Ratio and Proportion Worksheets - Math Monks - Free Printable

To determine whether each pair of ratios forms a proportion, we need to check if the two ratios are equivalent. Two ratios \( \frac{a}{b} \) and \( \frac{c}{d} \) form a proportion if:

\[
\frac{a}{b} = \frac{c}{d}
\]

This is equivalent to checking if the cross-products are equal:

\[
a \cdot d = b \cdot c
\]

Let's solve each pair step by step.

---

Pair 1: \( \frac{5}{15} \) and \( \frac{3}{9} \)

1. Simplify each fraction:
- \( \frac{5}{15} = \frac{1}{3} \)
- \( \frac{3}{9} = \frac{1}{3} \)

2. Compare the simplified fractions:
- Both are equal: \( \frac{1}{3} = \frac{1}{3} \)

Conclusion: These ratios form a proportion.

---

Pair 2: \( \frac{2}{3} \) and \( \frac{18}{27} \)

1. Simplify the second fraction:
- \( \frac{18}{27} = \frac{2}{3} \) (dividing numerator and denominator by 9)

2. Compare the fractions:
- Both are equal: \( \frac{2}{3} = \frac{2}{3} \)

Conclusion: These ratios form a proportion.

---

Pair 3: \( \frac{68}{7} \) and \( \frac{19}{3} \)

1. Check the cross-products:
- \( 68 \cdot 3 = 204 \)
- \( 7 \cdot 19 = 133 \)

2. Compare the cross-products:
- \( 204 \neq 133 \)

Conclusion: These ratios do not form a proportion.

---

Pair 4: \( \frac{6}{12} \) and \( \frac{2}{4} \)

1. Simplify each fraction:
- \( \frac{6}{12} = \frac{1}{2} \)
- \( \frac{2}{4} = \frac{1}{2} \)

2. Compare the simplified fractions:
- Both are equal: \( \frac{1}{2} = \frac{1}{2} \)

Conclusion: These ratios form a proportion.

---

Pair 5: \( \frac{12}{8} \) and \( \frac{4}{5} \)

1. Simplify the first fraction:
- \( \frac{12}{8} = \frac{3}{2} \)

2. Check the cross-products:
- \( 3 \cdot 5 = 15 \)
- \( 2 \cdot 4 = 8 \)

3. Compare the cross-products:
- \( 15 \neq 8 \)

Conclusion: These ratios do not form a proportion.

---

Pair 6: \( \frac{3}{27} \) and \( \frac{1}{9} \)

1. Simplify the first fraction:
- \( \frac{3}{27} = \frac{1}{9} \) (dividing numerator and denominator by 3)

2. Compare the fractions:
- Both are equal: \( \frac{1}{9} = \frac{1}{9} \)

Conclusion: These ratios form a proportion.

---

Pair 7: \( \frac{18}{4} \) and \( \frac{9}{2} \)

1. Simplify the first fraction:
- \( \frac{18}{4} = \frac{9}{2} \) (dividing numerator and denominator by 2)

2. Compare the fractions:
- Both are equal: \( \frac{9}{2} = \frac{9}{2} \)

Conclusion: These ratios form a proportion.

---

Pair 8: \( \frac{4}{5} \) and \( \frac{20}{25} \)

1. Simplify the second fraction:
- \( \frac{20}{25} = \frac{4}{5} \) (dividing numerator and denominator by 5)

2. Compare the fractions:
- Both are equal: \( \frac{4}{5} = \frac{4}{5} \)

Conclusion: These ratios form a proportion.

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Final Answers:

1. Yes
2. Yes
3. No
4. Yes
5. No
6. Yes
7. Yes
8. Yes

\[
\boxed{\text{Yes, Yes, No, Yes, No, Yes, Yes, Yes}}
\]