ISEE Lower 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)

Generate Unlimited Practice Questions

Start Free Practice

Learn This Topic

Imagine you and your friends order a giant pepperoni pizza! 🍕 You eat $\frac{3}{8}$ of it, and your best friend eats $\frac{1}{4}$ . How much is left? To figure that out, you need fraction operations! Working with fractions on the ISEE is like learning the rules of a fun new board game. Once you know the moves, you can win every time!

For adding and subtracting, fractions are a bit picky. They refuse to work together unless their bottom numbers (denominators) match. It’s like trying to play soccer with a basketball—you need the right equipment! So, we find a common denominator first, and then only add or subtract the top numbers.

Multiplying fractions is super chill. No matching needed! You just multiply the top numbers straight across, and then the bottom numbers straight across. Easy peasy! 😎

Dividing fractions? Time for a cool skateboard trick! We use a move called 'Keep-Change-Flip.' Keep the first fraction, change the division sign to multiplication, and flip the second fraction upside down. 🛹

On the ISEE, you'll see fractions in two ways. In the Mathematics Achievement section, you'll just do the math. In the Quantitative Reasoning section, you might compare two columns. Don't worry, just use your fraction rules and you'll crush it!

Key Formula

For division, remember Keep-Change-Flip!

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Practice Questions

5 practice questions for ISEE Lower Level

Q1 Easy

Maria has a piece of ribbon that is

7 \frac{1}{4}

feet long. She uses

2 \frac{2}{3}

feet of the ribbon to decorate a gift. How many feet of ribbon does she have left?

4 \frac{7}{12}

5 \frac{1}{12}

5 \frac{5}{12}

9 \frac{11}{12}

Show Solution

To find how much ribbon is left, subtract the amount used from the total length: $7 \frac{1}{4} - 2 \frac{2}{3}$ . First, find a common denominator for the fractions, which is 12. The fractions become $\frac{3}{12}$ and $\frac{8}{12}$ . The problem is now $7 \frac{3}{12} - 2 \frac{8}{12}$ . Since you cannot subtract $\frac{8}{12}$ from $\frac{3}{12}$ , borrow 1 whole (which is $\frac{12}{12}$ ) from the 7. This makes the expression $6 \frac{15}{12} - 2 \frac{8}{12}$ . Subtract the whole numbers: $6 - 2 = 4$ . Subtract the fractions: $\frac{15}{12} - \frac{8}{12} = \frac{7}{12}$ . The remaining ribbon is $4 \frac{7}{12}$ feet.

Answer: A

Q2 Easy

The ingredients in the recipe were evenly mixed and equally divided into 4 bowls.

RECIPE
8 cups of flour
4 cups of sugar
3 cups of oats
2 cups of chocolate chips

How many cups of the mixture were placed in each bowl?

A 4

4 \frac{1}{4}

4 \frac{1}{2}

D 5

Show Solution

First, find the total number of cups of ingredients by adding them all together: $8 + 4 + 3 + 2 = 17$ cups. Next, divide the total number of cups by the number of bowls: $17 \div 4$ . Because 4 goes into 17 four times with a remainder of 1, the division results in $4 \frac{1}{4}$ . Therefore, $4 \frac{1}{4}$ cups of the mixture were placed in each bowl.

Answer: B

Q3 Easy

A large rectangular garden is divided into 16 equal-sized square plots. Carrots are planted in 4 of the plots, and tomatoes are planted in 8 of the plots. The rest of the plots are empty. What fraction of the garden is empty?

\frac{1}{8}

\frac{1}{4}

\frac{1}{2}

\frac{3}{4}

Show Solution

First, find the total number of planted plots: $4$ (carrots) + $8$ (tomatoes) = $12$ planted plots. Next, find the number of empty plots by subtracting the planted plots from the total number of plots: $16 - 12 = 4$ empty plots. To find the fraction of the garden that is empty, write the number of empty plots over the total number of plots: $\frac{4}{16}$ . Finally, simplify the fraction by dividing the numerator and the denominator by 4 to get $\frac{1}{4}$ .

Answer: B

Q4 Easy

Bucket A and Bucket B can each hold exactly 1 gallon of water. Bucket A is filled about

\frac{1}{4}

of the way to the top. Bucket B is filled about

\frac{2}{3}

of the way to the top. If the water from both buckets is poured into a large empty tub, approximately how much water will be in the tub?

\frac{1}{2}

gallon

B 1 gallon

1 \frac{1}{2}

gallons

D 2 gallons

Show Solution

To estimate the combined amount of water, add the two fractions: $\frac{1}{4} + \frac{2}{3}$ . Finding a common denominator of 12 gives $\frac{3}{12} + \frac{8}{12} = \frac{11}{12}$ . Because $\frac{11}{12}$ is very close to $\frac{12}{12}$ , the total amount of water is approximately 1 gallon.

Answer: B

Q5 Easy

On Saturday, Leo ran

2 \frac{4}{5}

miles. On Sunday, he ran

1 \frac{1}{2}

miles. How many miles did Leo run in all over the weekend?

3 \frac{3}{10}

3 \frac{5}{7}

4 \frac{1}{10}

4 \frac{3}{10}

Show Solution

To find the total distance, add the two mixed numbers: $2 \frac{4}{5} + 1 \frac{1}{2}$ . First, find a common denominator for the fractional parts, which is 10. Convert the fractions: $\frac{4}{5} = \frac{8}{10}$ and $\frac{1}{2} = \frac{5}{10}$ . The expression is now $2 \frac{8}{10} + 1 \frac{5}{10}$ . Add the whole numbers: $2 + 1 = 3$ . Add the fractions: $\frac{8}{10} + \frac{5}{10} = \frac{13}{10}$ . Since $\frac{13}{10}$ is an improper fraction, convert it to $1 \frac{3}{10}$ . Finally, add this back to the whole number total: $3 + 1 \frac{3}{10} = 4 \frac{3}{10}$ miles.

Answer: D

Tips & Strategies

Always convert mixed numbers to improper fractions before multiplying or dividing! It saves you from making silly mistakes.
On Quantitative Comparison questions (Column A vs Column B), look for a shortcut before doing the math. Sometimes you can tell they are equal just by using rules like Keep-Change-Flip!
Remember that adding and subtracting require a common denominator, but multiplying and dividing DO NOT. Don't do extra work if you don't have to!

Common Mistakes

Watch out for adding the denominators! When you add $\frac{1}{4} + \frac{1}{4}$ , the answer is $\frac{2}{4}$ , NOT $\frac{2}{8}$ . The bottom number stays the same!
Don't forget to simplify your final answer. If you get $\frac{15}{12}$ , the ISEE will usually want you to reduce it to $\frac{5}{4}$ .

Frequently Asked Questions

Do I have to simplify my fractions on the ISEE?

Yes! The ISEE almost always puts the answer choices in their simplest form. If your answer isn't there, see if you can divide the top and bottom by the same number.

What if I forget the common denominator?

You can always just multiply the two bottom numbers together to find a common denominator! It might not be the smallest one, but it will always work.

Is there a penalty for guessing if I'm totally stuck?

Nope! The ISEE has zero guessing penalty. If a fraction problem is taking too long, pick your favorite letter and move on.

How do I remember which fraction to flip when dividing?

Always flip the SECOND fraction! Think of the phrase 'Keep-Change-Flip' reading from left to right, just like reading a book.

Generate Unlimited Practice Questions

Learn This Topic

Practice Questions

Tips & Strategies

Common Mistakes

Frequently Asked Questions

Related Topics

More Fractions, Decimals, Ratios & Percents

Other Levels

Browse

Generate Unlimited Practice Questions