Question

To evaluate: the proportions \frac{60}{15}=\frac{12}{y} by cross products property.

Ratios, rates, proportions
ANSWERED
asked 2021-08-15
To evaluate: the proportions \(\displaystyle{\frac{{{60}}}{{{15}}}}={\frac{{{12}}}{{{y}}}}\) by cross products property.

Answers (1)

2021-08-16
Calculation:
The product of the numerator of the ratio and of the denominator of the other is known as a cross product. Cross products can be used to determine whether the ratios form a proportion or not. If the cross products are equal, then the ratios form a proportion.
\(\displaystyle{\frac{{{60}}}{{{15}}}}={\frac{{{12}}}{{{y}}}}\) [Write the proportion.]
\(\displaystyle{60}\times{y}={15}\times{12}\) [Apply cross products property.]
\(\displaystyle{60}{y}={180}\) [Multiply.]
\(\displaystyle{\frac{{{60}{y}}}{{{60}}}}={\frac{{{180}}}{{{60}}}}\) [Divide each side by 24 to place the variable on one side of the equation]
\(\displaystyle{y}={3}\) [Simplify.]
Hence, the solution of the proportions \(\displaystyle{\frac{{{60}}}{{{15}}}}={\frac{{{12}}}{{{y}}}}\) is \(\displaystyle{y}={3}\).
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