In these lessons, 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.

### Fraction Word Problems

**Example 1: **
*boys* = 30

Step 2: Denominator:*class* = 20 + 30 = 50

Step 3: Part or fraction**Answer**:

**Algebra Fraction Word Problems**

Examples:

(1) The denominator of a fraction is 5 more than the numerator. If 1 is subtracted from the numerator, the resulting fraction is 1/3. Find the original fraction.

(2) If 3 is subtracted from the numerator of a fraction, the value of the resulting fraction is 1/2. If 13 is added to the denominator of the original fraction, the value of the new fraction is 1/3. Find the original fraction.

(3) A fraction has a value of 3/4. When 14 is added to the numerator, the resulting fraction has a value equal to the reciprocal of the original fraction, Find the original fraction.

**Algebra - Fractional Equations**

Solving a fraction equation that appears in a word problem

Example: One third of a number is 6 more than one fourth of the number. Find the number.**Fraction and Decimal Word Problems**

How to solve algebra word problems with fractions and decimals?

Examples:

(1) If 1/2 of the cards had been sold and there were 172 cards left, how many cards were printed?

(2) Only 1/3 of the university students wanted to become teachers. If 3,360 did not wan to become teachers, how many university were there?

(3) Rodney guessed the total was 34.71, but this was 8.9 times the total. What was the total?### Comparing Fractions Word Problems

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

Example:

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

Example:

Regina rode her bike 2 1/4 miles from her house to school and then 1 5/8 miles to her friend's house. How many miles did Regina ride in total?### Subtracting Mixed Numbers Word Problems

Example:

Shelagh and Luana realized that they could express their ages more specifically if they used fractions. Doing this will allow them to calculate the difference in their ages more precisely. If Shelagh describe her age as 15 1/2 years old and Luana is 7 7/12 years old, what is the difference in their ages? Write the answer as a simplified mixed number.

### Multiplying Fractions Word Problems

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

Example:

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? Example:

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.

Example:

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

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? Example:

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?

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

**Solution:**

Step 2: Denominator:

Step 3: Part or fraction

**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 = x* – *y
*Step 2: Denominator:

**Answer:**

Examples:

(1) The denominator of a fraction is 5 more than the numerator. If 1 is subtracted from the numerator, the resulting fraction is 1/3. Find the original fraction.

(2) If 3 is subtracted from the numerator of a fraction, the value of the resulting fraction is 1/2. If 13 is added to the denominator of the original fraction, the value of the new fraction is 1/3. Find the original fraction.

(3) A fraction has a value of 3/4. When 14 is added to the numerator, the resulting fraction has a value equal to the reciprocal of the original fraction, Find the original fraction.

Solving a fraction equation that appears in a word problem

Example: One third of a number is 6 more than one fourth of the number. Find the number.

How to solve algebra word problems with fractions and decimals?

Examples:

(1) If 1/2 of the cards had been sold and there were 172 cards left, how many cards were printed?

(2) Only 1/3 of the university students wanted to become teachers. If 3,360 did not wan to become teachers, how many university were there?

(3) Rodney guessed the total was 34.71, but this was 8.9 times the total. What was the total?

Example:

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?

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

Shelagh and Luana realized that they could express their ages more specifically if they used fractions. Doing this will allow them to calculate the difference in their ages more precisely. If Shelagh describe her age as 15 1/2 years old and Luana is 7 7/12 years old, what is the difference in their ages? Write the answer as a simplified mixed number.

Example:

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? Example:

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?

Example:

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

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? Example:

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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