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Fraction of a fraction

P6 · Fractions · PSLE Maths

Question

In P6 Kindness, 2/3 of the pupils were girls. 3/4 of the girls joined the choir. If 30 girls joined the choir, how many pupils were there in the class?

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Hint

First divide the class into 3 large parts for 2/3, then split each large part into 2 small parts so the girls are 4 small parts.

Show the answer and step-by-step explanation

Answer: Number of pupils in the class 60 pupils

  1. Draw the class — 2/3 of the class are girls. To split it more easily later, divide each of the 3 large parts into 2 small units, so the whole class has 6 small units.
  2. Take 3/4 of girls — The girls make up 4 small units. 3/4 of the girls joined the choir, so that is 3 out of the 4 small units.
  3. Match 30 pupils — The question says 30 girls joined the choir. So the 3 small units in the model represent 30 pupils.
  4. Find 1 unit — If 3 units are 30 pupils, then 1 unit is 30 ÷ 3 = 10 pupils.
  5. Find the class — The whole class has 6 small units. So the number of pupils in the class is 6 × 10 = 60. 📌 Key idea: for a fraction of a fraction, draw the whole first, then split the required part again, and use the given number to find 1 unit.

Method: Use a bar model in layers: first show 2/3 of the class, then take 3/4 of the girls. Match the known number to the small units, find 1 unit, then find the whole class.

Practice: 3 similar questions

  1. In P6 Respect, 2/3 of the pupils were girls. 3/4 of the girls joined the dance club. If 24 girls joined the dance club, how many pupils were there in the class?
    Answer

    48 pupils — Treat the class as 6 small units. Since girls are 2/3 = 4/6, the girls make up 4 units. 3/4 of the girls joined the dance club, so the dance club girls make up 3 units. 3 units = 24 pupils, so 1 unit = 24 ÷ 3 = 8 pupils. The whole class is 6 units = 6 × 8 = 48 pupils.

  2. In a school volunteer group, 3/5 of the members were P6 pupils. 2/3 of the P6 pupils were girls. If there were 18 P6 girls, how many members were there in the volunteer group?
    Answer

    45 members — The P6 pupils are 3/5 of the total. The P6 girls are 2/3 of the P6 pupils, so they are 2/3 × 3/5 = 2/5 of the total. 2/5 of the total = 18 members, so 1/5 = 18 ÷ 2 = 9 members. Total number of members = 5 × 9 = 45.

  3. In P6 Harmony, 2/3 of the pupils were girls. 3/4 of the girls joined the choir. There were 9 girls who did not join the choir. How many pupils were there in the class?
    Answer

    54 pupils — 3/4 of the girls joined the choir, so 1/4 of the girls did not join. 1/4 of the girls = 9 pupils, so the number of girls = 9 × 4 = 36. The girls are 2/3 of the class, so 2/3 of the class = 36 pupils. 1/3 of the class = 36 ÷ 2 = 18 pupils, so the whole class = 18 × 3 = 54 pupils.

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