What is (4+2 3/5)\times 1/66 ?

The solution to (4+2 3/5)\times 1/66 is 1/10

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(4+2 3/5)\times 1/66

(4 + 2 \frac{3}{5}) \cdot \frac{1}{66}

\frac{1}{10}

Solution steps

(4 + 2 \frac{3}{5}) \cdot \frac{1}{66}

Convert mixed numbers to improper fractions:

2 \frac{3}{5} = \frac{13}{5}

2 \frac{3}{5}

Convert mixed numbers to improper fraction:

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

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

= \frac{13}{5}

= (4 + \frac{13}{5}) \cdot \frac{1}{66}

Follow the PEMDAS order of operations

Calculate within parentheses

(4 + \frac{13}{5}) : \frac{33}{5}

4 + \frac{13}{5}

4 + \frac{13}{5} = \frac{33}{5}

4 + \frac{13}{5}

Convert element to fraction:

4 = \frac{4 \cdot 5}{5}

= \frac{4 \cdot 5}{5} + \frac{13}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{4 \cdot 5 + 13}{5}

4 \cdot 5 + 13 = 33

4 \cdot 5 + 13

Multiply the numbers:

4 \cdot 5 = 20

= 20 + 13

Add the numbers:

20 + 13 = 33

= 33

= \frac{33}{5}

= \frac{33}{5}

= \frac{33}{5} \cdot \frac{1}{66}

Multiply and divide (left to right)

\frac{33}{5} \cdot \frac{1}{66} : \frac{1}{10}

\frac{33}{5} \cdot \frac{1}{66}

Apply the fraction rule:

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

= \frac{33 \cdot 1}{5 \cdot 66}

Cancel

\frac{33 \cdot 1}{5 \cdot 66} : \frac{1}{10}

\frac{33 \cdot 1}{5 \cdot 66}

Multiply the numbers:

33 \cdot 1 = 33

= \frac{33}{5 \cdot 66}

Cancel the numbers:

\frac{33}{66} = \frac{1}{2}

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

Multiply the numbers:

5 \cdot 2 = 10

= \frac{1}{10}

= \frac{1}{10}

= \frac{1}{10}

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