# Word Problems with Fractions

Word problems that contain fractions are exactly like word problems with whole numbers, but sometimes they can look confusing.

A few tips to remember for working specifically with fractions:

**If you have a fraction "of" something, you multiply the fraction you have times the total to find how many you have**("of" always means multiply in word problems).

"Probability of" just means fraction of. If you are choosing a card and have a 4/52 probability of choosing a "queen," that means that 4 out of the 52 cards are "queens."

**A fraction that is equal to 1****has the same numerator and denominator**(any numerator and denominator!). So, two halfs $\dfrac{2}{2}$ or five fifths $\dfrac{5}{5}$ both equal one whole.

If you have or use a fraction of something, and want to know what's "left" or what you "don't" have, you can just subtract the fraction from 1 (the whole).

These two tips can help you solve almost any fraction word problem.

**The first type of fraction word problems ask you to find the fraction of something.**

*Example: A class of 35 students took a test. $\dfrac{2}{5}$ of the students got a B. How many students got a B?*

$$\eqalign{\dfrac{2}{5} \text{ of } 35& = ?\\\dfrac{2}{5} \times 35&=?&&\text{of means multiply}\\\dfrac{2}{5}\times\dfrac{35}{1}&=\dfrac{70}{5}&&\text{Write 32 as a fraction and multiply}\\&=14&&\text{Reduce the fraction for your final answer}}$$

14 students got a B

Sometimes a word problem will ask you to find a fraction of a fraction:

*Example: A group of 42 students tried out for a play. Half of the students got a second audition. Of those students, one third got a part in the play. How many students got a part in the play?*

$$\eqalign{\dfrac{1}{3} \text{ of } \dfrac{1}{2} \text{ of } 42& = ?\\\dfrac{1}{3} \times \dfrac{1}{2} \times 42&=?&&\text{of means multiply - even with several fractions}\\\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{1}{6}\times \dfrac{42}{1}&=\dfrac{42}{6}&&\text{Multiply the fractions together, then write 42 as a fraction and multiply}\\&=7&&\text{Reduce the fraction for your final answer}}$$

7 students got a part in the play.

**The second type of fraction word problems ask you to find a leftover fraction.**

*Example: You have a delicious cake. You eat $\dfrac{1}{7}$ of it and your sister eats $\dfrac{1}{3}$ of it. How much of the cake is left?*

$$\eqalign{\dfrac{1}{7}+ \dfrac{1}{3} &= \dfrac{10}{21} &&\text{Add the eaten fractions}\\1-\dfrac{10}{21} &=?&&\text{Subtract eaten fraction from whole cake}\\\dfrac{21}{21}-\dfrac{10}{21}&=\dfrac{11}{21}&&\text{Turn one into a fraction with the same denominator as other fraction, subtract}}$$

There's $\dfrac{11}{21}$ of the cake left.

Overall, fraction word problems are just like any other word problems, but these tips will help you figure out the best way to set them up!

#### Practice Problems:

## Word Problems with Fractions

Solve the following fraction word problems:

- Anne planted eight sunflowers. One fourth of them died. She then planted three more. How many sunflowers does Anne have now?
- Tom bought four bananas. Half of them rotted, so Tom threw them away and bought three more. How many bananas does Tom have now?
- Maria planted six trees. One third of them died. She planted one more. How many trees does Maria have now?
- Andrew had fourteen math problems to do for homework. She already did $\dfrac{1}{7}$ of them. How many problems does she have left?
- Avery has ten surf boards in his garage. First he gave one to a friend. Then he sold one third of the remaining boards to his brother. How many boards does he have left?
- Jackie bought four mangoes. Half went bad and she bought four more. How many does she have now?
- Room 27 has raised \$37 for the school festival. One student, John, raised $\dfrac{1}{3}$ of the money. How much money did he raise?
- Amy needs \$9.50 for a new book. She saved half of the money. Her mom gave her one fourth of the money she still needed. How much does she still need?
- James spent $\dfrac{3}{4}$ of his allowance on baseball cards. He put the remainder, \$2.50, in his piggy bank. What is his weekly allowance?
- Deshawn saved $\dfrac{7}{8}$ of his allowance. He spent the remainder, \$1.50, on a new toy. How much did he save?
- Three students have a project to complete. Billy does $\dfrac{1}{5}$ of the work. Karen does $\dfrac{3}{9}$ of the work. How much work is left for Casey?
- There is a huge bowl of candy in the living room. Thaddeus ate $\dfrac{4}{5}$ of it. His brother ate $\dfrac{1}{6}$ of what was left. What fraction of the candy is still in the bowl?

#### Answer Key:

#### Test Prep Practice

## Pre Algebra: Word Problems with Fractions

1. Sunny went grocery shopping but had to go to multiple stores to get everything off of his wife's list. He bought $\dfrac{1}{3}$ of what he needed from the mega mart. He then bought $\dfrac{1}{5}$ of the list from the local market. Finally, he bought $\dfrac{3}{10}$ of the list from the farmers market. What fraction of his groceries does he still need to get?

(A) $\dfrac{5}{6}$

(B) $\dfrac{13}{15}$

(C) $\dfrac{1}{5}$

(D) $\dfrac{23}{30}$

(E) $\dfrac{1}{6}$

2. Fiona's classroom were going to have a party. The students voted for what type of party they wanted. $\dfrac{1}{3}$ of the class voted for pizza, $\dfrac{1}{5}$ voted for donuts, and the rest said they didn't care what type of party it was. What fraction of students didn't care?

(A)$\dfrac{5}{7}$

(B)$\dfrac{7}{15}$

(C)$\dfrac{8}{15}$

(D)$\dfrac{1}{9}$

(E)$\dfrac{2}{7}$

3. Fiona's classroom were going to have a party. The students voted for what type of party they wanted. $\dfrac{1}{3}$ of the class voted for pizza, $\dfrac{1}{5}$ voted for donuts, and the rest said they didn't care what type of party it was. If there were 21 students who didn't care what type of party the class was going to have, then how many students are in the class including the teacher?

(A) 40

(B) 46

(C) 45

(D) 44

(E) 22

4. In a biology class, a report is due in 1 month. One week before the assignment is due, $\dfrac{1}{8}$ of the class has finished the report and $\dfrac{2}{3}$ of the class started the research. What fraction of students haven't started the report?

#### Answer Key: