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

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

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1/4 \times (3 3/5-2)

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

\frac{2}{5}

Solution steps

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

Convert mixed numbers to improper fractions:

3 \frac{3}{5} = \frac{18}{5}

3 \frac{3}{5}

Convert mixed numbers to improper fraction:

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

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

= \frac{18}{5}

= \frac{1}{4} \cdot (\frac{18}{5} - 2)

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{18}{5} - 2) : \frac{8}{5}

\frac{18}{5} - 2

\frac{18}{5} - 2 = \frac{8}{5}

\frac{18}{5} - 2

Convert element to fraction:

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

= - \frac{2 \cdot 5}{5} + \frac{18}{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 + 18}{5}

- 2 \cdot 5 + 18 = 8

- 2 \cdot 5 + 18

Multiply the numbers:

2 \cdot 5 = 10

= - 10 + 18

Add/Subtract the numbers:

- 10 + 18 = 8

= 8

= \frac{8}{5}

= \frac{8}{5}

= \frac{1}{4} \cdot \frac{8}{5}

Multiply and divide (left to right)

\frac{1}{4} \cdot \frac{8}{5} : \frac{2}{5}

\frac{1}{4} \cdot \frac{8}{5}

Apply the fraction rule:

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

= \frac{1 \cdot 8}{4 \cdot 5}

\frac{1 \cdot 8}{4 \cdot 5} = \frac{2}{5}

\frac{1 \cdot 8}{4 \cdot 5}

Multiply the numbers:

1 \cdot 8 = 8

= \frac{8}{4 \cdot 5}

Factor the number:

8 = 4 \cdot 2

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

Cancel the common factor:

4

= \frac{2}{5}

= \frac{2}{5}

= \frac{2}{5}

5 + 4 - 3

7^{2} - (9 \cdot 3 + 4^{2})

(7 + 5)^{2}

- 4 - 8 \div (- 4)

5^{2} - 9