To solve these problems, we need to find the missing number that makes each pair of ratios equal. We do this by looking at how one side changes and applying the same change to the other side.
Here is the step-by-step work for each problem:
1) 2 : 8 = 6 : __
* Look at the first numbers: 2 becomes 6.
* To get from 2 to 6, we multiply by 3 ($2 \times 3 = 6$).
* We must do the same to the second number: $8 \times 3 = 24$.
*
Answer: 24
2) 3 : 9 = __ : 18
* Look at the second numbers: 9 becomes 18.
* To get from 9 to 18, we multiply by 2 ($9 \times 2 = 18$).
* We must do the same to the first number: $3 \times 2 = 6$.
*
Answer: 6
3) __ : 10 = 4 : 5
* Look at the second numbers: 5 becomes 10.
* To get from 5 to 10, we multiply by 2 ($5 \times 2 = 10$).
* We must do the same to the first number: $4 \times 2 = 8$.
*
Answer: 8
4) 6 : __ = 12 : 48
* Look at the first numbers: 6 becomes 12.
* To get from 6 to 12, we multiply by 2 ($6 \times 2 = 12$).
* We must do the same to the second number: $48 \div 2 = 24$. (Or think: what times 2 is 48? It's 24).
*
Answer: 24
5) __ : 40 = 30 : 80
* Look at the second numbers: 80 becomes 40.
* To get from 80 to 40, we divide by 2 ($80 \div 2 = 40$).
* We must do the same to the first number: $30 \div 2 = 15$.
*
Answer: 15
6) 20 : 30 = __ : 150
* Look at the second numbers: 30 becomes 150.
* To get from 30 to 150, we multiply by 5 ($30 \times 5 = 150$).
* We must do the same to the first number: $20 \times 5 = 100$.
*
Answer: 100
7) 120 : __ = 30 : 4
* Look at the first numbers: 30 becomes 120.
* To get from 30 to 120, we multiply by 4 ($30 \times 4 = 120$).
* We must do the same to the second number: $4 \times 4 = 16$.
*
Answer: 16
8) 99 : 9 = 11 : __
* Look at the first numbers: 99 becomes 11.
* To get from 99 to 11, we divide by 9 ($99 \div 9 = 11$).
* We must do the same to the second number: $9 \div 9 = 1$.
*
Answer: 1
Final Answer:
1) 24
2) 6
3) 8
4) 24
5) 15
6) 100
7) 16
8) 1
Parent Tip: Review the logic above to help your child master the concept of equivalent ratio worksheets.
