Math  /  Numbers & Operations

QuestionWhich of the following ratios is equivalent to 2:3? A 12\frac{1}{2} C 1213\frac{12}{13} B 46\frac{4}{6} D 2025\frac{20}{25}

Studdy Solution

STEP 1

1. We are given the ratio 2:32:3.
2. We need to determine which of the given options is equivalent to this ratio.
3. A ratio a:ba:b is equivalent to a fraction ab\frac{a}{b}.

STEP 2

1. Convert the given ratio to a fraction.
2. Simplify each option to check for equivalence.
3. Compare simplified fractions to the original ratio.

STEP 3

Convert the given ratio 2:32:3 to a fraction.
23\frac{2}{3}

STEP 4

Simplify each option to check for equivalence.
Option A: 12\frac{1}{2}
Option B: 46\frac{4}{6}
Option C: 1213\frac{12}{13}
Option D: 2025\frac{20}{25}

STEP 5

Simplify each fraction:
Option A: 12\frac{1}{2} is already in simplest form.
Option B: 46\frac{4}{6} simplifies to 23\frac{2}{3}.
Option C: 1213\frac{12}{13} is already in simplest form.
Option D: 2025\frac{20}{25} simplifies to 45\frac{4}{5}.

STEP 6

Compare the simplified fractions to 23\frac{2}{3}.
Option A: 1223\frac{1}{2} \neq \frac{2}{3}
Option B: 23=23\frac{2}{3} = \frac{2}{3}
Option C: 121323\frac{12}{13} \neq \frac{2}{3}
Option D: 4523\frac{4}{5} \neq \frac{2}{3}
The equivalent ratio to 2:32:3 is:
46 (Option B)\boxed{\frac{4}{6} \text{ (Option B)}}

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