Ratio Worksheets - Free Printable
Educational worksheet: Ratio Worksheets. Download and print for classroom or home learning activities.
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Step-by-step solution for: Ratio Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Ratio Worksheets
Let's solve each of these equivalent ratios problems step by step. The goal is to find the missing numbers so that each ratio is equivalent to the original one.
We use the concept:
> If $ a : b = c : d $, then $ \frac{a}{b} = \frac{c}{d} $, or $ a \times d = b \times c $.
> So we can multiply both terms of a ratio by the same number to get an equivalent ratio.
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- $ 1 : 7 = x : 14 $ → $ x = \frac{1 \times 14}{7} = 2 $
- $ 1 : 7 = x : 21 $ → $ x = \frac{1 \times 21}{7} = 3 $
- $ 4 : x = 1 : 7 $ → $ x = \frac{4 \times 7}{1} = 28 $
- $ 5 : x = 1 : 7 $ → $ x = \frac{5 \times 7}{1} = 35 $
- $ x : 42 = 1 : 7 $ → $ x = \frac{1 \times 42}{7} = 6 $
✔ Answer:
$ 1 : 7 = \boxed{2} : 14 = \boxed{3} : 21 = 4 : \boxed{28} = 5 : \boxed{35} = \boxed{6} : 42 $
---
- $ 1 : 2 = x : 4 $ → $ x = \frac{1 \times 4}{2} = 2 $
- $ 3 : x = 1 : 2 $ → $ x = \frac{3 \times 2}{1} = 6 $
- $ 4 : x = 1 : 2 $ → $ x = \frac{4 \times 2}{1} = 8 $
- $ 5 : x = 1 : 2 $ → $ x = \frac{5 \times 2}{1} = 10 $
- $ 6 : x = 1 : 2 $ → $ x = \frac{6 \times 2}{1} = 12 $
✔ Answer:
$ 1 : 2 = \boxed{2} : 4 = 3 : \boxed{6} = 4 : \boxed{8} = 5 : \boxed{10} = 6 : \boxed{12} $
---
- $ 1 : 3 = x : 6 $ → $ x = \frac{1 \times 6}{3} = 2 $
- $ 3 : x = 1 : 3 $ → $ x = \frac{3 \times 3}{1} = 9 $
- $ x : 12 = 1 : 3 $ → $ x = \frac{1 \times 12}{3} = 4 $
- $ 5 : x = 1 : 3 $ → $ x = \frac{5 \times 3}{1} = 15 $
- $ 6 : x = 1 : 3 $ → $ x = \frac{6 \times 3}{1} = 18 $
✔ Answer:
$ 1 : 3 = \boxed{2} : 6 = 3 : \boxed{9} = \boxed{4} : 12 = 5 : \boxed{15} = 6 : \boxed{18} $
---
- $ 1 : 2 = x : 4 $ → $ x = 2 $
- $ 1 : 2 = x : 6 $ → $ x = 3 $
- $ 1 : 2 = x : 8 $ → $ x = 4 $
- $ 1 : 2 = x : 10 $ → $ x = 5 $
- $ 6 : x = 1 : 2 $ → $ x = \frac{6 \times 2}{1} = 12 $
✔ Answer:
$ 1 : 2 = \boxed{2} : 4 = \boxed{3} : 6 = \boxed{4} : 8 = \boxed{5} : 10 = 6 : \boxed{12} $
---
- $ 1 : 8 = x : 16 $ → $ x = 2 $
- $ 1 : 8 = x : 24 $ → $ x = 3 $
- $ 4 : x = 1 : 8 $ → $ x = \frac{4 \times 8}{1} = 32 $
- $ x : 40 = 1 : 8 $ → $ x = \frac{1 \times 40}{8} = 5 $
