Equivalent Fractions Worksheet for Solving for X

To solve these problems, we need to find the value of $X$ that makes the two fractions equal. This is called finding equivalent fractions.

The easiest way to do this is by using cross-multiplication.
If $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$.

Let's solve each problem step-by-step:

1) $\frac{1}{4} = \frac{X}{6}$
* Cross-multiply: $1 \times 6 = 4 \times X$
* $6 = 4X$
* Divide by 4: $X = \frac{6}{4} = \frac{3}{2}$ or $1.5$

2) $\frac{7}{13} = \frac{X}{26}$
* Notice that $13 \times 2 = 26$. So, multiply the top by 2 as well.
* $7 \times 2 = 14$
* $X = 14$

3) $\frac{8}{26} = \frac{X}{13}$
* Notice that $26 \div 2 = 13$. So, divide the top by 2 as well.
* $8 \div 2 = 4$
* $X = 4$

4) $\frac{X}{12} = \frac{6}{8}$
* Cross-multiply: $8 \times X = 12 \times 6$
* $8X = 72$
* Divide by 8: $X = 9$

5) $\frac{1}{6} = \frac{2}{X}$
* Cross-multiply: $1 \times X = 6 \times 2$
* $X = 12$

6) $\frac{X}{9} = \frac{2}{3}$
* Notice that $3 \times 3 = 9$. So, multiply the top by 3.
* $2 \times 3 = 6$
* $X = 6$

7) $\frac{2}{X} = \frac{4}{11}$
* Cross-multiply: $2 \times 11 = X \times 4$
* $22 = 4X$
* Divide by 4: $X = \frac{22}{4} = \frac{11}{2}$ or $5.5$

8) $\frac{X}{7} = \frac{8}{14}$
* Notice that $14 \div 2 = 7$. So, divide the top by 2.
* $8 \div 2 = 4$
* $X = 4$

9) $\frac{X}{14} = \frac{6}{7}$
* Notice that $7 \times 2 = 14$. So, multiply the top by 2.
* $6 \times 2 = 12$
* $X = 12$

10) $\frac{X}{12} = \frac{4}{6}$
* Simplify $\frac{4}{6}$ to $\frac{2}{3}$. Now $\frac{X}{12} = \frac{2}{3}$.
* Since $3 \times 4 = 12$, multiply the top by 4.
* $2 \times 4 = 8$
* $X = 8$

11) $\frac{3}{14} = \frac{X}{7}$
* Notice that $14 \div 2 = 7$. So, divide the top by 2.
* $3 \div 2 = 1.5$ or $\frac{3}{2}$
* $X = 1.5$

12) $\frac{9}{X} = \frac{1}{4}$
* Cross-multiply: $9 \times 4 = X \times 1$
* $36 = X$
* $X = 36$

13) $\frac{5}{X} = \frac{9}{14}$
* Cross-multiply: $5 \times 14 = X \times 9$
* $70 = 9X$
* Divide by 9: $X = \frac{70}{9}$ (or approx $7.78$)

14) $\frac{4}{5} = \frac{3}{X}$
* Cross-multiply: $4 \times X = 5 \times 3$
* $4X = 15$
* Divide by 4: $X = \frac{15}{4}$ or $3.75$

15) $\frac{6}{7} = \frac{X}{21}$
* Notice that $7 \times 3 = 21$. So, multiply the top by 3.
* $6 \times 3 = 18$
* $X = 18$

16) $\frac{7}{9} = \frac{X}{27}$
* Notice that $9 \times 3 = 27$. So, multiply the top by 3.
* $7 \times 3 = 21$
* $X = 21$

17) $\frac{5}{X} = \frac{2}{9}$
* Cross-multiply: $5 \times 9 = X \times 2$
* $45 = 2X$
* Divide by 2: $X = \frac{45}{2}$ or $22.5$

18) $\frac{1}{6} = \frac{X}{24}$
* Notice that $6 \times 4 = 24$. So, multiply the top by 4.
* $1 \times 4 = 4$
* $X = 4$

19) $\frac{8}{11} = \frac{10}{X}$
* Cross-multiply: $8 \times X = 11 \times 10$
* $8X = 110$
* Divide by 8: $X = \frac{110}{8} = \frac{55}{4}$ or $13.75$

20) $\frac{6}{8} = \frac{X}{16}$
* Notice that $8 \times 2 = 16$. So, multiply the top by 2.
* $6 \times 2 = 12$
* $X = 12$

Final Answer:
1) 1.5 (or 3/2)
2) 14
3) 4
4) 9
5) 12
6) 6
7) 5.5 (or 11/2)
8) 4
9) 12
10) 8
11) 1.5 (or 3/2)
12) 36
13) 70/9
14) 3.75 (or 15/4)
15) 18
16) 21
17) 22.5 (or 45/2)
18) 4
19) 13.75 (or 55/4)
20) 12