What is 3/4 [ 1/4 \div (-1/2)] ?

The solution to 3/4 [ 1/4 \div (-1/2)] is -3/8

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3/4 [ 1/4 \div (-1/2)]

\frac{3}{4} [\frac{1}{4} \div (- \frac{1}{2})]

- \frac{3}{8}

Solution steps

\frac{3}{4} [\frac{1}{4} \div (- \frac{1}{2})]

Follow the PEMDAS order of operations

Calculate within parentheses

[\frac{1}{4} \div (- \frac{1}{2})] : - \frac{1}{2}

\frac{1}{4} \div (- \frac{1}{2})

Multiply and divide (left to right)

Apply rule

a \div (- b) = - a \div b

\frac{1}{4} \div (- \frac{1}{2}) = - \frac{1}{4} \div \frac{1}{2}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= - \frac{1}{4} \cdot \frac{2}{1}

Cross-cancel common factor:

2

2, 4

Greatest Common Divisor (GCD)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

The prime factors common to

2, 4

are

= 2

= - \frac{1}{2}

= \frac{3}{4} (- \frac{1}{2})

Multiply and divide (left to right)

\frac{3}{4} (- \frac{1}{2}) : - \frac{3}{8}

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

Apply rule

a \cdot (- b) = - a \cdot b

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

Apply the fraction rule:

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

\frac{3}{4} \cdot \frac{1}{2} = \frac{3 \cdot 1}{4 \cdot 2}

= - \frac{3 \cdot 1}{4 \cdot 2}

Multiply the numbers:

3 \cdot 1 = 3

= - \frac{3}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= - \frac{3}{8}

= - \frac{3}{8}

7 (2)^{3} - 3 (2)^{2} - (2) + 10

7 (5 + (- 4) - (- 1))

- 2 (- 1)^{2} + 4 (- 1) + 1

- \frac{1}{3} \cdot 3 - 6

3^{2} \div 5^{2}