Question

directions: solve each proportion below for x. write the value of x in the cell provided. hint: if your answer is “x = 3”, type “3” into the cell.

1. $\frac{2}{6}=\frac{10}{x}$ 30 8. $\frac{x}{6}=\frac{7}{3}$
2. $\frac{5}{10}=\frac{x}{6}$ 3 9. $\frac{4}{x}=\frac{3}{9}$
3. $\frac{6}{4}=\frac{x}{8}$ 10. $\frac{3}{4}=\frac{6}{x}$
4. $\frac{4}{x}=\frac{2}{9}$ 11. $\frac{x}{4}=\frac{10}{8}$
5. $\frac{4}{8}=\frac{2}{x}$ 12. $\frac{4}{12}=\frac{x}{3}$
6. $\frac{3}{x}=\frac{6}{8}$ 13. $\frac{4}{6}=\frac{x}{3}$
7. 14.

Explanation:

Step1: Cross - multiply the proportion

For a proportion $\frac{a}{b}=\frac{c}{d}$, we use the rule $a\times d = b\times c$.

Step2: Solve for x

After cross - multiplying, we isolate x by performing arithmetic operations.

Problem 3:

Given $\frac{6}{4}=\frac{x}{8}$

Step1: Cross - multiply

$6\times8 = 4\times x$, so $48 = 4x$.

Step2: Solve for x

Divide both sides by 4: $x=\frac{48}{4}=12$.

Problem 4:

Given $\frac{4}{x}=\frac{2}{9}$

Step1: Cross - multiply

$4\times9 = 2\times x$, so $36 = 2x$.

Step2: Solve for x

Divide both sides by 2: $x = \frac{36}{2}=18$.

Problem 5:

Given $\frac{4}{8}=\frac{2}{x}$

Step1: Cross - multiply

$4\times x=8\times2$, so $4x = 16$.

Step2: Solve for x

Divide both sides by 4: $x=\frac{16}{4}=4$.

Problem 6:

Given $\frac{3}{x}=\frac{6}{8}$

Step1: Cross - multiply

$3\times8 = 6\times x$, so $24 = 6x$.

Step2: Solve for x

Divide both sides by 6: $x=\frac{24}{6}=4$.

Problem 8:

Given $\frac{x}{6}=\frac{7}{3}$

Step1: Cross - multiply

$x\times3 = 6\times7$, so $3x = 42$.

Step2: Solve for x

Divide both sides by 3: $x=\frac{42}{3}=14$.

Problem 9:

Given $\frac{4}{x}=\frac{3}{9}$

Step1: Cross - multiply

$4\times9 = 3\times x$, so $36 = 3x$.

Step2: Solve for x

Divide both sides by 3: $x=\frac{36}{3}=12$.

Problem 10:

Given $\frac{3}{4}=\frac{6}{x}$

Step1: Cross - multiply

$3\times x = 4\times6$, so $3x = 24$.

Step2: Solve for x

Divide both sides by 3: $x=\frac{24}{3}=8$.

Problem 11:

Given $\frac{x}{4}=\frac{10}{8}$

Step1: Cross - multiply

$x\times8 = 4\times10$, so $8x = 40$.

Step2: Solve for x

Divide both sides by 8: $x=\frac{40}{8}=5$.

Problem 12:

Given $\frac{4}{12}=\frac{x}{3}$

Step1: Cross - multiply

$4\times3 = 12\times x$, so $12 = 12x$.

Step2: Solve for x

Divide both sides by 12: $x=\frac{12}{12}=1$.

Problem 13:

Given $\frac{4}{6}=\frac{x}{3}$

Step1: Cross - multiply

$4\times3 = 6\times x$, so $12 = 6x$.

Step2: Solve for x

Divide both sides by 6: $x=\frac{12}{6}=2$.

Answer:

1. 12
2. 18
3. 4
4. 4
5. 14
6. 12
7. 8
8. 5
9. 1
10. 2