Question

Perform the indicated operations; reduce the answer to lowest terms. a. 3⁄10 + 6⁄10 b. 1⁄3 + 1⁄4 + 1⁄6 c. 5⁄6 – 3⁄6 d. 2⁄3 – 6⁄10 e. 4⁄10 × 3⁄7 f. 1⁄6 × 6⁄15 g. 1⁄8 ÷ 4⁄9 h. 1⁄5 ÷ 3⁄4

Answer 1

a)

`(9)/(10)`

b)

`(3)/(4)`

c)

`(1)/(3)`

d)

`(1)/(15)`

e)

`(6)/(35)`

f)

`(1)/(15)`

g)

`(9)/(32)`

h)

`(4)/(15)`

Explanation:

a)

`(3)/(10)+(6)/(10)`

Now, this expression could also be given by:

`=(6+3)/(10)\\\\=(9)/(10)`

b)

`(1)/(3)+(1)/(4)+(1)/(6)`

On taking the least common multiple of the denominator we have:

`L.C.M\{3,4,6\}=12`

Hence, we have:

`=(1* 4+1* 3+1* 2)/(12)\\\\=(4+3+2)/(12)\\\\=(9)/(12)\\\\=(3* 3)/(3* 4)\\\\=(3)/(4)`

c)

`(5)/(6)-(3)/(6)`

Now, this expression could also be given by:

`=(5-3)/(6)\\\\=(2)/(6)`

which on reducing to the lowest terms is given by:

`=(1)/(3)`

d)

`(2)/(3)-(6)/(10)`

on reducing the second term we have:

`=(2)/(3)-(3)/(5)`

Now on simplifying the expression we have:

`=(2* 5-3* 3)/(15)\\\\=(10-9)/(15)\\\\=(1)/(15)`

e)

`(4)/(10)* (3)/(7)`

We know that:

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

Hence, we have:

`=(2)/(5)* (3)/(7)\\\\=(6)/(35)`

f)

`(1)/(6)* (6)/(15)`

which on simplifying gives:

`=(1)/(15)`

g)

`((1)/(8))/((4)/(9))`

which is further written as:

`=(1* 9)/(4* 8)\\\\=(9)/(32)`

h)

`((1)/(5))/((3)/(4))`

which is given by:

`=(1* 4)/(3* 5)\\\\=(4)/(15)`

Answer 2

a. 3⁄10 + 6⁄10 = 9/10

b. 1⁄3 + 1⁄4 + 1⁄6 = 3/4

c. 5⁄6 – 3⁄6 = 1/3

d. 2⁄3 – 6⁄10 = 1/15

e. 4⁄10 × 3⁄7 = 6/35

f. 1⁄6 × 6⁄15 = 1/15

g. 1⁄8 ÷ 4⁄9 = 9/32

h. 1⁄5 ÷ 3⁄4 = 4/15

Explanation:

a. 3⁄10 + 6⁄10

= 3*1 + 6*1 / 10

= 3+6/10

= 9/10

b. 1⁄3 + 1⁄4 + 1⁄6

since denominators are different we take LCM of 3,4,6 which is 12

= 1*4 + 1*3 + 1*2 / 12

= 4+3+2/12

= 9 ÷ 3 / 12 ÷ 3

= 3 / 4

c. 5⁄6 – 3⁄6

= 5 - 3 / 6

= 2 ÷ 2 / 6 ÷ 2 = 1/3

d. 2⁄3 – 6⁄10

LCM of 3 and 10 is 30

= 2 * 10 - 6 * 3 / 30

= 20 - 18 / 30

= 2 ÷ 2 / 30 ÷ 2 = 1/15

e. 4⁄10 × 3⁄7

= 12 ÷ 2 / 70 ÷ 2 = 6/35

f. 1⁄6 × 6⁄15

= 6 ÷ 6/90 ÷ 6 = 1/15

g. 1⁄8 ÷ 4⁄9

= 1/ 8 * 9/4

=9/32

h. 1⁄5 ÷ 3⁄4

=1/5 * 4/3

= 4/15