Question Find the product of two fractions: $\left(\frac{-2}{7}\right)\left(\frac{-9}{22}\right)$ . Type the simplified result.

Studdy Solution

STEP 1

Assumptions1. We are multiplying two fractions $\frac{-}{7}$ and $\frac{-9}{22}$

STEP 2

To multiply fractions, we multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together.
$\left(\frac{a}{b}\right)\left(\frac{c}{d}\right) = \frac{a \times c}{b \times d}$

STEP 3

Now, plug in the given values for the numerators and the denominators to calculate the product.
$\left(\frac{-2}{7}\right)\left(\frac{-9}{22}\right) = \frac{-2 \times -9}{7 \times22}$

STEP 4

Calculate the product of the numerators and the product of the denominators.
$\frac{-2 \times -9}{7 \times22} = \frac{18}{154}$

STEP 5

implify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it. The GCD of18 and154 is2.
$\frac{18}{154} = \frac{18 \div2}{154 \div2} = \frac{9}{77}$ The product of $\left(\frac{-2}{7}\right)\left(\frac{-9}{22}\right)$ is $\frac{9}{77}$ .

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