Algebra: Fraction Problems



In this lesson, we will learn how to solve fraction word problems that deal with fractions i.e. parts of a whole. Remember to read the question carefully to determine the numerator and denominator of the fraction.

We will also learn how to solve word problems that involve comparing fractions, adding mixed numbers, subtracting mixed numbers, multiplying fractions and dividing fractions.

Related Topics: More Algebra Word Problems

Fraction Word Problems

Example 1:

A class has 20 girls and 30 boys. What part of the class are boys?

Solution:

Step 1: Numerator: boys = 30
Step 2: Denominator: class = 20 + 30 = 50
Step 3: Part or fraction

3/5

Answer: 3/5 are boys



Example 2:

If John earns $x in a week and spend $y, what part of his weekly salary did he save?

Solution:

Step 1: Numerator: amount saved= xy
Step 2: Denominator: salary = x
Step 3: Part or fraction

x-y/x

Answer: x-y/x



Example 3:

14 is 2/3 of what number?

Solution:

Step 1: Assign variables :

Let x = number

Step 2: Solve the equation

14=2/3 x

Isolate variable x
x = 21

Answer: The number is 21.


Comparing Fractions Word Problems


The following video shows an example of fraction word problem that involves comparing fractions.

On the last math quiz, Tara answered 5/7 of the problems correctly and Julia answered 7/10 of them correctly. If each problem is worth the same amount, who got the higher grade?



Adding Mixed Numbers Word Problems

Regina rode her bike 2 and 1/4 miles from her house to school and the 1 and 5/8 miles to her friend's house. How many miles did Regina ride in total?





Subtracting Mixed Numbers Word Problems


If Shelagh describe her age as 15 and 1/2 years old and Luana is 7 and 7/12 years old, what is the difference in their ages? Write the answer as a simplified mixed number.





Mutliplying Fractions Word Problems

The following video is a fraction word problem that involves multiplying fractions.

A recipe for banana oat muffin calls for 3/4 cup of old fashioned oats. You are making have of the recipe. How much oats should you use?

Before leaving for a road trip, Tiffany filled up her gas rank, which holds 16 gallons of gas. After 4 hours, Tiffany notices that the gas tank was 7/8 full. How many gallons of gas were left in the tank?





Dividing Fractions Word Problems

The following videos are fraction word problem that involve dividing fractions.

A baby t-shirt requires 4/5 yards of fabric. How many t-shirts can be made from 48 yards?

Diya thought that it would be nice to include 2/21 of a pound of chocolate in each of the holiday gift bags she made for her friends and family. How many holiday gift bags could Diya make with 2/3 of a pound of chocolate?



As the swim coach, Minli selects which athletes will participate in the state-wide swim relay. The relay team swims 2/3 of a mile altogether, with each team member responsible for swimming 2/9 of a mile. The team must complete the swim in 2/5 of an hour. How many swimmers does Minli need on the relay team?




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