Identify Numbers and Operation: Identify the numbers and the operation. We got 2(1)/(5) and we're dividing it by (4)/(-9).Rewrite as Multiplication: Rewrite the division as multiplication by the reciprocal. So, 2(1)/(5) ÷ (4)/(-9) becomes 2(1)/(5) * (-9)/(4).Multiply Numerators and Denominators: Multiply the numerators and denominators separately. That's 2 * 1 * -9 for the top and 5 * 4 for the bottom.Do the Multiplication: Do the multiplication. So, 2 * 1 * -9 = -18 and 5 * 4 = 20.Put It Together: Put it all together. We got -18/20.Simplify the Fraction: Simplify the fraction. -18/20 can be reduced to -9/10.

Grade 8

Powers with negative bases

Full solution

2 \frac{1}{5} \div \frac{4}{-9}=

Identify Numbers and Operation: Identify the numbers and the operation. $\newline$ We got $2\left(\frac{1}{5}\right)$ and we're dividing it by $\left(\frac{4}{-9}\right)$ .
Rewrite as Multiplication: Rewrite the division as multiplication by the reciprocal. $\newline$ So, $2\left(\frac{1}{5}\right) \div \left(\frac{4}{-9}\right)$ becomes $2\left(\frac{1}{5}\right) \times \left(\frac{-9}{4}\right)$ .
Multiply Numerators and Denominators: Multiply the numerators and denominators separately. $\newline$ That's $2 \times 1 \times -9$ for the top and $5 \times 4$ for the bottom.
Do the Multiplication: Do the multiplication. $\newline$ So, $2 \times 1 \times -9 = -18$ and $5 \times 4 = 20$ .
Put It Together: Put it all together. $\newline$ We got $-\frac{18}{20}.$
Simplify the Fraction: Simplify the fraction. $\newline$ $-\frac{18}{20}$ can be reduced to $-\frac{9}{10}$ .