Equivalent Ratio Worksheets - Math Monks - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

Part 1: Find the missing number in the ratio

To find the missing number, we look at how the numbers change from one side of the equals sign to the other. We can multiply or divide both parts of the ratio by the same number.

1) $12 : \_\_\_ = 3 : 8$
* Look at the first numbers: To get from $3$ to $12$, you multiply by $4$ ($3 \times 4 = 12$).
* Do the same to the second number: $8 \times 4 = 32$.
* Answer: 32

2) $42 : \_\_\_ = 6 : 5$
* Look at the first numbers: To get from $6$ to $42$, you multiply by $7$ ($6 \times 7 = 42$).
* Do the same to the second number: $5 \times 7 = 35$.
* Answer: 35

3) $56 : \_\_\_ = 8 : 7$
* Look at the first numbers: To get from $8$ to $56$, you multiply by $7$ ($8 \times 7 = 56$).
* Do the same to the second number: $7 \times 7 = 49$.
* Answer: 49

4) $\_\_\_ : 8 = 9 : 2$
* Look at the second numbers: To get from $2$ to $8$, you multiply by $4$ ($2 \times 4 = 8$).
* Do the same to the first number: $9 \times 4 = 36$.
* Answer: 36

5) $48 : \_\_\_ = 6 : 7$
* Look at the first numbers: To get from $6$ to $48$, you multiply by $8$ ($6 \times 8 = 48$).
* Do the same to the second number: $7 \times 8 = 56$.
* Answer: 56

6) $\_\_\_ : 36 = 10 : 9$
* Look at the second numbers: To get from $9$ to $36$, you multiply by $4$ ($9 \times 4 = 36$).
* Do the same to the first number: $10 \times 4 = 40$.
* Answer: 40

7) $24 : \_\_\_ = 4 : 7$
* Look at the first numbers: To get from $4$ to $24$, you multiply by $6$ ($4 \times 6 = 24$).
* Do the same to the second number: $7 \times 6 = 42$.
* Answer: 42

8) $7 : \_\_\_ = 28 : 44$
* Look at the first numbers: To get from $28$ down to $7$, you divide by $4$ ($28 \div 4 = 7$).
* Do the same to the second number: $44 \div 4 = 11$.
* Answer: 11

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Part 2: Find the unknown variable

These work the same way as the problems above, but we use letters like $j$, $x$, $y$, and $l$ instead of blank lines.

9) $15 : j = 3 : 5$
* Compare the known numbers: To get from $3$ to $15$, multiply by $5$.
* Apply to the variable: $5 \times 5 = 25$. So, $j = 25$.
* Answer: $j = 25$

10) $27 : 30 = x : 10$
* Compare the known numbers on the right side: To get from $30$ down to $10$, divide by $3$.
* Apply to the left side: $27 \div 3 = 9$. So, $x = 9$.
* Answer: $x = 9$

11) $24 : y = 8 : 9$
* Compare the known numbers: To get from $8$ to $24$, multiply by $3$.
* Apply to the variable: $9 \times 3 = 27$. So, $y = 27$.
* Answer: $y = 27$

12) $5 : 2 = 30 : l$
* Compare the known numbers: To get from $5$ to $30$, multiply by $6$.
* Apply to the variable: $2 \times 6 = 12$. So, $l = 12$.
* Answer: $l = 12$

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Part 3: Write any two equivalent ratios

To find equivalent ratios, you can multiply (or divide) both numbers in the ratio by the same amount. There are many correct answers here; below are simple examples using multiplication.

13) $8 : 7$
* Multiply by 2: $16 : 14$
* Multiply by 3: $24 : 21$
* Answer: $16 : 14$ and $24 : 21$

14) $4 : 7$
* Multiply by 2: $8 : 14$
* Multiply by 3: $12 : 21$
* Answer: $8 : 14$ and $12 : 21$

15) $11 : 12$
* Multiply by 2: $22 : 24$
* Multiply by 3: $33 : 36$
* Answer: $22 : 24$ and $33 : 36$

16) $4 : 13$
* Multiply by 2: $8 : 26$
* Multiply by 3: $12 : 39$
* Answer: $8 : 26$ and $12 : 39$

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Final Answer:

1) 32
2) 35
3) 49
4) 36
5) 56
6) 40
7) 42
8) 11

9) $j = 25$
10) $x = 9$
11) $y = 27$
12) $l = 12$

13) $16 : 14$, $24 : 21$ *(Answers may vary)*
14) $8 : 14$, $12 : 21$ *(Answers may vary)*
15) $22 : 24$, $33 : 36$ *(Answers may vary)*
16) $8 : 26$, $12 : 39$ *(Answers may vary)*