Question

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

Ratios, rates, proportions
To evaluate: the proportions $$\displaystyle{\frac{{{60}}}{{{15}}}}={\frac{{{12}}}{{{y}}}}$$ by cross products property.

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 $$\displaystyle{y}={3}$$.