## Key Concepts

- Addition of fractions in solving problems
- Subtraction of fractions in solving problems

## Introduction:

In this chapter, we will learn about addition and subtraction of fractions to solve problems.

There are several ways we use fractions unknowingly while performing our day to day activities. Let us see an example.

**Example 1:**

Kayla walked 1/2 of a mile to school and then walked another 1/2 mile back. How can you find the total distance walked by Kayla?

**Solution:**

To find the total distance Kayla walked, we need to add 1/2 and 1/2.

The total distance walked by Kayla is 1 mile.

### 7.5.1 Addition of fractions in solving problems

**Example 1:**

Tyler and Dean ordered pizza. Tyler ate 1/2 of the pizza and Dean ate 1/3 of the pizza. How much of the pizza was eaten? Solve this problem any way you choose.

**Solution**:

**Step 1:**

Add the parts of the pizza eaten by Tyler and Dean.

To do this, we need to make their denominators same.

Convert 1/2 to 3/6

Convert 1/3 to 2/6

Now add both the fractions

3/6 + 2/6 = 5/6

Tyler and Dean together ate 5/6 of the pizza.

**Example 2:**

The students made muffins in cooking class. They get to take some muffins home. There are 12 muffins in a muffin tray.

- John says, “I’m taking 1/4 of a tray.”

Katie says, “I’m taking 1/3 of a tray.”

What fraction of a tray are John and Katie taking altogether? - Marjoe says, “I’m taking 1/6 of a tray.”

Sandeep says, “I’m taking 1/12 of a tray.”

What fraction of a tray are Marjoe and Sandeep taking altogether?

**Solution:**

- Add the portions of the tray taking by John and Katie.

To do this, we need to make their denominators same.

Convert 1/4 to 3/12

Convert 1/3 to 4/12

Now add both the fractions

3/12 + 4/12 = 7/12

John and Katie taking 7/12 of the tray altogether. - Add the portions of the tray taking by Marjoe and Sandeep.

To do this, we need to make their denominators same.

Convert 1/6 to 2/12

Now add both the fractions

2/12 + 1/12 = 3/12

Write the fraction in lowest terms.

3/12 = 1/4

Marjoe and Sandeep taking 1/4 of the tray altogether.

### 7.5.2 Subtraction of fractions in solving problems

**Example 1:**

A morning trip from San Francisco to Los Angeles took 13/12 hours. The return trip took 57/60 hours. How much longer did the morning trip take?

**Solution:**

**Step 1:**

Do find how much longer it took, we need to subtract the return trip from morning trip.

To do this, we need to make their denominators same.

Convert 13/12 to 65/60

Now subtract both the fractions

65/60 – 57/60 = 8/60

Write the fraction in lowest terms,

8/60 = 2/15

The morning trip took 2/15 longer than the return trip.

## Exercise:

- Jack jumped 1/7 m in a long jump competition. Shane jumped 2/9 m. Who jumped longer and by how many metres?
- Mary gave 1/8 part of her money to Shelly. What fraction of money is left with her?
- Rex had some money. He spent 1/6 of it on Monday, 3/8 on Thursday and 1/4 on Wednesday. What part of money is still left with him?
- A football player advances 2/3 of a yard. A second player in the same team advances 5/4 of a yard. How much more yard did the second player advance?
- John lives 3/8 mile from the Museum of Science. Sylvia lives 1/4 mile from the Museum of Science. How much closer is Sylvia from the museum?
- Mary is making cupcakes. She needs 3/4 of a cup of flour. She had 2/4 of a cup flour left in the pantry. How much more does she need ?
- Stefanie swam four-fifths of a lap in the morning and seven-fifteenths of a lap in the evening. How much farther did Stefanie swim in the morning than in the evening?
- The penguin nursery is open two times a day: 2/3 hour at noon and 5/12 hour in the afternoon. How much time is the penguin nursery open every day?
- An octopus weighed 5/6 kilograms. After two weeks, its weight was increased by 3/10 kilograms. But afterwards, it lost 1/5 kilograms in weight as it was sick. What is its current weight?
- The coffee cups can hold 7/9 of a pint of liquid. If Emily pours 2/3 of a pint of coffee into a cup, how much milk can a customer add?

**Concept Map:**

### What have we learned :

- Calculation of addition of two or more fractions to solve problems
- Calculation of subtraction of two or more fractions to solve problems

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