High School

Type the missing number that makes these fractions equal:

[tex]\frac{16}{\square} = \frac{32}{40}[/tex]

Answer :

We need to find the missing number [tex]$x$[/tex] in the equation

[tex]$$
\frac{16}{x} = \frac{32}{40}.
$$[/tex]

Step 1: Cross Multiply

Multiply both sides of the equation by [tex]$x$[/tex] and by [tex]$40$[/tex] to eliminate the fractions:

[tex]$$
16 \cdot 40 = 32 \cdot x.
$$[/tex]

Step 2: Simplify the Equation

Calculate the product on the left side:

[tex]$$
16 \cdot 40 = 640.
$$[/tex]

This gives us:

[tex]$$
640 = 32x.
$$[/tex]

Step 3: Solve for [tex]$x$[/tex]

Divide both sides of the equation by [tex]$32$[/tex]:

[tex]$$
x = \frac{640}{32}.
$$[/tex]

Simplify the fraction:

[tex]$$
x = 20.
$$[/tex]

Conclusion

The missing number that makes the fractions equal is [tex]$\boxed{20}$[/tex].