A recipe calls for 3/4 cup of flour. If you want to make 2/3 of the recipe, how much flour do you need?

To find a fraction of a fraction, multiply them: 3/4 × 2/3 = (3 × 2)/(4 × 3) = 6/12 = 1/2 cup. The word 'of' between fractions means multiply. Multiply the numerators (3 × 2 = 6) and the denominators (4 × 3 = 12), then reduce 6/12 to 1/2. A useful shortcut is to cancel before multiplying: the 3 in the numerator and the 3 in the denominator cancel, leaving 1/4 × 2/1 = 2/4 = 1/2. Fraction-of-a-quantity problems appear often in arithmetic reasoning, and the reliable method is to multiply and then reduce.