- $ x : 48 = 1 : 8 $ → $ x = \frac{1 \times 48}{8} = 6 $
✔ Answer:
$ 1 : 8 = \boxed{2} : 16 = \boxed{3} : 24 = 4 : \boxed{32} = \boxed{5} : 40 = \boxed{6} : 48 $
---
- $ 2 : 5 = x : 10 $ → $ x = \frac{2 \times 10}{5} = 4 $
- $ 2 : 5 = x : 15 $ → $ x = \frac{2 \times 15}{5} = 6 $
- $ 8 : x = 2 : 5 $ → $ x = \frac{8 \times 5}{2} = 20 $
- $ x : 25 = 2 : 5 $ → $ x = \frac{2 \times 25}{5} = 10 $
- $ x : 30 = 2 : 5 $ → $ x = \frac{2 \times 30}{5} = 12 $
✔ Answer:
$ 2 : 5 = \boxed{4} : 10 = \boxed{6} : 15 = 8 : \boxed{20} = \boxed{10} : 25 = \boxed{12} : 30 $
---
- $ 10 : x = 5 : 9 $ → $ x = \frac{10 \times 9}{5} = 18 $
- $ 15 : x = 5 : 9 $ → $ x = \frac{15 \times 9}{5} = 27 $
- $ 20 : x = 5 : 9 $ → $ x = \frac{20 \times 9}{5} = 36 $
- $ 25 : x = 5 : 9 $ → $ x = \frac{25 \times 9}{5} = 45 $
- $ x : 54 = 5 : 9 $ → $ x = \frac{5 \times 54}{9} = 30 $
✔ Answer:
$ 5 : 9 = 10 : \boxed{18} = 15 : \boxed{27} = 20 : \boxed{36} = 25 : \boxed{45} = \boxed{30} : 54 $
---
- $ 1 : 2 = x : 4 $ → $ x = 2 $
- $ 1 : 2 = x : 6 $ → $ x = 3 $
- $ 4 : x = 1 : 2 $ → $ x = 8 $
- $ x : 10 = 1 : 2 $ → $ x = 5 $
- $ 6 : x = 1 : 2 $ → $ x = 12 $
✔ Answer:
$ 1 : 2 = \boxed{2} : 4 = \boxed{3} : 6 = 4 : \boxed{8} = \boxed{5} : 10 = 6 : \boxed{12} $
---
- $ 2 : x = 1 : 2 $ → $ x = 4 $
- $ x : 6 = 1 : 2 $ → $ x = 3 $
- $ 4 : x = 1 : 2 $ → $ x = 8 $
- $ x : 10 = 1 : 2 $ → $ x = 5 $
- $ x : 12 = 1 : 2 $ → $ x = 6 $
✔ Answer:
$ 1 : 2 = 2 : \boxed{4} = \boxed{3} : 6 = 4 : \boxed{8} = \boxed{5} : 10 = \boxed{6} : 12 $
---
- $ 1 : 3 = x : 6 $ → $ x = 2 $
- $ 1 : 3 = x : 9 $ → $ x = 3 $
- $ 4 : x = 1 : 3 $ → $ x = 12 $
- $ x : 15 = 1 : 3 $ → $ x = 5 $
- $ x : 18 = 1 : 3 $ → $ x = 6 $
✔ Answer:
$ 1 : 3 = \boxed{2} : 6 = \boxed{3} : 9 = 4 : \boxed{12} = \boxed{5} : 15 = \boxed{6} : 18 $
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1) 2, 3, 28, 35, 6
2) 2, 6, 8, 10, 12
3) 2, 9, 4, 15, 18
4) 2, 3, 4, 5, 12
5) 2, 3, 32, 5, 6
6) 4, 6, 20, 10, 12
7) 18, 27, 36, 45, 30
8) 2, 3, 8, 5, 12
9) 4, 3, 8, 5, 6
10) 2, 3, 12, 5, 6
---
Let me know if you'd like this in a printable format or need explanations for any specific steps!
We use the concept:
> If $ a : b = c : d $, then $ \frac{a}{b} = \frac{c}{d} $, or $ a \times d = b \times c $.
> So we can multiply both terms of a ratio by the same number to get an equivalent ratio.
