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Inessa [10]
3 years ago
15

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 – 6⁄1

0 e. 4⁄10 × 3⁄7 f. 1⁄6 × 6⁄15 g. 1⁄8 ÷ 4⁄9 h. 1⁄5 ÷ 3⁄4
Mathematics
2 answers:
pychu [463]3 years ago
7 0
<h2>Answer:</h2>

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}

<h2>Step-by-step explanation:</h2>

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}

Setler [38]3 years ago
3 0

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

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