If 24 is 2/3 of 3/4 of a number, then what will be 1/4 of that number?

When a value is stated to be one fraction of another fraction of an unknown number — that is, value = (fraction one × fraction two) × number — the first step is always to combine the two given fractions into a single multiplying factor. Dividing the stated value by that combined factor recovers the whole number, after which multiplying the number by whatever other fraction is asked for gives the final answer.

1. Combine the two given fractions first: two-thirds of three-fourths works out to (2/3) × (3/4) = 6/12 = 1/2.

2. Use this combined fraction to write the given condition as an equation: 24 = 1/2 × (the number).

3. Solve the equation for the number: the number = 24 ÷ (1/2) = 24 × 2 = 48.

4. Now find the share the question actually asks for — one-fourth of the number: 1/4 × 48 = 12.

Verify by substituting back into the original statement: two-thirds of three-fourths of 48 is (1/2) × 48 = 24, which matches the value given in the question, confirming the number is indeed 48 and one-fourth of it is 12.