Grade 6 Ratios Worksheet: Simple Proportions Practice

To solve these proportions, we use cross-multiplication. This means we multiply the top number (numerator) of one fraction by the bottom number (denominator) of the other fraction. Then we set those two products equal to each other and solve for the missing number.

Here is the step-by-step solution for each problem:

1. $\frac{x}{6} = \frac{15}{18}$
* Cross-multiply: $18 \cdot x = 6 \cdot 15$
* Calculate: $18x = 90$
* Divide by 18: $x = \frac{90}{18}$
* Result: $x = 5$

2. $\frac{x}{3} = \frac{16}{24}$
* Cross-multiply: $24 \cdot x = 3 \cdot 16$
* Calculate: $24x = 48$
* Divide by 24: $x = \frac{48}{24}$
* Result: $x = 2$

3. $\frac{3}{5} = \frac{x}{15}$
* Cross-multiply: $5 \cdot x = 3 \cdot 15$
* Calculate: $5x = 45$
* Divide by 5: $x = \frac{45}{5}$
* Result: $x = 9$

4. $\frac{x}{6} = \frac{2}{12}$
* Cross-multiply: $12 \cdot x = 6 \cdot 2$
* Calculate: $12x = 12$
* Divide by 12: $x = \frac{12}{12}$
* Result: $x = 1$

5. $\frac{x}{5} = \frac{18}{20}$
* Cross-multiply: $20 \cdot x = 5 \cdot 18$
* Calculate: $20x = 90$
* Divide by 20: $x = \frac{90}{20}$
* Result: $x = 4.5$ (or $\frac{9}{2}$)

6. $\frac{1}{2} = \frac{x}{8}$
* Cross-multiply: $2 \cdot x = 1 \cdot 8$
* Calculate: $2x = 8$
* Divide by 2: $x = \frac{8}{2}$
* Result: $x = 4$

7. $\frac{x}{8} = \frac{10}{16}$
* Cross-multiply: $16 \cdot x = 8 \cdot 10$
* Calculate: $16x = 80$
* Divide by 16: $x = \frac{80}{16}$
* Result: $x = 5$

8. $\frac{x}{2} = \frac{4}{8}$
* Cross-multiply: $8 \cdot x = 2 \cdot 4$
* Calculate: $8x = 8$
* Divide by 8: $x = \frac{8}{8}$
* Result: $x = 1$

9. $\frac{x}{4} = \frac{9}{12}$
* Cross-multiply: $12 \cdot x = 4 \cdot 9$
* Calculate: $12x = 36$
* Divide by 12: $x = \frac{36}{12}$
* Result: $x = 3$

10. $\frac{1}{3} = \frac{x}{3}$
* Cross-multiply: $3 \cdot x = 1 \cdot 3$
* Calculate: $3x = 3$
* Divide by 3: $x = \frac{3}{3}$
* Result: $x = 1$

11. $\frac{x}{2} = \frac{4}{8}$
* Cross-multiply: $8 \cdot x = 2 \cdot 4$
* Calculate: $8x = 8$
* Divide by 8: $x = \frac{8}{8}$
* Result: $x = 1$

12. $\frac{x}{2} = \frac{10}{20}$
* Cross-multiply: $20 \cdot x = 2 \cdot 10$
* Calculate: $20x = 20$
* Divide by 20: $x = \frac{20}{20}$
* Result: $x = 1$

Final Answer:
1. 5
2. 2
3. 9
4. 1
5. 4.5
6. 4
7. 5
8. 1
9. 3
10. 1
11. 1
12. 1