---
1) 1 : 7 = __ : 14 = __ : 21 = 4 : __ = 5 : __ = __ : 42
- $ 1 : 7 = x : 14 $ → $ x = \frac{1 \times 14}{7} = 2 $
- $ 1 : 7 = x : 21 $ → $ x = \frac{1 \times 21}{7} = 3 $
- $ 4 : x = 1 : 7 $ → $ x = \frac{4 \times 7}{1} = 28 $
- $ 5 : x = 1 : 7 $ → $ x = \frac{5 \times 7}{1} = 35 $
- $ x : 42 = 1 : 7 $ → $ x = \frac{1 \times 42}{7} = 6 $
✔ Answer:
$ 1 : 7 = \boxed{2} : 14 = \boxed{3} : 21 = 4 : \boxed{28} = 5 : \boxed{35} = \boxed{6} : 42 $
---
2) 1 : 2 = __ : 4 = 3 : __ = 4 : __ = 5 : __ = 6 : __
- $ 1 : 2 = x : 4 $ → $ x = \frac{1 \times 4}{2} = 2 $
- $ 3 : x = 1 : 2 $ → $ x = \frac{3 \times 2}{1} = 6 $
- $ 4 : x = 1 : 2 $ → $ x = \frac{4 \times 2}{1} = 8 $
- $ 5 : x = 1 : 2 $ → $ x = \frac{5 \times 2}{1} = 10 $
- $ 6 : x = 1 : 2 $ → $ x = \frac{6 \times 2}{1} = 12 $
✔ Answer:
$ 1 : 2 = \boxed{2} : 4 = 3 : \boxed{6} = 4 : \boxed{8} = 5 : \boxed{10} = 6 : \boxed{12} $
---
3) 1 : 3 = __ : 6 = 3 : __ = __ : 12 = 5 : __ = 6 : __
- $ 1 : 3 = x : 6 $ → $ x = \frac{1 \times 6}{3} = 2 $
- $ 3 : x = 1 : 3 $ → $ x = \frac{3 \times 3}{1} = 9 $
- $ x : 12 = 1 : 3 $ → $ x = \frac{1 \times 12}{3} = 4 $
- $ 5 : x = 1 : 3 $ → $ x = \frac{5 \times 3}{1} = 15 $
- $ 6 : x = 1 : 3 $ → $ x = \frac{6 \times 3}{1} = 18 $
✔ Answer:
$ 1 : 3 = \boxed{2} : 6 = 3 : \boxed{9} = \boxed{4} : 12 = 5 : \boxed{15} = 6 : \boxed{18} $
---
4) 1 : 2 = __ : 4 = __ : 6 = __ : 8 = __ : 10 = 6 : __
- $ 1 : 2 = x : 4 $ → $ x = 2 $
- $ 1 : 2 = x : 6 $ → $ x = 3 $
- $ 1 : 2 = x : 8 $ → $ x = 4 $
- $ 1 : 2 = x : 10 $ → $ x = 5 $
- $ 6 : x = 1 : 2 $ → $ x = \frac{6 \times 2}{1} = 12 $
✔ Answer:
$ 1 : 2 = \boxed{2} : 4 = \boxed{3} : 6 = \boxed{4} : 8 = \boxed{5} : 10 = 6 : \boxed{12} $
---
5) 1 : 8 = __ : 16 = __ : 24 = 4 : __ = __ : 40 = __ : 48
- $ 1 : 8 = x : 16 $ → $ x = 2 $
- $ 1 : 8 = x : 24 $ → $ x = 3 $
- $ 4 : x = 1 : 8 $ → $ x = \frac{4 \times 8}{1} = 32 $
- $ x : 40 = 1 : 8 $ → $ x = \frac{1 \times 40}{8} = 5 $
- $ x : 48 = 1 : 8 $ → $ x = \frac{1 \times 48}{8} = 6 $
✔ Answer:
$ 1 : 8 = \boxed{2} : 16 = \boxed{3} : 24 = 4 : \boxed{32} = \boxed{5} : 40 = \boxed{6} : 48 $
---
6) 2 : 5 = __ : 10 = __ : 15 = 8 : __ = __ : 25 = __ : 30
- $ 2 : 5 = x : 10 $ → $ x = \frac{2 \times 10}{5} = 4 $
- $ 2 : 5 = x : 15 $ → $ x = \frac{2 \times 15}{5} = 6 $
