Compare fractions with unlike numerators and denominators

Comparing fractions with unlike numerators and denominators means determining which represents the greater quantity when the fractions refer to the same whole, using equivalent fractions, common benchmarks such as 0, 1/2, and 1, or positions on a number line. The reasoning depends on the values represented, not on comparing numerators or denominators independently, and is limited to familiar positive fractions; negative fractions, abstract rational-number comparison, and generalized cross-multiplication methods are outside this scope.

Detailed Explanation: Compare fractions with unlike numerators and denominators

To compare fractions, decide which fraction shows the greater amount of the same whole. You cannot compare only the numerators or only the denominators.

Example: Compare $\frac{3}{4}$ and $\frac{5}{8}$

Rewrite the fractions with the same denominator.

Since $4 \times 2=8$ , multiply the numerator and denominator of $\frac{3}{4}$ by $2$ :

\frac{3}{4}=\frac{3\times2}{4\times2}=\frac{6}{8}

Now compare:

\frac{6}{8} \quad \text{and} \quad \frac{5}{8}

The denominators are the same, so compare the numerators. Since $6>5$ ,

\frac{6}{8}>\frac{5}{8}

Therefore,

\boxed{\frac{3}{4}>\frac{5}{8}}

Both fractions name the same whole, and $\frac{3}{4}$ represents the greater amount.

Learn by doing: Compare fractions with unlike numerators and denominators

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Fraction Comparison - Basic - Two Changed Denominators

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