Week 2 Review Answers and Solutions

Below are the solutions and answers to the Practice Exercises and Problems for the Week 2 Review on Addition and Subtraction of Fractions.

Practice Exercises 1 Answers
1.) 3/5
2.) 2/5
3.) 4/7
4.) 2
5) 3/5

Practice Exercises 2
Convert the following improper fractions to mixed form.
1.) 3 3/5
2.) 1 5/7
3.) 4 1/2
4.) 12 3/4
5) 10 1/12

Practice Problems Solutions and Answers

1. The LCM of the denominators 2 and 8 is 8. We convert ½ to a fraction whose denominator is 8 in order for the two fractions to be similar. To do this, we divided 8 by 2 and the multiply by 1. The result will be the numerator of the fraction. That is

\dfrac{8}{2} \times \dfrac{ 1}{8} = \dfrac{4}{8}.

So, \dfrac{4}{8} + \dfrac{9}{8} = \dfrac{13}{8}.

Converting the answer to mixed form, we have 1\dfrac{5}{8}

Answer: 1 5/8

2. The LCM of 5 and 4 is 20. After getting the LCM, we convert 3/5 and 1/4 to their equivalent fractions whose denominator is 20.

The equivalent fraction for 3/5 is 12/20.
The equivalent fraction of 1/4 is 5/20.

12/20 + 5/20 = 17/20

Answer: 17/20

3. The LCM of 2, 3 and 4 is 12. After getting the LCM, we convert 1/2, 1/3, and 1/4 to their respective equivalent fractions whose denominator is 12.

The equivalent fraction for 1/2 is 6/12.
The equivalent fraction of 1/3 is 4/12.
The equivalent fraction of 1/4 is 3/12.

6/12 + 4/12 + 3/12 = 13/12

Converting 13/12 to mixed fractions, we get 1 1/12.

Answer: 1 1/12

4. The LCM of 12, 2 and 3 is 12. After getting the LCM, we convert 5/12, 1/2, and 2/3 to their respective equivalent fractions whose denominator is 12.

The equivalent fraction for 5/12 is still 5/12.
The equivalent fraction of 1/2 is 6/12.
The equivalent fraction of 2/3 is 8/12.

5/12 + 6/12 + 8/12 = 19/12

Converting 19/12 to mixed fractions, we get 1 7/12.

Answer: 1 7/12

5. The LCM of 4 and 6 is 12. Therefore, we convert 3/4 and 1/6 to their respective equivalent fractions whose denominator is 12.

The equivalent fraction for 3/4 is still 9/12.
The equivalent fraction of 1/6 is 2/12.

9/12 – 2/12 = 7/12

Answer: 7/12

6. The LCM of 15 and 30 is 30. Therefore, we convert 13/15 and 7/30 to their respective equivalent fractions whose denominator is 30.

The equivalent fraction for 13/15 is still 26/30.
The equivalent fraction of 15/30 is 15/30.

26/30 – 7/30 = 19/30

Answer: 19/30

7. In this problem, we can just add the fractions first. We add ¾ and ½ which is equal to 1 ¼ kg. We now add the 4 and 1 which is 5 ¼ kg.

8.  We need to add 1/8 and 1/2.
The LCM of 8 and 2 is 8. Therefore, we convert 1/2 to a fraction whose denominator is 8.

The equivalent fraction of 1/2 is 4/8.

1/8 + 4/8 = 5/8

Answer: 5/8

9. We need to add 1 1/2 and 3/4. We just add the fractions and then add the whole numbers later. We first add ½ and ¾.

The LCM of 2 and 4 is 4. Therefore, we convert 1/2 to a fraction whose denominator is 4.

The equivalent fraction of 1/2 is 3/4.

2/4 + 3/4 = 5/4

Converting 5/4 to mixed fractions, we have 1 ¼.

We add 1 ¼ to 1 from the original given. The answer 2 ¼.

Answer: 2 1/4

10. We need to add ¼, 1/5, and 3/10.

The LCM of 4, 5 and 10 is 20. Therefore, we convert 1/4, 1/5, and 3/10 to their respective equivalent fractions whose denominator is 20.

The equivalent fraction for 1/4 is still 5/20.
The equivalent fraction of 1/5 is 4/20.
The equivalent fraction of 3/10 is 6/20.

5/20 + 4/20 + 6/20 = 15/20

Changing 15/20 to lowest terms, we have ¾.

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