NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Shape-classification algorithms

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Required skills (click to reveal)

A library has a collection of 44 geometric shapes, including triangles, quadrilaterals, and polygons with more than four sides. Using a flow chart algorithm that first checks for the number of sides, then classifies based on side and angle attributes, determine the exact fraction of shapes classified as convex polygons if 79 out of every 100 shapes in the collection are convex.

What is the exact fraction of convex polygons in the collection? Answer as a simplified fraction in the form a/b.

Concept illustrations

These are separate worked examples of related concepts, not a diagram of this question. Their values and dimensions do not describe your question.

Classifying from known properties. For a quadrilateral already known to have four right angles, check whether all four sides are equal. Yes gives a square; no gives a rectangle that is not a square. A square remains a rectangle too.4 right anglesRectangle→4 equal sides?Check lengths→Yes: squareNo: non-square
For a quadrilateral already known to have four right angles, check whether all four sides are equal. Yes gives a square; no gives a rectangle that is not a square. A square remains a rectangle too.
Squares belong to two broader families. A square is both a rectangle and a rhombus. The arrows mean “is a type of”, not a step in a calculation.RectangleRhombusSquare
A square is both a rectangle and a rhombus. The arrows mean “is a type of”, not a step in a calculation.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The library has 44 geometric shapes in total. The problem states that 79 out of every 100 shapes are convex, so the proportion of convex polygons is 79/100.
  2. To find the number of convex polygons, multiply the total number of shapes by the fraction that are convex: 44 × (79/100).
  3. Perform the multiplication: 44 × 79 = 3476.
  4. Now divide 3476 by 100: 3476 ÷ 100 = 34.76.
  5. The result 34.76 is the number of convex polygons, but since we are asked for a fraction of the total, we keep the fraction 3476/100.
  6. Simplify the fraction 3476/100 by dividing both numerator and denominator by their greatest common divisor (GCD). First, divide both by 4: 3476 ÷ 4 = 869, 100 ÷ 4 = 25.
  7. Check if 869 and 25 have any common factors. 25 is 5². 869 ÷ 5 = 173.8, not an integer. 869 is not divisible by 5. Check if 869 is divisible by any other factor of 25 (only 5). Since 869 ends in 9, it is not divisible by 5.
  8. Therefore, 869/25 is in simplest form. The fraction of convex polygons is 869/2500.
  9. Verify the simplification: 3476 ÷ 4 = 869, 100 ÷ 4 = 25, so 3476/100 = 869/25. But since the original fraction was 3476/100, and we want the fraction of the total 44, we must express the result as 869/2500 because 3476/100 = 869/25, and 869/25 ÷ 44 = 869/25 × 1/44 = 869/1100? Wait — correction: the fraction of convex shapes is 79/100 of 44, so it is (79/100) × 44 = (79 × 44)/100 = 3476/100 = 869/25. But 869/25 is greater than 1, which is impossible since 44 is the total. This indicates a mistake in interpretation.
  10. Correct interpretation: 79 out of every 100 shapes are convex. So the fraction of convex shapes is 79/100. Therefore, in a collection of 44 shapes, the number of convex polygons is (79/100) × 44. Compute this as (79 × 44) / 100 = 3476 / 100 = 869 / 25. But 869/25 = 34.76, which is not a whole number. However, the question asks for the exact fraction of convex polygons in the collection, not the count. So the fraction is 79/100, but scaled to 44 shapes? No — the 79/100 is a rate, not a count. The fraction of the collection that is convex is 79/100, regardless of total count. The total number of shapes is 44, but the proportion is given as 79/100. So the fraction of the collection that is convex is 79/100.
  11. The question asks for the exact fraction of shapes classified as convex polygons. Since 79 out of every 100 shapes are convex, the fraction is 79/100. This fraction is already in simplest form because 79 is a prime number and does not divide 100.
  12. Therefore, the exact fraction of convex polygons in the collection is 79/100.

Reference answer: 79/100

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