Printable primary math worksheet for math grades 1 to 6 based on - Free Printable

Let's solve each proportion step by step. A proportion is an equation stating that two ratios are equal. To solve for the unknown variable, we use cross-multiplication.

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1) $ \frac{2}{x} = \frac{6}{5} $

Cross-multiply:

$$
2 \cdot 5 = 6 \cdot x \Rightarrow 10 = 6x
$$

Divide both sides by 6:

$$
x = \frac{10}{6} = \frac{5}{3}
$$

✔ Answer: $ x = \frac{5}{3} $

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2) $ \frac{48}{4} = \frac{12}{x} $

Simplify left side:

$$
\frac{48}{4} = 12 \Rightarrow 12 = \frac{12}{x}
$$

Now solve:

$$
12x = 12 \Rightarrow x = 1
$$

✔ Answer: $ x = 1 $

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3) $ \frac{15}{19} = \frac{30}{x} $

Cross-multiply:

$$
15x = 19 \cdot 30 = 570
$$

$$
x = \frac{570}{15} = 38
$$

✔ Answer: $ x = 38 $

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4) $ \frac{1}{x} = \frac{6}{53} $

Cross-multiply:

$$
1 \cdot 53 = 6 \cdot x \Rightarrow 53 = 6x
$$

$$
x = \frac{53}{6}
$$

✔ Answer: $ x = \frac{53}{6} $

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5) $ \frac{24}{56} = \frac{52}{x} $

First simplify $ \frac{24}{56} $:

$$
\frac{24}{56} = \frac{3}{7}
$$

So:

$$
\frac{3}{7} = \frac{52}{x}
$$

Cross-multiply:

$$
3x = 7 \cdot 52 = 364
\Rightarrow x = \frac{364}{3}
$$

✔ Answer: $ x = \frac{364}{3} $

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6) $ \frac{4}{5} = \frac{24}{x} $

Cross-multiply:

$$
4x = 5 \cdot 24 = 120
\Rightarrow x = \frac{120}{4} = 30
$$

✔ Answer: $ x = 30 $

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7) $ \frac{35}{25} = \frac{84}{x} $

Simplify $ \frac{35}{25} = \frac{7}{5} $

So:

$$
\frac{7}{5} = \frac{84}{x}
$$

Cross-multiply:

$$
7x = 5 \cdot 84 = 420
\Rightarrow x = \frac{420}{7} = 60
$$

✔ Answer: $ x = 60 $

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8) $ \frac{6}{7} = \frac{87}{x} $

Cross-multiply:

$$
6x = 7 \cdot 87 = 609
\Rightarrow x = \frac{609}{6} = 101.5
$$

Or as a fraction:

$$
\frac{609}{6} = \frac{203}{2}
$$

✔ Answer: $ x = \frac{203}{2} $ or $ 101.5 $

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9) $ \frac{1}{10} = \frac{31}{x} $

Cross-multiply:

$$
1 \cdot x = 10 \cdot 31 = 310
\Rightarrow x = 310
$$

✔ Answer: $ x = 310 $

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10) $ \frac{8}{3} = \frac{35}{x} $

Cross-multiply:

$$
8x = 3 \cdot 35 = 105
\Rightarrow x = \frac{105}{8}
$$

✔ Answer: $ x = \frac{105}{8} $

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✔ Final Answers:

1) $ \frac{5}{3} $
2) $ 1 $
3) $ 38 $
4) $ \frac{53}{6} $
5) $ \frac{364}{3} $
6) $ 30 $
7) $ 60 $
8) $ \frac{203}{2} $
9) $ 310 $
10) $ \frac{105}{8} $

Let me know if you'd like these as decimals or mixed numbers!