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How to solve Fraction Word Problems using Algebra

More Singapore Math Lessons

Here are some examples and solutions of fraction word problems.

The first example is a one-step word problem.

The second example shows how blocks can be used to help illustrate the problem.

The third example is a two-step word problem.

More examples and solutions using the bar modeling method to solve fraction word problems are shown in the videos. The bar modeling method, also called tape diagrams, are use in Singapore Math and the Common Core.

*Example:*

**Bar Modeling with Fractions**

Examples:

1) Grace thought that a plane journey would take 7/10 hr but the actual journey took 1/5 hr longer. How long did the actual journey take?

2) Timothy took 2/3 hr to paint a portrait. This was 1/3 hr shorter than the time he took to paint scenery. How long did he take to paint scenery?**Word Problem on Subtracting Fractions From Whole Numbers**

Example: A craft store has a 9 yd spool of ribbon. In the morning, a customer buys 1/5 yd of ribbon from the spool. In the afternoon another customer buys 7/10 yd of ribbon from the spool. How much ribbon is left?**How to solve real world problems involving multiplication of fractions by using visual fraction models or equations to represent the problem?**

Examples:

1. At the animal shelter 4/6 of the animals are cats. Of the cats 1/2 are male. What fraction of the animals at the shelter are male cats?

2. A taco recipe called for 2/3 cup of cheese per taco. If Andrew wanted to make 3 tacos, how much cheese would he need?**How to solve word problems using tape diagrams and fraction-by-fraction multiplication?**

Examples:

1. Ethan is icing 30 cupcakes. He spreads mint icing on 1/5 of the cupcakes and chocolate on 1/2 of the remaining cupcakes. The rest will get vanilla frosting. How many cupcakes have vanilla frosting?

2. Maddox puts 1/4 of her lawn-mowing money in savings and uses 1/2 of the remaining money to pay back her suster. If she has $15 left, how much did she have at first?

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

How to solve Fraction Word Problems using Algebra

More Singapore Math Lessons

Here are some examples and solutions of fraction word problems.

The first example is a one-step word problem.

The second example shows how blocks can be used to help illustrate the problem.

The third example is a two-step word problem.

More examples and solutions using the bar modeling method to solve fraction word problems are shown in the videos. The bar modeling method, also called tape diagrams, are use in Singapore Math and the Common Core.

Martha spent of her allowance on food and shopping. What fraction of her allowance had she left?

* Solution: *

She had of her allowance left.

*Example: *

of a group of children were girls. If there were 24 girls, how many children were there in the group?

* Solution: *

3 units = 24

1 unit = 24 ÷ 3 = 8

5 units = 5 × 8 = 40

There were 40 children in the group.

*Example: *

Sam had 120 teddy bears in his toy store. He sold of them at $12 each. How much did he receive?

* Solution: *

**Step 1:** Find the number of teddy bears sold.

He sold 80 teddy bears.

**Step 2:** Find how much money he received.

80 × 12 = 960

He received $960.Examples:

1) Grace thought that a plane journey would take 7/10 hr but the actual journey took 1/5 hr longer. How long did the actual journey take?

2) Timothy took 2/3 hr to paint a portrait. This was 1/3 hr shorter than the time he took to paint scenery. How long did he take to paint scenery?

Example: A craft store has a 9 yd spool of ribbon. In the morning, a customer buys 1/5 yd of ribbon from the spool. In the afternoon another customer buys 7/10 yd of ribbon from the spool. How much ribbon is left?

Examples:

1. At the animal shelter 4/6 of the animals are cats. Of the cats 1/2 are male. What fraction of the animals at the shelter are male cats?

2. A taco recipe called for 2/3 cup of cheese per taco. If Andrew wanted to make 3 tacos, how much cheese would he need?

Examples:

1. Ethan is icing 30 cupcakes. He spreads mint icing on 1/5 of the cupcakes and chocolate on 1/2 of the remaining cupcakes. The rest will get vanilla frosting. How many cupcakes have vanilla frosting?

2. Maddox puts 1/4 of her lawn-mowing money in savings and uses 1/2 of the remaining money to pay back her suster. If she has $15 left, how much did she have at first?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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