simplify the ratio

Question

simplify the ratio

ScanSolve AI Tutor · Accepted Answer

To find the missing number in each ratio, we use the principle that equivalent ratios have the same proportion. If $a:b = c:d$ , then $\frac{a}{b} = \frac{c}{d}$ . We can solve for the missing number $d$ by cross-multiplication: $ad = bc$ , so $d = \frac{bc}{a}$ .

1) Find the missing number for 2:3 = 4:\text{_}

Set up the proportion.
$\frac{2}{3} = \frac{4}{x}$
Cross-multiply to solve for $x$ .
$2x = 3 \times 4$ $2x = 12$
Divide to find $x$ .
$x = \frac{12}{2}$ $x = 6$
The missing number is $\boxed{\text{6}}$ .

2) Find the missing number for 3:6 = 6:\text{_}
Set up the proportion.
$\frac{3}{6} = \frac{6}{x}$
Cross-multiply to solve for $x$ .
$3x = 6 \times 6$ $3x = 36$
Divide to find $x$ .
$x = \frac{36}{3}$ $x = 12$
The missing number is $\boxed{\text{12}}$ .

3) Find the missing number for 4:7 = 8:\text{_}
Set up the proportion.
$\frac{4}{7} = \frac{8}{x}$
Cross-multiply to solve for $x$ .
$4x = 7 \times 8$ $4x = 56$
Divide to find $x$ .
$x = \frac{56}{4}$ $x = 14$
The missing number is $\boxed{\text{14}}$ .

4) Find the missing number for 5:2 = 15:\text{_}
Set up the proportion.
$\frac{5}{2} = \frac{15}{x}$
Cross-multiply to solve for $x$ .
$5x = 2 \times 15$ $5x = 30$
Divide to find $x$ .
$x = \frac{30}{5}$ $x = 6$
The missing number is $\boxed{\text{6}}$ .

Simplify the ratio

Answer

Step-by-step solution

Set up the proportion.

Cross-multiply to solve for $x$ .

Divide to find $x$ .

Set up the proportion.

Cross-multiply to solve for $x$ .

Divide to find $x$ .

Set up the proportion.

Cross-multiply to solve for $x$ .

Divide to find $x$ .

Set up the proportion.

Cross-multiply to solve for $x$ .

Divide to find $x$ .

Try one yourself

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More Mathematics Questions

Simplify the ratio

Answer

Step-by-step solution

Set up the proportion.

Cross-multiply to solve for xxx.

Divide to find xxx.

Set up the proportion.

Cross-multiply to solve for xxx.

Divide to find xxx.

Set up the proportion.

Cross-multiply to solve for xxx.

Divide to find xxx.

Set up the proportion.

Cross-multiply to solve for xxx.

Divide to find xxx.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Cross-multiply to solve for $x$ .

Divide to find $x$ .

Cross-multiply to solve for $x$ .

Divide to find $x$ .

Cross-multiply to solve for $x$ .

Divide to find $x$ .

Cross-multiply to solve for $x$ .

Divide to find $x$ .