NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Equivalent fractions and decimals

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A student walks from their home in Sydney to a park located 13 km away. On the first day, they walk 5 km and on the second day, they walk 9 km.

What fraction of the total distance has the student walked after two days? Express your answer as an exact simplified fraction.

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Half in three forms. 1/2 = 0.5 = 50%. The whole is divided into two equal parts.1 of 2 equal parts
1/2 = 0.5 = 50%. The whole is divided into two equal parts.
Common denominators as equal strips. The first strip selects 4/12 = 1/3; the second selects 3/12 = 1/4. The result selects 7/12. Every strip represents the same whole.1/31/47/124/12 + 3/12 = 7/12
The first strip selects 4/12 = 1/3; the second selects 3/12 = 1/4. The result selects 7/12. Every strip represents the same whole.

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Explanation

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Worked solution

  1. The total distance from home to the park is 13 km.
  2. On the first day, the student walks 5 km.
  3. On the second day, the student walks 9 km.
  4. Add the distances walked: 5 km + 9 km = 14 km.
  5. The student has walked 14 km, but the total distance is only 13 km. This means they have walked more than the full distance.
  6. The fraction of the total distance walked is calculated as: (distance walked) / (total distance) = 14 / 13.
  7. Simplify the fraction 14/13. The greatest common divisor of 14 and 13 is 1, so the fraction is already in simplest form.
  8. The fraction 14/13 is an improper fraction, but it is still a valid representation of the part of the distance walked.
  9. The student has walked 14/13 of the total distance, which is more than the full journey.
  10. Check: 14/13 = 1.0769..., which is greater than 1, confirming the student walked past the park.
  11. The fraction of the total distance walked is 14/13, and it is already simplified.
  12. The student has walked 14/13 of the total distance.

Reference answer: 14/13

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