Grade 7 math worksheet on ratios and proportions with interactive questions and a friendly robot character.

Let's solve each of the proportion problems step by step. A proportion is a statement that two ratios are equal. To check if two ratios form a proportion, we can use cross-multiplication:

If $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$. If the cross products are equal, the ratios form a proportion.

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Problem 1: Is this a proportion?

$$
\frac{1}{4} = \frac{8}{32}
$$

Step 1: Cross-multiply:
$1 \times 32 = 32$
$4 \times 8 = 32$

Since $32 = 32$, the cross products are equal.

✔ Yes, this is a proportion.

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Problem 2: Is this a proportion?

$$
\frac{25}{40} = \frac{15}{24}
$$

Step 1: Cross-multiply:
$25 \times 24 = 600$
$40 \times 15 = 600$

Since $600 = 600$, the cross products are equal.

✔ Yes, this is a proportion.

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Problem 3: Is this a proportion?

$$
\frac{3}{5} = \frac{23}{25}
$$

Step 1: Cross-multiply:
$3 \times 25 = 75$
$5 \times 23 = 115$

Since $75 \neq 115$, the cross products are not equal.

✘ No, this is not a proportion.

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Problem 4: Is this a proportion?

$$
\frac{6}{72} = \frac{10}{120}
$$

Step 1: Cross-multiply:
$6 \times 120 = 720$
$72 \times 10 = 720$

Since $720 = 720$, the cross products are equal.

✔ Yes, this is a proportion.

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Problem 5: Is this a proportion?

$$
\frac{9}{12} = \frac{2}{4}
$$

Step 1: Cross-multiply:
$9 \times 4 = 36$
$12 \times 2 = 24$

Since $36 \neq 24$, the cross products are not equal.

✘ No, this is not a proportion.

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✔ Final Answers:

1. YES – $\frac{1}{4} = \frac{8}{32}$ → Proportion
2. YES – $\frac{25}{40} = \frac{15}{24}$ → Proportion
3. NO – $\frac{3}{5} = \frac{23}{25}$ → Not a proportion
4. YES – $\frac{6}{72} = \frac{10}{120}$ → Proportion
5. NO – $\frac{9}{12} = \frac{2}{4}$ → Not a proportion

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💡 Explanation Summary:

To determine if two ratios form a proportion:
- Use cross multiplication.
- If the products are equal → it's a proportion.
- If not → it's not a proportion.

You can also simplify fractions to check:
- For example, $\frac{1}{4} = \frac{8}{32}$ because both simplify to $0.25$.
- But $\frac{3}{5} = 0.6$, and $\frac{23}{25} = 0.92$ → not equal.

This method works every time!

Let me know if you'd like a printable version or explanation for students! 😊