Question

1. if \\(\frac{2}{3}\\) of \\(\frac{3}{4}\\) of a number is 24, what is \\(\frac{1}{4}\\) of the same number?

(a) 8
(b) 12
(c) 6
(d) 20

Explanation:

Translate the word problem into an equation

Using the Algebraic Modeling knowledge point

$$ \text{Let } x \text{ be the unknown number.} $$

$$ \frac{2}{3} \cdot \frac{3}{4} \cdot x = 24 $$

Simplify the fraction product

Using the Fraction Multiplication knowledge point

$$ \frac{2}{3} \cdot \frac{3}{4} = \frac{2 \cdot 3}{3 \cdot 4} = \frac{6}{12} = \frac{1}{2} $$

$$ \frac{1}{2}x = 24 $$

Solve for the unknown number

Using the Algebraic Modeling knowledge point

$$ x = 24 \cdot 2 = 48 $$

Calculate the target fraction of the number

Using the Fraction Multiplication knowledge point

$$ \frac{1}{4} \cdot x = \frac{1}{4} \cdot 48 = 12 $$

Answer:

• (A) 8
• (B) 12 (Correct answer)
• (C) 6
• (D) 20