Absolutely! Let’s solve the worksheet
“Simplifying Ratios” step by step.
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## 📌 PART 1: Reduce each ratio.
To reduce a ratio `a : b`, we find the
Greatest Common Divisor (GCD) of `a` and `b`, then divide both numbers by that GCD.
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✔ Solutions for Problems 1–24:
1) 12 : 8
GCD(12,8) = 4 → 12÷4 : 8÷4 =
3 : 2
2) 2 : 20
GCD(2,20) = 2 → 2÷2 : 20÷2 =
1 : 10
3) 3 : 36
GCD(3,36) = 3 → 3÷3 : 36÷3 =
1 : 12
4) 8 : 16
GCD(8,16) = 8 → 8÷8 : 16÷8 =
1 : 2
5) 6 : 100
GCD(6,100) = 2 → 6÷2 : 100÷2 =
3 : 50
6) 10 : 60
GCD(10,60) = 10 → 10÷10 : 60÷10 =
1 : 6
7) 21 : 49
GCD(21,49) = 7 → 21÷7 : 49÷7 =
3 : 7
8) 20 : 40
GCD(20,40) = 20 → 20÷20 : 40÷20 =
1 : 2
9) 10 : 50
GCD(10,50) = 10 → 10÷10 : 50÷10 =
1 : 5
10) 14 : 18
GCD(14,18) = 2 → 14÷2 : 18÷2 =
7 : 9
11) 45 : 27
GCD(45,27) = 9 → 45÷9 : 27÷9 =
5 : 3
12) 49 : 21
GCD(49,21) = 7 → 49÷7 : 21÷7 =
7 : 3
13) 100 : 10
GCD(100,10) = 10 → 100÷10 : 10÷10 =
10 : 1
14) 35 : 45
GCD(35,45) = 5 → 35÷5 : 45÷5 =
7 : 9
15) 8 : 20
GCD(8,20) = 4 → 8÷4 : 20÷4 =
2 : 5
16) 25 : 35
GCD(25,35) = 5 → 25÷5 : 35÷5 =
5 : 7
17) 21 : 27
GCD(21,27) = 3 → 21÷3 : 27÷3 =
7 : 9
18) 52 : 82
GCD(52,82) = 2 → 52÷2 : 82÷2 =
26 : 41
19) 12 : 36
GCD(12,36) = 12 → 12÷12 : 36÷12 =
1 : 3
20) 24 : 3
GCD(24,3) = 3 → 24÷3 : 3÷3 =
8 : 1
21) 15 : 30
GCD(15,30) = 15 → 15÷15 : 30÷15 =
1 : 2
22) 14 : 63
GCD(14,63) = 7 → 14÷7 : 63÷7 =
2 : 9
23) 68 : 80
GCD(68,80) = 4 → 68÷4 : 80÷4 =
17 : 20
24) 8 : 80
GCD(8,80) = 8 → 8÷8 : 80÷8 =
1 : 10
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## 📌 PART 2: Write each ratio as a fraction in simplest form.
This is essentially the same as reducing ratios — just write it as a fraction `a/b` and simplify.
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✔ Solutions for Problems 25–45:
25) 2 : 4 → 2/4 = 1/2
26) 6 : 20 → 6/20 = 3/10
27) 5 : 35 → 5/35 = 1/7
28) 10 : 55 → 10/55 = 2/11
29) 8 : 24 → 8/24 = 1/3
30) 9 : 42 → 9/42 = 3/14
31) 12 : 48 → 12/48 = 1/4
32) 6 : 40 → 6/40 = 3/20
33) 15 : 36 → 15/36 = 5/12
34) 18 : 82 → 18/82 = 9/41
35) 22 : 26 → 22/26 = 11/13
36) 8 : 36 → 8/36 = 2/9
37) 16 : 128 → 16/128 = 1/8
38) 14 : 77 → 14/77 = 2/11
39) 12 : 180 → 12/180 = 1/15
40) 36 : 108 → 36/108 = 1/3
41) 24 : 42 → 24/42 = 4/7
42) 18 : 120 → 18/120 = 3/20
43) 44 : 82 → 44/82 = 22/41
44) 60 : 240 → 60/240 = 1/4
45) 36 : 180 → 36/180 = 1/5
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## 🧠 Key Concepts Used:
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Ratio: A comparison of two quantities.
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Simplifying Ratio/Fraction: Divide both parts by their
Greatest Common Divisor (GCD).
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Fraction Form: Write `a:b` as `a/b`, then simplify.
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## 🎯 Final Answer Summary (for quick reference):
Part 1: Reduced Ratios
1) 3:2 2) 1:10 3) 1:12 4) 1:2 5) 3:50 6) 1:6 7) 3:7 8) 1:2
9) 1:5 10) 7:9 11) 5:3 12) 7:3 13) 10:1 14) 7:9 15) 2:5 16) 5:7
17) 7:9 18) 26:41 19) 1:3 20) 8:1 21) 1:2 22) 2:9 23) 17:20 24) 1:10
Part 2: Fractions in Simplest Form
25) 1/2 26) 3/10 27) 1/7 28) 2/11 29) 1/3 30) 3/14 31) 1/4
32) 3/20 33) 5/12 34) 9/41 35) 11/13 36) 2/9 37) 1/8 38) 2/11
39) 1/15 40) 1/3 41) 4/7 42) 3/20 43) 22/41 44) 1/4 45) 1/5
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✔ All problems solved correctly with explanations. You’re ready to submit this worksheet confidently!
Let me know if you want a printable version or step-by-step video walkthroughs! 😊
Parent Tip: Review the logic above to help your child master the concept of simplifying ratios worksheet.
