Question

Adding and subtracting fractions with different denominators

Answer 1

1)23/20

2)14/5

3)47

4)27/56

5)10/7

6)23/14

7)73/35

8)7/4

Explanation:

1)multiply both fractions to get 20 as a common denominator

15/20+8/20=23/20

2)make 1 be 5/5

5/5+9/5=14/5

3)multiply both fractions to get 14 as a common denominator

26/14+21/14=47

4) multiply both sides to get 56 as a common denominator

35/56-8/56=27/56

5)make one 7/7

7/7+3/7=10/7

6)make 14 as the common denominator

2/14+21/14=23/14

7)make 35 the common denominator

28/35+45/35=73/35

8)make 1/2 be 2/4

5/4+2/4=7/4

Answer 2

1.
`1(3)/(20)`
2.
`2(4)/(5)`
3.
`3(5)/(14)`
4.
`(27)/(56)`
5.
`1(3)/(7)`
6.
`1(9)/(14)`
7.
`2(3)/(35)`
8.
`1(3)/(4)`

Explanation:

Given the following questions:

In order to add or subtract fractions we must find the common denominator, and then add the numerators. To subtract we complete the same steps but subtract the numerators instead of adding them. Of course, converting the improper fraction into a mixed number if needed.

Question one:


`(3)/(4) +(2)/(5)`

`CD=20`

`(3)/(4) *5=(15)/(20)`

`(2)/(5) *4=(8)/(20)`

`(15)/(20) +(8)/(20)`

`15+8=23`

`=(23)/(20)`

Convert into mixed number:

`(23)/(20)`

`=(23)/(20)=23/20=1(3)/(20)`

`=1(3)/(20)`

Your first answer is indeed "1 3/20."

Question two:


`1+(9)/(5)`

`1=(1)/(1)`

`(1)/(1) +(9)/(5)`

`CD=5`

`(1)/(1) *5=(5)/(5)`

`(9)/(5) *1=(9)/(5)`

`(5)/(5) +(9)/(5)`

`5+9=14`

`=(14)/(5)`

Convert into mixed number:

`(14)/(5)`

`(14)/(5)\di=14/5=2(4)/(5)`

`=2(4)/(5)`

Your second answer is indeed "2 4/5."

Question three:


`(13)/(7) +(3)/(2)`

`CD=14`

`(13)/(7) *2=(26)/(14)`

`(3)/(2)*7=(21)/(14)`

`(26)/(14) +(21)/(14)`

`26+21=47=(47)/(14)`

`=(47)/(14)`

Convert into mixed number:

`(47)/(14)`

`(47)/(14)=47/14=3(5)/(14)`

`=3(5)/(14)`

Your third answer is indeed "3 5/14."

Question four:


`(5)/(8) -(1)/(7)`

`CD=56`

`(5)/(8) *7=(35)/(56)`

`(1)/(7) *8=(8)/(56)`

`(35)/(56) -(8)/(56)`

`35-8=27`

`=(27)/(56)`

Your fourth answer is indeed "27/56."

Question five:


`1+(3)/(7)`

`1=(1)/(1)`

`CD=7`

`(1)/(1)*7=(7)/(7)`

`(3)/(7) *1=(3)/(7)`

`(7)/(7) +(3)/(7)`

`7+3=10`

`=(10)/(7)`

Convert into mixed number:

`(10)/(7)`

`(10)/(7) =10/7=1(3)/(7)`

`=1(3)/(7)`

Your fifth answer is indeed "1 3/7."

Question six:


`(1)/(7) +(3)/(2)`

`CD=14`

`(1)/(7) *2=(2)/(14)`

`(3)/(2) *7=(21)/(14)`

`(2)/(14) +(21)/(14)`

`2+21=23`

`=(23)/(14)`

Convert into mixed number:

`(23)/(14)`

`(23)/(14)=23/14=1(9)/(14)`

`=1(9)/(14)`

Your sixth answer is indeed "1 9/14."

Question seven:


`(4)/(5) +(9)/(7)`

`CD=35`

`(4)/(5) *7=(28)/(35)`

`(9)/(7) *5=(45)/(35)`

`(28)/(35) +(45)/(35)`

`28+45=73`

`=(73)/(35)`

Convert into mixed number:

`(73)/(35)`

`=(73)/(35)=73/35=2(3)/(35)`

`=2(3)/(35)`

Your seventh answer is indeed "2 3/35."

Question eight:


`(5)/(4) +(1)/(2)`

`CD=8`

`(5)/(4)*2=(10)/(8)`

`(1)/(2) *4=(4)/(8)`

`(10)/(8)+(4)/(8)`

`10+4=14`

`=(14)/(8)`

Simplify by reducing:

`(14)/(8)`

`(14)/(8)/2=(7)/(4)`

`=(7)/(4)`

Convert into mixed number:

`(7)/(4)`

`(7)/(4) =7/4=1(3)/(4)`

`=1(3)/(4)`

Your final answer is indeed "1 3/4."

Hope this helps.