Answer:

3. C. 6 8/15

4. D. 4 11/24

5. A. 3

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Answer:

1. .
2. .
3. C
4. D
5. A

Step-by-step explanation:

number 3.

Conversion a mixed number 2 1

3

to a improper fraction: 2 1/3 = 2 1

3

= 2 · 3 + 1

3

= 6 + 1

3

= 7

3

To find new numerator:

a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3

3

= 6

3

b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 3.

Conversion a mixed number 4 1

5

to a improper fraction: 4 1/5 = 4 1

5

= 4 · 5 + 1

5

= 20 + 1

5

= 21

5

To find new numerator:

a) Multiply the whole number 4 by the denominator 5. Whole number 4 equally 4 * 5

5

= 20

5

b) Add the answer from previous step 20 to the numerator 1. New numerator is 20 + 1 = 21

c) Write a previous answer (new numerator 21) over the denominator 5.

Four and one fifth is twenty-one fifths

Add: 7

3

+ 21

5

= 7 · 5

3 · 5

+ 21 · 3

5 · 3

= 35

15

+ 63

15

= 35 + 63

15

= 98

15

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(3, 5) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - seven thirds plus twenty-one fifths = ninety-eight fifteenths.

number 4.

Conversion a mixed number 1 2

6

to a improper fraction: 1 2/6 = 1 2

6

= 1 · 6 + 2

6

= 6 + 2

6

= 8

6

To find new numerator:

a) Multiply the whole number 1 by the denominator 6. Whole number 1 equally 1 * 6

6

= 6

6

b) Add the answer from previous step 6 to the numerator 2. New numerator is 6 + 2 = 8

c) Write a previous answer (new numerator 8) over the denominator 6.

One and two sixths is eight sixths

Conversion a mixed number 3 1

8

to a improper fraction: 3 1/8 = 3 1

8

= 3 · 8 + 1

8

= 24 + 1

8

= 25

8

To find new numerator:

a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8

8

= 24

8

b) Add the answer from previous step 24 to the numerator 1. New numerator is 24 + 1 = 25

c) Write a previous answer (new numerator 25) over the denominator 8.

Three and one eighth is twenty-five eighths

Add: 8

6

+ 25

8

= 8 · 4

6 · 4

+ 25 · 3

8 · 3

= 32

24

+ 75

24

= 32 + 75

24

= 107

24

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(6, 8) = 24. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 8 = 48. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - eight sixths plus twenty-five eighths = one hundred seven twenty-fourths.

number 5.

Conversion a mixed number 1 1

2

to a improper fraction: 1 1/2 = 1 1

2

= 1 · 2 + 1

2

= 2 + 1

2

= 3

2

To find new numerator:

a) Multiply the whole number 1 by the denominator 2. Whole number 1 equally 1 * 2

2

= 2

2

b) Add the answer from previous step 2 to the numerator 1. New numerator is 2 + 1 = 3

c) Write a previous answer (new numerator 3) over the denominator 2.

One and one half is three halfs

Conversion a mixed number 1 4

8

to a improper fraction: 1 4/8 = 1 4

8

= 1 · 8 + 4

8

= 8 + 4

8

= 12

8

To find new numerator:

a) Multiply the whole number 1 by the denominator 8. Whole number 1 equally 1 * 8

8

= 8

8

b) Add the answer from previous step 8 to the numerator 4. New numerator is 8 + 4 = 12

c) Write a previous answer (new numerator 12) over the denominator 8.

One and four eighths is twelve eighths

Add: 3

2

+ 12

8

= 3 · 4

2 · 4

+ 12

8

= 12

8

+ 12

8

= 12 + 12

8

= 24

8

= 8 · 3

8 · 1

= 3

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(2, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the next intermediate step , cancel by a common factor of 8 gives 3

1

.

In words - three halfs plus twelve eighths = three.