What is (2+1 1/5)\times 1/8 ?

The solution to (2+1 1/5)\times 1/8 is 2/5

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(2+1 1/5)\times 1/8

(2 + 1 \frac{1}{5}) \cdot \frac{1}{8}

\frac{2}{5}

Solution steps

(2 + 1 \frac{1}{5}) \cdot \frac{1}{8}

Convert mixed numbers to improper fractions:

1 \frac{1}{5} = \frac{6}{5}

1 \frac{1}{5}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

1 \frac{1}{5} = \frac{1 \cdot 5 + 1}{5}

= \frac{6}{5}

= (2 + \frac{6}{5}) \cdot \frac{1}{8}

Follow the PEMDAS order of operations

Calculate within parentheses

(2 + \frac{6}{5}) : \frac{16}{5}

2 + \frac{6}{5}

2 + \frac{6}{5} = \frac{16}{5}

2 + \frac{6}{5}

Convert element to fraction:

2 = \frac{2 \cdot 5}{5}

= \frac{2 \cdot 5}{5} + \frac{6}{5}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{2 \cdot 5 + 6}{5}

2 \cdot 5 + 6 = 16

2 \cdot 5 + 6

Multiply the numbers:

2 \cdot 5 = 10

= 10 + 6

Add the numbers:

10 + 6 = 16

= 16

= \frac{16}{5}

= \frac{16}{5}

= \frac{16}{5} \cdot \frac{1}{8}

Multiply and divide (left to right)

\frac{16}{5} \cdot \frac{1}{8} : \frac{2}{5}

\frac{16}{5} \cdot \frac{1}{8}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{16 \cdot 1}{5 \cdot 8}

\frac{16 \cdot 1}{5 \cdot 8} = \frac{2}{5}

\frac{16 \cdot 1}{5 \cdot 8}

Multiply the numbers:

16 \cdot 1 = 16

= \frac{16}{5 \cdot 8}

Factor the number:

16 = 8 \cdot 2

= \frac{8 \cdot 2}{5 \cdot 8}

Cancel the common factor:

8

= \frac{2}{5}

= \frac{2}{5}

= \frac{2}{5}

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