Maths Olympiad Prep

Library / /22 of 165

Algebra Difficulty 2.0 Junior Find the answer

What is the value of the expression 20+16×2020×16\frac{20+16 \times 20}{20 \times 16}?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Evaluating, 20+16×2020×16=20+320320=340320=1716\frac{20+16 \times 20}{20 \times 16}=\frac{20+320}{320}=\frac{340}{320}=\frac{17}{16}. Alternatively, we could notice that each of the numerator and denominator is a multiple of 20, and so 20+16×2020×16=20(1+16)20×16=1+1616=1716\frac{20+16 \times 20}{20 \times 16}=\frac{20(1+16)}{20 \times 16}=\frac{1+16}{16}=\frac{17}{16}.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.