A recipe needs 3/4 cup of sugar — how much for 2.5 times the recipe

Question

A recipe requires $\dfrac{3}{4}$ cup of sugar. How much sugar is needed to make 2.5 times the recipe?

Solution — Step by Step

If one batch needs $\frac{3}{4}$ cup, then 2.5 batches need $2.5 \times \frac{3}{4}$ cups.

We are multiplying a fraction by a decimal.

2.5 = \frac{5}{2}

Now we multiply two fractions:

\frac{5}{2} \times \frac{3}{4}

\frac{5}{2} \times \frac{3}{4} = \frac{5 \times 3}{2 \times 4} = \frac{15}{8}

\frac{15}{8} = 1\frac{7}{8} \text{ cups}

So we need $1\frac{7}{8}$ cups of sugar, or equivalently $1.875$ cups.

Why This Works

“2.5 times the recipe” is a scaling problem. Scaling means multiplying all ingredients by the same factor. When the factor is a fraction or decimal, we use multiplication — the same rule applies whether the scale factor is a whole number or not.

The conversion of 2.5 to $\frac{5}{2}$ lets us use fraction multiplication rules directly: multiply numerators, multiply denominators, then simplify.

Alternative Method — Decimal Throughout

2.5 \times \frac{3}{4} = 2.5 \times 0.75 = 1.875 \text{ cups}

Converting $1.875$ to a fraction: $1.875 = 1 + 0.875 = 1 + \frac{7}{8} = 1\frac{7}{8}$ .

Both methods give the same answer.

Common Mistake

A common error is adding instead of multiplying: writing $\frac{3}{4} + 2.5 = 3.25$ . “2.5 times” means multiplication, not addition. “How much for 2.5 times the recipe” = original amount × 2.5.

When multiplying a fraction by a decimal, always convert the decimal to a fraction first — it’s cleaner and avoids rounding errors. $2.5 = \frac{5}{2}$ , $0.25 = \frac{1}{4}$ , $1.75 = \frac{7}{4}$ are common conversions worth memorising.

Question

Solution — Step by Step

Why This Works

Alternative Method — Decimal Throughout

Common Mistake

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