To reduce a ratio to its lowest form, we need to find the Greatest Common Divisor (GCD) for the two numbers and divide both of them by that number. The GCD is the largest number that divides evenly into both numbers.
Here is the step-by-step solution for each problem:
1) 36 : 9
* Both numbers are divisible by 9.
* $36 \div 9 = 4$
* $9 \div 9 = 1$
*
Answer: 4 : 1
2) 48 : 30
* Both numbers are even, so they are divisible by 2: $24 : 15$.
* Both 24 and 15 are divisible by 3.
* $24 \div 3 = 8$
* $15 \div 3 = 5$
*
Answer: 8 : 5
3) 45 : 27
* Both numbers are in the 9 times table.
* $45 \div 9 = 5$
* $27 \div 9 = 3$
*
Answer: 5 : 3
4) 6 : 18
* Both numbers are divisible by 6.
* $6 \div 6 = 1$
* $18 \div 6 = 3$
*
Answer: 1 : 3
5) 54 : 9
* Both numbers are divisible by 9.
* $54 \div 9 = 6$
* $9 \div 9 = 1$
*
Answer: 6 : 1
6) 30 : 42
* Both numbers are in the 6 times table.
* $30 \div 6 = 5$
* $42 \div 6 = 7$
*
Answer: 5 : 7
7) 49 : 70
* Both numbers are in the 7 times table.
* $49 \div 7 = 7$
* $70 \div 7 = 10$
*
Answer: 7 : 10
8) 12 : 32
* Both numbers are divisible by 4.
* $12 \div 4 = 3$
* $32 \div 4 = 8$
*
Answer: 3 : 8
9) 35 : 30
* Both numbers end in 5 or 0, so they are divisible by 5.
* $35 \div 5 = 7$
* $30 \div 5 = 6$
*
Answer: 7 : 6
10) 8 : 6
* Both numbers are even, so divide by 2.
* $8 \div 2 = 4$
* $6 \div 2 = 3$
*
Answer: 4 : 3
11) 36 : 30
* Both numbers are divisible by 6.
* $36 \div 6 = 6$
* $30 \div 6 = 5$
*
Answer: 6 : 5
12) 50 : 90
* Both numbers end in 0, so divide by 10.
* $50 \div 10 = 5$
* $90 \div 10 = 9$
*
Answer: 5 : 9
13) 8 : 72
* Both numbers are in the 8 times table.
* $8 \div 8 = 1$
* $72 \div 8 = 9$
*
Answer: 1 : 9
14) 5 : 10
* Both numbers are divisible by 5.
* $5 \div 5 = 1$
* $10 \div 5 = 2$
*
Answer: 1 : 2
15) 50 : 20
* Both numbers end in 0, so divide by 10.
* $50 \div 10 = 5$
* $20 \div 10 = 2$
*
Answer: 5 : 2
16) 90 : 70
* Both numbers end in 0, so divide by 10.
* $90 \div 10 = 9$
* $70 \div 10 = 7$
*
Answer: 9 : 7
17) 8 : 14
* Both numbers are even, so divide by 2.
* $8 \div 2 = 4$
* $14 \div 2 = 7$
*
Answer: 4 : 7
18) 70 : 10
* Both numbers end in 0, so divide by 10.
* $70 \div 10 = 7$
* $10 \div 10 = 1$
*
Answer: 7 : 1
19) 20 : 30
* Both numbers end in 0, so divide by 10.
* $20 \div 10 = 2$
* $30 \div 10 = 3$
*
Answer: 2 : 3
20) 90 : 80
* Both numbers end in 0, so divide by 10.
* $90 \div 10 = 9$
* $80 \div 10 = 8$
*
Answer: 9 : 8
Final Answer:
1) 4 : 1
2) 8 : 5
3) 5 : 3
4) 1 : 3
5) 6 : 1
6) 5 : 7
7) 7 : 10
8) 3 : 8
9) 7 : 6
10) 4 : 3
11) 6 : 5
12) 5 : 9
13) 1 : 9
14) 1 : 2
15) 5 : 2
16) 9 : 7
17) 4 : 7
18) 7 : 1
19) 2 : 3
20) 9 : 8
Parent Tip: Review the logic above to help your child master the concept of reducing ratios worksheet.
