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

Answer:

a)

$\dfrac{9}{10}$

b)

$\dfrac{3}{4}$

c)

$\dfrac{1}{3}$

d)

$\dfrac{1}{15}$

e)

$\dfrac{6}{35}$

f)

$\dfrac{1}{15}$

g)

$\dfrac{9}{32}$

h)

$\dfrac{4}{15}$

Step-by-step explanation:

a)

$\dfrac{3}{10}+\dfrac{6}{10}$

Now, this expression could also be given by:

$=\dfrac{6+3}{10}\\\\=\dfrac{9}{10}$

b)

$\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{6}$

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

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

Hence, we have:

$=\dfrac{1\times 4+1\times 3+1\times 2}{12}\\\\=\dfrac{4+3+2}{12}\\\\=\dfrac{9}{12}\\\\=\dfrac{3\times 3}{3\times 4}\\\\=\dfrac{3}{4}$

c)

$\dfrac{5}{6}-\dfrac{3}{6}$

Now, this expression could also be given by:

$=\dfrac{5-3}{6}\\\\=\dfrac{2}{6}$

which on reducing to the lowest terms is given by:

$=\dfrac{1}{3}$

d)

$\dfrac{2}{3}-\dfrac{6}{10}$

on reducing the second term we have:

$=\dfrac{2}{3}-\dfrac{3}{5}$

Now on simplifying the expression we have:

$=\dfrac{2\times 5-3\times 3}{15}\\\\=\dfrac{10-9}{15}\\\\=\dfrac{1}{15}$

e)

$\dfrac{4}{10}\times \dfrac{3}{7}$

We know that:

$\dfrac{4}{10}=\dfrac{2}{5}$

Hence, we have:

$=\dfrac{2}{5}\times \dfrac{3}{7}\\\\=\dfrac{6}{35}$

f)

$\dfrac{1}{6}\times \dfrac{6}{15}$

which on simplifying gives:

$=\dfrac{1}{15}$

g)

$\dfrac{\dfrac{1}{8}}{\dfrac{4}{9}}$

which is further written as:

$=\dfrac{1\times 9}{4\times 8}\\\\=\dfrac{9}{32}$

h)

$\dfrac{\dfrac{1}{5}}{\dfrac{3}{4}}$

which is given by:

$=\dfrac{1\times 4}{3\times 5}\\\\=\dfrac{4}{15}$

Answer 2

Answer:

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

Step-by-step 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