Lessons on solving fraction word problems using visual methods like bar models or tape diagrams.

**Related Pages**

Fraction Word Problems: Examples

Harder Fraction Word Problems

Singapore Math Lessons

Fraction Problems Using Algebra

More Math Word Problems

Here are some examples of fraction word problems. We will illustrate how block diagrams can be used to help you to visualize the fraction word problems in terms of the information given and the answer that needs to be found. Block Diagrams, (also called Tape Diagrams) are used in Singapore Math and the Common Core.

**Example:**

If of a sum
of money is $21, what is the sum of money?

**Solution:**

1 unit = 21

3 units = 21 × 3 = 63

Answer:

The sum of money is $63

**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

Answer:

There were 40 children in the group.

**Example:**

Bill had some stamps. He gave of them to Tim. If he gave 14 stamps to Tim, how many stamps had Bill at first?

**Solution:**

2 units = 14

1 unit = 7

5 units = 7 × 5 = 35

Answer:

Bill originally had 35 stamps.

**Example:**

Lionel bought 30 pizzas and burgers altogether. of the food bought were pizzas. How many burgers did he buy?

**Solution:**

5 units = 30

1 unit = 6

3 units = 3 × 6 = 18

Answer:

He bought 18 burgers.

**How to create bar models for fraction word problems?**

Problem 1:

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

Problem 2:

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

**How to solve fraction word problems using bar models?**

Problem:

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 use bar models to solve a word problem that involves adding fractions with unlike denominators?**

The first step is to find the same denominator. Then add and subtract because you have the same unit or denominator.

Problem:

Kayla counted her Halloween treats. She counted 1/4 of a pound of lollipops and 2/7 of a pound of
gobstoppers. She also counted 1/3 of a pound of mints.

How many pounds of candy did Kayla have altogether?

**How to solve a problem involving fractions of fractions and fractions of remaining parts?**

Problem:

1/4 of my trail mix recipe is raisins and the rest is nuts. 3/5 of the nuts are peanuts and the
rest are almonds. What fraction of my trail mix are almonds?

**How to solve word problems by multiplying a fraction by a whole number?**

It uses the Singapore math modeling strategy of a bar model and the “unitary method”.

Problem:

Sean has 63 classical song in his mp3 player. That is 7/8 of his entire collection. How many songs
does Sean have altogether?

**How to use bar models in a word problem that involves multiplying fractions?**

Example:

Philip purchased 1/4 pound of fruit. He ate half of the fruit after lunch. How much fruit did Philip eat?

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