## Lesson 7 Divide with Fractions Answer Key

### Introduction

Division is an essential mathematical operation that allows us to distribute quantities equally. When it comes to dividing with fractions, it can often be challenging to grasp the concept and find the correct answers. In this lesson, we will provide you with the answer key for Lesson 7: Divide with Fractions, allowing you to check your work and gain a better understanding of this topic.

### Understanding Division with Fractions

Before we dive into the answer key, let's briefly recap what division with fractions entails. When dividing fractions, we need to remember that division is essentially the same as multiplying by the reciprocal of the divisor.

### Answer Key for Lesson 7: Divide with Fractions

Now, let's go through the answer key for Lesson 7: Divide with Fractions. Please note that the answers provided below are based on the specific problems given in this lesson.

### Problem 1:

Divide 3/4 by 1/2.

Answer: To divide fractions, we multiply the first fraction by the reciprocal of the second. Therefore, 3/4 ÷ 1/2 is equal to 3/4 * 2/1, which simplifies to 6/4 or 1 2/4.

### Problem 2:

Divide 5/6 by 2/3.

Answer: Similarly, we multiply the first fraction by the reciprocal of the second. Therefore, 5/6 ÷ 2/3 is equal to 5/6 * 3/2, which simplifies to 15/12 or 1 3/12. We can further simplify this to 1 1/4.

### Problem 3:

Divide 1/3 by 1/4.

Answer: Again, we multiply the first fraction by the reciprocal of the second. Therefore, 1/3 ÷ 1/4 is equal to 1/3 * 4/1, which simplifies to 4/3 or 1 1/3.

### Problem 4:

Divide 2/5 by 3/4.

Answer: Following the same process, we multiply the first fraction by the reciprocal of the second. Therefore, 2/5 ÷ 3/4 is equal to 2/5 * 4/3, which simplifies to 8/15.

### Problem 5:

Divide 7/8 by 5/6.

Answer: Once again, we multiply the first fraction by the reciprocal of the second. Therefore, 7/8 ÷ 5/6 is equal to 7/8 * 6/5, which simplifies to 42/40 or 1 2/40. We can further simplify this to 1 1/20.

### Problem 6:

Divide 4/7 by 3/10.

Answer: By multiplying the first fraction by the reciprocal of the second, we get 4/7 ÷ 3/10 = 4/7 * 10/3 = 40/21.

### Problem 7:

Divide 2/3 by 5/8.

Answer: Following the same steps, we have 2/3 ÷ 5/8 = 2/3 * 8/5 = 16/15.

### Problem 8:

Divide 5/6 by 7/9.

Answer: By multiplying the first fraction by the reciprocal of the second, we get 5/6 ÷ 7/9 = 5/6 * 9/7 = 45/42. We can simplify this to 15/14.

### Problem 9:

Divide 3/4 by 4/5.

Answer: Following the same process, we have 3/4 ÷ 4/5 = 3/4 * 5/4 = 15/16.

### Problem 10:

Divide 5/8 by 9/10.

Answer: By multiplying the first fraction by the reciprocal of the second, we get 5/8 ÷ 9/10 = 5/8 * 10/9 = 50/72. We can simplify this to 25/36.

### Problem 11:

Divide 1/2 by 1/3.

Answer: To divide fractions, we multiply the first fraction by the reciprocal of the second. Therefore, 1/2 ÷ 1/3 is equal to 1/2 * 3/1, which simplifies to 3/2 or 1 1/2.

### Problem 12:

Divide 4/5 by 2/3.

Answer: Similarly, we multiply the first fraction by the reciprocal of the second. Therefore, 4/5 ÷ 2/3 is equal to 4/5 * 3/2, which simplifies to 12/10 or 1 2/10. We can further simplify this to 1 1/5.

### Problem 13:

Divide 2/3 by 3/4.

Answer: Again, we multiply the first fraction by the reciprocal of the second. Therefore, 2/3 ÷ 3/4 is equal to 2/3 * 4/3, which simplifies to 8/9.

### Problem 14:

Divide 1/4 by 1/5.

Answer: Following the same process, we multiply the first fraction by the reciprocal of the second. Therefore, 1/4 ÷ 1/5 is equal to 1/4 * 5/1, which simplifies to 5/4 or 1 1/4.

### Problem 15:

Divide 3/4 by 5/6.

Answer: Once again, we multiply the first fraction by the reciprocal of the second. Therefore, 3/4 ÷ 5/6 is equal to 3/4 * 6/5, which simplifies to 18/20 or 9/10.

### Problem 16:

Divide 2/5 by 7/8.

Answer: By multiplying the first fraction by the reciprocal of the second, we get 2/5 ÷ 7/8 = 2/5 * 8/7 = 16/35.

### Problem 17:

Divide 7/8 by 2/3.

Answer: Following the same steps, we have 7/8 ÷ 2/3 = 7/8 * 3/2 = 21/16.

### Problem 18:

Divide 5/6 by 4/7.

Answer: By multiplying the first fraction by the reciprocal of the second, we get 5/6 ÷ 4/7 = 5/6 * 7/4 = 35/24.

### Problem 19:

Divide 3/4 by 5/6.

Answer: Following the same process, we have 3/4 ÷ 5/6 = 3/4 * 6/5 = 18/20 or 9/10.

### Problem 20:

Divide 5/8 by 4/5.

Answer: By multiplying the first fraction by the reciprocal of the second, we get 5/8 ÷ 4/5 = 5/8 * 5/4 = 25/32.

### Conclusion

Division with fractions can be challenging, but with practice and understanding, you can master this concept. By using the answer key provided for Lesson 7: Divide with Fractions, you can verify your solutions and enhance your understanding of this topic. Remember, practice makes perfect, and with continued effort, you'll become proficient in dividing with fractions.