work from left to right. First, evaluate the division by multiplying by the reciprocal: $\frac{3}{5} \div \frac{9}{10} = \frac{3}{5} \times \frac{10}{9} = \frac{30}{45}$ . Simplify $\frac{30}{45}$ to $\frac{2}{3}$ . Next, multiply this result by $\frac{1}{2}$ : $\frac{2}{3} \times \frac{1}{2} = \frac{2}{6}$ . Simplify $\frac{2}{6}$ to get $\frac{1}{3}$ .

Answer: C

Q3 Medium

A bakery makes 150 muffins in a day. Of the muffins,

\frac{2}{5}

are blueberry, and the rest are divided between banana and chocolate chip. If

\frac{1}{3}

of the remaining muffins are banana, how many chocolate chip muffins did the bakery make?

A 30

B 45

C 50

D 60

E 90

Show Solution

First, find the number of muffins that are blueberry: $\frac{2}{5} \times 150 = 60$ . This leaves $150 - 60 = 90$ remaining muffins. Of these 90 muffins, $\frac{1}{3}$ are banana, which means $\frac{2}{3}$ must be chocolate chip. Calculate the number of chocolate chip muffins: $\frac{2}{3} \times 90 = 60$ .

Answer: D

Q4 Medium

Sarah spends

\frac{1}{4}

of her weekly allowance on a movie ticket and

\frac{3}{8}

of her allowance on snacks. If she has $15 left over, what is her total weekly allowance?

A $24

B $30

C $32

D $40

E $48

Show Solution

First, find the total fraction of the allowance Sarah spent. She spent $\frac{1}{4} + \frac{3}{8}$ . Convert $\frac{1}{4}$ to $\frac{2}{8}$ . So, $\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$ . This means she has $1 - \frac{5}{8} = \frac{3}{8}$ of her allowance left. If $\frac{3}{8}$ of her total allowance equals $15, you can find the total by multiplying $15 by the reciprocal of $\frac{3}{8}$ . Total allowance = $15 \times \frac{8}{3} = \frac{120}{3} = 40$ .

Answer: D

Q5 Medium

Compute:

\frac{\frac{1}{2} + \frac{1}{3}}{\frac{3}{4}}

\frac{5}{8}

\frac{8}{9}

\frac{9}{8}

\frac{10}{9}

\frac{15}{8}

Show Solution

First, simplify the numerator by finding a common denominator for $\frac{1}{2}$ and $\frac{1}{3}$ , which is 6. $\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ . Now, divide this result by the denominator: $\frac{5}{6} \div \frac{3}{4}$ . To divide fractions, multiply by the reciprocal of the second fraction: $\frac{5}{6} \times \frac{4}{3} = \frac{20}{18}$ . Finally, simplify the fraction by dividing the numerator and denominator by 2 to get $\frac{10}{9}$ .

Answer: D

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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