- $ 8 : x = 2 : 5 $ → $ x = \frac{8 \times 5}{2} = 20 $
- $ x : 25 = 2 : 5 $ → $ x = \frac{2 \times 25}{5} = 10 $
- $ x : 30 = 2 : 5 $ → $ x = \frac{2 \times 30}{5} = 12 $
✔ Answer:
$ 2 : 5 = \boxed{4} : 10 = \boxed{6} : 15 = 8 : \boxed{20} = \boxed{10} : 25 = \boxed{12} : 30 $
---
7) 5 : 9 = 10 : __ = 15 : __ = 20 : __ = 25 : __ = __ : 54
- $ 10 : x = 5 : 9 $ → $ x = \frac{10 \times 9}{5} = 18 $
- $ 15 : x = 5 : 9 $ → $ x = \frac{15 \times 9}{5} = 27 $
- $ 20 : x = 5 : 9 $ → $ x = \frac{20 \times 9}{5} = 36 $
- $ 25 : x = 5 : 9 $ → $ x = \frac{25 \times 9}{5} = 45 $
- $ x : 54 = 5 : 9 $ → $ x = \frac{5 \times 54}{9} = 30 $
✔ Answer:
$ 5 : 9 = 10 : \boxed{18} = 15 : \boxed{27} = 20 : \boxed{36} = 25 : \boxed{45} = \boxed{30} : 54 $
---
8) 1 : 2 = __ : 4 = __ : 6 = 4 : __ = __ : 10 = 6 : __
- $ 1 : 2 = x : 4 $ → $ x = 2 $
- $ 1 : 2 = x : 6 $ → $ x = 3 $
- $ 4 : x = 1 : 2 $ → $ x = 8 $
- $ x : 10 = 1 : 2 $ → $ x = 5 $
- $ 6 : x = 1 : 2 $ → $ x = 12 $
✔ Answer:
$ 1 : 2 = \boxed{2} : 4 = \boxed{3} : 6 = 4 : \boxed{8} = \boxed{5} : 10 = 6 : \boxed{12} $
---
9) 1 : 2 = 2 : __ = __ : 6 = 4 : __ = __ : 10 = __ : 12
- $ 2 : x = 1 : 2 $ → $ x = 4 $
- $ x : 6 = 1 : 2 $ → $ x = 3 $
- $ 4 : x = 1 : 2 $ → $ x = 8 $
- $ x : 10 = 1 : 2 $ → $ x = 5 $
- $ x : 12 = 1 : 2 $ → $ x = 6 $
✔ Answer:
$ 1 : 2 = 2 : \boxed{4} = \boxed{3} : 6 = 4 : \boxed{8} = \boxed{5} : 10 = \boxed{6} : 12 $
---
10) 1 : 3 = __ : 6 = __ : 9 = 4 : __ = __ : 15 = __ : 18
- $ 1 : 3 = x : 6 $ → $ x = 2 $
- $ 1 : 3 = x : 9 $ → $ x = 3 $
- $ 4 : x = 1 : 3 $ → $ x = 12 $
- $ x : 15 = 1 : 3 $ → $ x = 5 $
- $ x : 18 = 1 : 3 $ → $ x = 6 $
✔ Answer:
$ 1 : 3 = \boxed{2} : 6 = \boxed{3} : 9 = 4 : \boxed{12} = \boxed{5} : 15 = \boxed{6} : 18 $
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✔ Final Answers:
1) 2, 3, 28, 35, 6
2) 2, 6, 8, 10, 12
3) 2, 9, 4, 15, 18
4) 2, 3, 4, 5, 12
5) 2, 3, 32, 5, 6
6) 4, 6, 20, 10, 12
7) 18, 27, 36, 45, 30
8) 2, 3, 8, 5, 12
9) 4, 3, 8, 5, 6
10) 2, 3, 12, 5, 6
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Let me know if you'd like this in a printable format or need explanations for any specific steps!
Parent Tip: Review the logic above to help your child master the concept of 6th grade ratio worksheets.
