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2013 AMC 10A Problem 2

2013 AMC 10A Problem 2AMC 10 Step by Step

Name: Date: September 13, 2026

Fractions & Decimals · difficulty 1 of 5 · about 1 min · position P1-10

Alice is making a batch of cookies and needs $2\frac{1}{2}$ cups of sugar. Unfortunately, her measuring cup holds only $\frac{1}{4}$ cup of sugar. How many times must she fill that cup to get the correct amount of sugar?

A)
$8$
B)
$10$
C)
$12$
D)
$16$
E)
$20$

Answer

Key insight

The number of fills is the total amount divided by the cup size: (5/2) divided by (1/4) equals 10.

Solution

Write the required amount as an improper fraction: $2\tfrac12 = \tfrac52$ cups. Each fill delivers $\tfrac14$ cup, so the number of fills is
$\frac{5/2}{1/4} = \frac52 \cdot 4 = 10.$

Check: $10$ quarter-cups make $\tfrac{10}{4} = 2\tfrac12$ cups.

Alice must fill the cup $\boxed{\textbf{(B)}\ 10}$ times.

Why this works

"How many of size $s$ make a total $T$ " is always $T \div s$ . Dividing by a fraction is multiplying by its reciprocal, which turns the question into "how many quarters are in five halves." Counting in quarter-cups directly (four per cup, two for the half cup) gives the same answer without any fraction arithmetic.

The trap

Multiplying by 1/4 instead of dividing, or forgetting the extra half cup and answering 8.

Common mistakes

Multiplying by 1/4 instead of dividing, or forgetting the extra half cup and answering 8.
Converting $2\tfrac12$ to $\tfrac{2}{2} + \tfrac12$ or some other wrong improper fraction.

Techniques

Set up the equation/formula and compute; no special trick needed