Ratio Worksheets | Ratio Worksheets for Teachers - Free Printable

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.

---

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 = 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 = \frac{1 \times 16}{8} = 2 $
- $ 1 : 8 = x : 24 $ → $ x = \frac{1 \times 24}{8} = 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 $

---

✔ 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 $

Let me know if you'd like this in a printable format or with explanations for students!