Ratios and Proportions Synthesis Worksheet | Fun and Engaging 6th ... - Free Printable

Let’s solve each part step by step.

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Section A: Simplify the ratios

To simplify a ratio like “a : b”, we divide both numbers by their greatest common factor (GCF).

1) 3 : 12 → GCF is 3 → 3÷3=1, 12÷3=4 → 1:4
2) 5 : 30 → GCF is 5 → 5÷5=1, 30÷5=6 → 1:6
3) 2 : 14 → GCF is 2 → 2÷2=1, 14÷2=7 → 1:7
4) 3 : 15 → GCF is 3 → 3÷3=1, 15÷3=5 → 1:5
5) 10 : 30 → GCF is 10 → 10÷10=1, 30÷10=3 → 1:3
6) 6 : 60 → GCF is 6 → 6÷6=1, 60÷6=10 → 1:10
7) 2 : 16 → GCF is 2 → 2÷2=1, 16÷2=8 → 1:8
8) 4 : 24 → GCF is 4 → 4÷4=1, 24÷4=6 → 1:6
9) 8 : 24 → GCF is 8 → 8÷8=1, 24÷8=3 → 1:3
10) 9 : 27 → GCF is 9 → 9÷9=1, 27÷9=3 → 1:3
11) 11 : 55 → GCF is 11 → 11÷11=1, 55÷11=5 → 1:5
12) 7 : 42 → GCF is 7 → 7÷7=1, 42÷7=6 → 1:6

Now right column:

13) 10 : 15 → GCF is 5 → 10÷5=2, 15÷5=3 → 2:3
14) 8 : 12 → GCF is 4 → 8÷4=2, 12÷4=3 → 2:3
15) 55 : 66 → GCF is 11 → 55÷11=5, 66÷11=6 → 5:6
16) 14 : 21 → GCF is 7 → 14÷7=2, 21÷7=3 → 2:3
17) 10 : 25 → GCF is 5 → 10÷5=2, 25÷5=5 → 2:5
18) 8 : 10 → GCF is 2 → 8÷2=4, 10÷2=5 → 4:5
19) 12 : 16 → GCF is 4 → 12÷4=3, 16÷4=4 → 3:4
20) 9 : 15 → GCF is 3 → 9÷3=3, 15÷3=5 → 3:5
21) 36 : 60 → GCF is 12 → 36÷12=3, 60÷12=5 → 3:5
22) 27 : 36 → GCF is 9 → 27÷9=3, 36÷9=4 → 3:4
23) 20 : 50 → GCF is 10 → 20÷10=2, 50÷10=5 → 2:5
24) 6 : 21 → GCF is 3 → 6÷3=2, 21÷3=7 → 2:7

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Section B: Share amounts into given ratios

We add up the parts of the ratio, then divide the total amount by that sum to find the value of one part. Then multiply each part by that value.

1) $100 into 3:7
Total parts = 3 + 7 = 10
One part = 100 ÷ 10 = $10
So: 3×10 = $30, 7×10 = $70 → $30 and $70

2) $48 into 2:2
Total parts = 2 + 2 = 4
One part = 48 ÷ 4 = $12
So: 2×12 = $24, 2×12 = $24 → $24 and $24

3) $24 into 1:3:8
Total parts = 1 + 3 + 8 = 12
One part = 24 ÷ 12 = $2
So: 1×2 = $2, 3×2 = $6, 8×2 = $16 → $2, $6, $16

4) $25 into 2:3
Total parts = 2 + 3 = 5
One part = 25 ÷ 5 = $5
So: 2×5 = $10, 3×5 = $15 → $10 and $15

5) $56 into 3:5
Total parts = 3 + 5 = 8
One part = 56 ÷ 8 = $7
So: 3×7 = $21, 5×7 = $35 → $21 and $35

6) $60 into 6:4:5
Total parts = 6 + 4 + 5 = 15
One part = 60 ÷ 15 = $4
So: 6×4 = $24, 4×4 = $16, 5×4 = $20 → $24, $16, $20

7) $18 into 4:5
Total parts = 4 + 5 = 9
One part = 18 ÷ 9 = $2
So: 4×2 = $8, 5×2 = $10 → $8 and $10

8) $77 into 5:2
Total parts = 5 + 2 = 7
One part = 77 ÷ 7 = $11
So: 5×11 = $55, 2×11 = $22 → $55 and $22

9) $28 into 4:3:7
Total parts = 4 + 3 + 7 = 14
One part = 28 ÷ 14 = $2
So: 4×2 = $8, 3×2 = $6, 7×2 = $14 → $8, $6, $14

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Final Answer:

Section A: Simplified Ratios

1) 1:4
2) 1:6
3) 1:7
4) 1:5
5) 1:3
6) 1:10
7) 1:8
8) 1:6
9) 1:3
10) 1:3
11) 1:5
12) 1:6
13) 2:3
14) 2:3
15) 5:6
16) 2:3
17) 2:5
18) 4:5
19) 3:4
20) 3:5
21) 3:5
22) 3:4
23) 2:5
24) 2:7

Section B: Shared Amounts

1) $30 and $70
2) $24 and $24
3) $2, $6, $16
4) $10 and $15
5) $21 and $35
6) $24, $16, $20
7) $8 and $10
8) $55 and $22
9) $8, $6, $14