A recipe calls for 2 cups of flour for every 3 cups of oats. You want to use 9 cups of oats. Which proportion correctly finds the number of cups of flour needed?
A2/3 = x/9
B2/3 = 9/x
C3/2 = x/9
Dx/3 = 9/2
2/3 = x/9 keeps flour-to-oats consistent on both sides. Cross-multiplying gives 3x = 18, so x = 6 cups of flour. The other options mix up numerator and denominator positions, inverting one ratio and breaking the unit consistency that makes a proportion valid.
Question 2 True / False
Cross-multiplication is the definition of a proportion — two ratios are proportional if and mainly if their cross products are equal.
TTrue
FFalse
Answer: False
Cross-multiplication is a consequence of fraction equality, not the definition. A proportion is defined as two equal ratios (a/b = c/d). Cross-multiplying is derived by multiplying both sides by bd to get ad = bc — a useful solving technique, but the underlying concept is ratio equality, not cross products.
Question 3 Short Answer
A map uses a scale of 1 inch = 25 miles. Two cities are 3.5 inches apart on the map. Set up and solve a proportion to find their real distance.
Think about your answer, then reveal below.
Model answer: 1/25 = 3.5/x → x = 87.5 miles
The proportion keeps units consistent: (map inches)/(real miles) = (map inches)/(real miles). Cross-multiplying gives x = 25 × 3.5 = 87.5. Setting up the proportion correctly — rather than guessing arithmetic — ensures the unit relationship stays intact no matter the scale.