To determine whether each pair of ratios forms a proportion, we need to check if the two fractions are equal. One way to do this is by simplifying both fractions and seeing if they reduce to the same value. Another method is cross-multiplying: if $ \frac{a}{b} = \frac{c}{d} $, then $ a \times d = b \times c $. We’ll use simplification where possible for clarity.
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Problem 1:
$ \frac{5}{15} $ and $ \frac{3}{9} $
Simplify $ \frac{5}{15} $ → divide numerator and denominator by 5 → $ \frac{1}{3} $
Simplify $ \frac{3}{9} $ → divide by 3 → $ \frac{1}{3} $
They are equal →
Yes, it’s a proportion.
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Problem 2:
$ \frac{2}{3} $ and $ \frac{18}{27} $
Simplify $ \frac{18}{27} $ → divide by 9 → $ \frac{2}{3} $
Same as first fraction →
Yes, it’s a proportion.
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Problem 3:
$ \frac{68}{7} $ and $ \frac{19}{3} $
These don’t simplify easily. Let’s cross-multiply:
$ 68 \times 3 = 204 $
$ 7 \times 19 = 133 $
204 ≠ 133 →
No, not a proportion.
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Problem 4:
$ \frac{6}{12} $ and $ \frac{2}{4} $
Simplify $ \frac{6}{12} $ → $ \frac{1}{2} $
Simplify $ \frac{2}{4} $ → $ \frac{1}{2} $
Equal →
Yes, it’s a proportion.
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Problem 5:
$ \frac{12}{8} $ and $ \frac{4}{5} $
Simplify $ \frac{12}{8} $ → divide by 4 → $ \frac{3}{2} $
$ \frac{4}{5} $ stays as is.
$ \frac{3}{2} \neq \frac{4}{5} $ →
No, not a proportion.
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Problem 6:
$ \frac{3}{27} $ and $ \frac{1}{9} $
Simplify $ \frac{3}{27} $ → divide by 3 → $ \frac{1}{9} $
Same as second fraction →
Yes, it’s a proportion.
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Problem 7:
$ \frac{18}{4} $ and $ \frac{9}{2} $
Simplify $ \frac{18}{4} $ → divide by 2 → $ \frac{9}{2} $
Same as second fraction →
Yes, it’s a proportion.
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Problem 8:
$ \frac{4}{5} $ and $ \frac{20}{25} $
Simplify $ \frac{20}{25} $ → divide by 5 → $ \frac{4}{5} $
Same as first fraction →
Yes, it’s a proportion.
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Final Answer:
1. Yes
2. Yes
3. No
4. Yes
5. No
6. Yes
7. Yes
8. Yes
Parent Tip: Review the logic above to help your child master the concept of 6th grade proportions worksheet.
