What is (4-2/5)\times (2-1 1/6) ?

The solution to (4-2/5)\times (2-1 1/6) is 3

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(4-2/5)\times (2-1 1/6)

(4 - \frac{2}{5}) \cdot (2 - 1 \frac{1}{6})

3

Solution steps

(4 - \frac{2}{5}) \cdot (2 - 1 \frac{1}{6})

Convert mixed numbers to improper fractions:

1 \frac{1}{6} = \frac{7}{6}

1 \frac{1}{6}

Convert mixed numbers to improper fraction:

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

1 \frac{1}{6} = \frac{1 \cdot 6 + 1}{6}

= \frac{7}{6}

= (4 - \frac{2}{5}) \cdot (2 - \frac{7}{6})

Follow the PEMDAS order of operations

Calculate within parentheses

(4 - \frac{2}{5}) : \frac{18}{5}

4 - \frac{2}{5}

4 - \frac{2}{5} = \frac{18}{5}

4 - \frac{2}{5}

Convert element to fraction:

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

= \frac{4 \cdot 5}{5} - \frac{2}{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 - 2}{5}

4 \cdot 5 - 2 = 18

4 \cdot 5 - 2

Multiply the numbers:

4 \cdot 5 = 20

= 20 - 2

Subtract the numbers:

20 - 2 = 18

= 18

= \frac{18}{5}

= \frac{18}{5}

= \frac{18}{5} (2 - \frac{7}{6})

Calculate within parentheses

(2 - \frac{7}{6}) : \frac{5}{6}

2 - \frac{7}{6}

2 - \frac{7}{6} = \frac{5}{6}

2 - \frac{7}{6}

Convert element to fraction:

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

= \frac{2 \cdot 6}{6} - \frac{7}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 6 - 7}{6}

2 \cdot 6 - 7 = 5

2 \cdot 6 - 7

Multiply the numbers:

2 \cdot 6 = 12

= 12 - 7

Subtract the numbers:

12 - 7 = 5

= 5

= \frac{5}{6}

= \frac{5}{6}

= \frac{18}{5} \cdot \frac{5}{6}

Multiply and divide (left to right)

\frac{18}{5} \cdot \frac{5}{6} : 3

\frac{18}{5} \cdot \frac{5}{6}

Cross-cancel common factor:

5

= \frac{18}{6}

Divide the numbers:

\frac{18}{6} = 3

= 3

= 3

\frac{49}{2} - 21 - (\frac{9}{2} - 9)

56 \cdot 9 \div 14 \cdot \frac{1}{3}

3^{2} + 21 \div 3

5^{2} + 2 (5) - 4

16 \div 12 \cdot 8