What is 1/5 \times (1+2 1/3) ?

The solution to 1/5 \times (1+2 1/3) is 2/3

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1/5 \times (1+2 1/3)

\frac{1}{5} \cdot (1 + 2 \frac{1}{3})

\frac{2}{3}

Solution steps

\frac{1}{5} \cdot (1 + 2 \frac{1}{3})

Convert mixed numbers to improper fractions:

2 \frac{1}{3} = \frac{7}{3}

2 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

2 \frac{1}{3} = \frac{2 \cdot 3 + 1}{3}

= \frac{7}{3}

= \frac{1}{5} \cdot (1 + \frac{7}{3})

Follow the PEMDAS order of operations

Calculate within parentheses

(1 + \frac{7}{3}) : \frac{10}{3}

1 + \frac{7}{3}

1 + \frac{7}{3} = \frac{10}{3}

1 + \frac{7}{3}

Convert element to fraction:

1 = \frac{1 \cdot 3}{3}

= \frac{1 \cdot 3}{3} + \frac{7}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 3 + 7}{3}

1 \cdot 3 + 7 = 10

1 \cdot 3 + 7

Multiply the numbers:

1 \cdot 3 = 3

= 3 + 7

Add the numbers:

3 + 7 = 10

= 10

= \frac{10}{3}

= \frac{10}{3}

= \frac{1}{5} \cdot \frac{10}{3}

Multiply and divide (left to right)

\frac{1}{5} \cdot \frac{10}{3} : \frac{2}{3}

\frac{1}{5} \cdot \frac{10}{3}

Apply the fraction rule:

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

= \frac{1 \cdot 10}{5 \cdot 3}

\frac{1 \cdot 10}{5 \cdot 3} = \frac{2}{3}

\frac{1 \cdot 10}{5 \cdot 3}

Multiply the numbers:

1 \cdot 10 = 10

= \frac{10}{5 \cdot 3}

Factor the number:

10 = 5 \cdot 2

= \frac{5 \cdot 2}{5 \cdot 3}

Cancel the common factor:

5

= \frac{2}{3}

= \frac{2}{3}

= \frac{2}{3}

30000 - 30 \times 6 + 5 - 9

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- 2 (2)^{2} - 2

- 2 (2)^{2} + 3

3 (- 3) + 3