Calculation, write the answer in the simplest form and show steps for each.

Question

1)2 5/7+ 4 4/21=
2)8 2/5- 1 18/20=
3) 2/10-1/5=
4) 1/6+2/3=
5) 7/15+2/9=
6) 7/9-1/4=
7) 3/8+1/3=
8) 3/16 -3/24=
9) 16/64+3/36=
10) 3/4-7/18=

Answer 1

1) 2 5/7 + 4 4/21
Convert mixed fractions to improper fractions:
2 5/7 => (2*7+5)/7 = 19/7
4 4/21 => (4*21+4)/21 = 88/21

Add the fractions:
19/7 + 88/21
LCD = 21
(19*3)/21 + 88/21 = 57/21 + 88/21 = 145/21

Convert back to mixed fraction:
145/21 => 6 19/21 = 6 19/21

Answer: 6 19/21

2) 8 2/5 - 1 18/20
Convert mixed fractions to improper fractions:
8 2/5 => (8*5+2)/5 = 42/5
1 18/20 => (1*20+18)/20 = 38/20

Subtract the fractions:
42/5 - 38/20
LCD = 20
42/5 - (38*1)/20 = 42/5 - 38/20 = (42*4)/20 - 38/20 = 168/20 - 38/20 = 130/20

Convert back to mixed fraction:
130/20 => 6 10/20 = 6 1/2

Answer: 6 1/2

3) 2/10 - 1/5
Convert both fractions to have a common denominator:
2/10 = 1/5

Subtract the fractions:
1/5 - 1/5 = 0

Answer: 0

4) 1/6 + 2/3
Add the fractions:
1/6 + 2/3
LCD = 6
(1+4)/6 = 5/6

Answer: 5/6

5) 7/15 + 2/9
Convert both fractions to have a common denominator:
7/15 = 14/30
2/9 = 20/90

Add the fractions:
14/30 + 20/90
LCD = 90
(14*3)/90 + 20/90 = 42/90 + 20/90 = 62/90

Simplify the fraction:
62/90 = 31/45

Answer: 31/45

6) 7/9 - 1/4
Convert both fractions to have a common denominator:
7/9 = 28/36
1/4 = 9/36

Subtract the fractions:
28/36 - 9/36 = 19/36

Answer: 19/36

7) 3/8 + 1/3
Convert both fractions to have a common denominator:
3/8 = 9/24
1/3 = 8/24

Add the fractions:
9/24 + 8/24 = 17/24

Answer: 17/24

8) 3/16 - 3/24
Convert both fractions to have a common denominator:
3/16 = 9/48
3/24 = 6/48

Subtract the fractions:
9/48 - 6/48 = 3/48

Simplify the fraction:
3/48 = 1/16

Answer: 1/16

9) 16/64 + 3/36
Convert both fractions to have a common denominator:
16/64 = 1/4
3/36 = 1/12

Add the fractions:
1/4 + 1/12
LCD = 12
(3+1)/12 = 4/12

Simplify the fraction:
4/12 = 1/3

Answer: 1/3

10) 3/4 - 7/18
Convert both fractions to have a common denominator:
3/4 = 27/36
7/18 = 14/36

Subtract the fractions:
27/36 - 14/36 = 13/36

Answer: 13/36