NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Evaluating statistical claims

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A community garden in Brisbane plans to allocate 79 square metres for vegetable plots and 58 square metres for compost and storage areas. The total area available is 137 square metres.

A statistical report claims that 79 out of every 137 square metres allocated are used for vegetables, and this proportion is representative of all community gardens in the state.

What is the exact fraction of the total area allocated to vegetable plots, expressed in simplest form?

Concept illustrations

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Median, mode and range in sorted data. The ordered values are 2,3,3,8,9. The middle value is 3, the most frequent value is 3, and the range is 9 − 2 = 7. The row uses equal spacing, not a number-line scale.23389↑ medianmode 3 range 7
The ordered values are 2,3,3,8,9. The middle value is 3, the most frequent value is 3, and the range is 9 − 2 = 7. The row uses equal spacing, not a number-line scale.
Comparing three category counts. Illustrative category counts: A = 2, B = 4, C = 9. Separate bars compare categories; the vertical scale starts at zero.05102A4B9C5
Illustrative category counts: A = 2, B = 4, C = 9. Separate bars compare categories; the vertical scale starts at zero.

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Explanation

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Worked solution

  1. The total area allocated is 137 square metres, and 79 square metres are used for vegetable plots. The fraction of the total area used for vegetables is calculated as the part divided by the whole.
  2. The fraction is 79 / 137. This is a ratio of two integers, so it is a rational number and can be simplified if the numerator and denominator share a common factor.
  3. To simplify the fraction, find the greatest common divisor (GCD) of 79 and 137. First, check if 79 is a prime number. 79 is not divisible by 2, 3, 5, or 7 (since 7×11=77 and 7×12=84), and 79 < 11²=121, so 79 is prime.
  4. Since 79 is prime, the only possible common factors with 137 are 1 or 79. Check if 137 is divisible by 79: 79 × 1 = 79, 79 × 2 = 158 > 137, so 79 does not divide 137.
  5. Since 79 is prime and does not divide 137, the GCD of 79 and 137 is 1. Therefore, the fraction 79/137 is already in its simplest form.
  6. The exact fraction of the total area allocated to vegetable plots is 79/137.

Reference answer: 79/137

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