Write and Solve Equations with Rational Numbers

Key Concepts

• Solve multiplication equations with decimals.

• Solve addition, subtraction, and division equations with decimals.

4.5.2 Write and Solve Equations with Rational Numbers 

Introduction

Solving equations with decimals: 

You can solve equations with decimals the same way that you solve equations with rational numbers: using inverse relationships and properties of equality to isolate the variable. 

For example, let us see an additional equation.  

4.5.2.1 Solve multiplication equations with decimals 

Example 1: 

Keith bought all the four T-shirts for $47.8. He paid the same amount for each T-shirt. Write and solve an equation to find m, the cost of each T-shirt. 

Solution: 

Use a bar diagram to show how the quantities are related and to write an equation. 

Example 2: 

Alex bought a bag of 8 apples for $3.60. Write and solve an equation to find how much Alex paid for each apple. 

Solution: 

Use a bar diagram to show how the quantities are related and to write an equation. 

4.5.2.2 Solve addition, subtraction, and division equations with decimals 

Example 3: 

Diane spent $12.50 for a new notebook and a compass. The notebook cost is 6.35. Write and solve an equation to find c, the cost of the compass. 

Solution: 

Example 4: 

Use inverse relationship to solve the following subtraction equation. 

y – 8.4 = 3.5 

Solution: 

Example 5: 

Use inverse relationship to solve the following division equation. 

m ÷ 4.5 = 50 

Solution: 

Exercise:

1. In the human body, 1.5 L of blood are supplied to the liver every minute. Solve the following equation to find the number of liters per hour. h+ 60 = 1.5

2. The length of the small intestine is 640 cm, or 51.2 times the length of the pancreas. Solve the following equation to find the length of the pancreas. 51.2p= 640

3. Aidan says that he solved the equation x3.5 – 7.2 by adding 3.5 to the left side of the equation. Explain whether Aidan is correct

4. Solve the following equation. 13.27 = t- 24.45

5. Solve the following equation. r+ 5.5 = 18.2

6. Solve the following equation. 1.8x= 40.14

7. Solve the following equation. 17.3 + v= 22.32

8. Solve the following equation. w – 3.2 = 5.6

9. The area, A, of a triangle is 15.3 square centimeters. Its base, A is 4.5 centimeters. The formula for finding the area of a triangle is A = 1/2 b/z. Write and solve an equation to find the height, 1), of the triangle.

10. In one study, the number of women classified as supertasters was 2.25 times the number of men classified as supertasters. Suppose 72 women were classified as supertasters. Write an equation that represents the number of men, m, who were classified as supertasters. Then solve the equation. How many men were classified as supertasters?

What have we learned:

• Solve multiplication equations with decimals by using inverse relationships and properties of equality.

• Solve addition, subtraction, and division equations with decimals by using inverse relationships and properties of equality.