Comparing Unlike Fractions
Compare fractions in Grade 6 math by finding a common denominator or cross-multiplying — determine which fraction is greater, lesser, or equal using equivalent fraction techniques.
Key Concepts
Property To compare fractions that do not have common denominators, rename one or both fractions so that they do have common denominators. Then, simply compare the numerators.
Examples $$ \text{Compare } \frac{2}{3} \text{ and } \frac{4}{5} \rightarrow \frac{10}{15} < \frac{12}{15}, \text{ so } \frac{2}{3} < \frac{4}{5} $$ $$ \text{Compare } \frac{3}{4} \text{ and } \frac{5}{6} \rightarrow \frac{9}{12} < \frac{10}{12}, \text{ so } \frac{3}{4} < \frac{5}{6} $$ $$ \text{Compare } \frac{1}{2} \text{ and } \frac{3}{8} \rightarrow \frac{4}{8} \frac{3}{8}, \text{ so } \frac{1}{2} \frac{3}{8} $$.
Explanation Which is bigger, $\frac{2}{3}$ of a candy bar or $\frac{4}{5}$ of one? It's tough to tell! By giving them a common denominator (like 15), you are basically cutting both bars into the same number of equal pieces. Now you can easily see who has more pieces, making the comparison a piece of cake, or in this case, a piece of candy!
Common Questions
How do you compare fractions with different denominators?
Find a common denominator for both fractions, convert them to equivalent fractions, then compare the numerators. The fraction with the larger numerator is greater.
What is cross-multiplication for comparing fractions?
Multiply the numerator of each fraction by the denominator of the other. Compare the products: 2/3 vs 3/4 → 2×4=8 and 3×3=9. Since 8 < 9, we have 2/3 < 3/4.
How can you use benchmarks like 1/2 to compare fractions?
Determine if each fraction is less than, equal to, or greater than 1/2. If one fraction is less than 1/2 and the other is greater, you can compare without finding a common denominator.
What common mistakes do students make when comparing fractions?
Students sometimes assume a larger denominator means a larger fraction (e.g., thinking 1/8 > 1/3). Remember: with the same numerator, a larger denominator means SMALLER pieces, so the fraction is smaller.