Benchmark Fractions
Benchmark fractions are familiar reference fractions — ¼, ½, ¾ — used to estimate and compare unfamiliar fractions in Grade 8 math (Yoshiwara Core Math). To compare 5/8 to benchmarks, convert: ½ = 4/8 and ¾ = 6/8. Since 4/8 < 5/8 < 6/8, the fraction 5/8 lies between ½ and ¾. This avoids computing exact decimals and builds number sense. Benchmark fractions are used in estimation, mental math, cooking, measurement, and data interpretation throughout Grade 8.
Key Concepts
Property The fractions $\frac{1}{2}$, $\frac{1}{4}$, and $\frac{3}{4}$ are called benchmark fractions because we have a good intuitive feel for their size. We can estimate other fractions by comparing them to the benchmarks. To compare a fraction to a benchmark, write the benchmark fraction with the same denominator.
Examples Is the fraction $\frac{7}{20}$ closer to $\frac{1}{4}$ or $\frac{1}{2}$? With a denominator of 20, $\frac{1}{4} = \frac{5}{20}$ and $\frac{1}{2} = \frac{10}{20}$. Since 7 is closer to 5 than to 10, $\frac{7}{20}$ is closer to $\frac{1}{4}$.
A team won 14 out of 30 games. Is this fraction, $\frac{14}{30}$, closest to $\frac{1}{4}$, $\frac{1}{2}$, or $\frac{3}{4}$? We know $\frac{1}{2}$ of 30 is 15. Since 14 is very close to 15, the fraction is closest to $\frac{1}{2}$.
Common Questions
What are benchmark fractions?
Common reference fractions — typically ¼, ½, and ¾ — used to estimate the size of other fractions.
How do you compare 5/8 to benchmarks?
½ = 4/8 and ¾ = 6/8. Since 4/8 < 5/8 < 6/8, the fraction lies between ½ and ¾.
Why use benchmarks instead of converting to decimals?
Benchmark comparisons are faster as mental math and build intuitive number sense.
Is 7/12 closer to ½ or ¾?
½ = 6/12 and ¾ = 9/12. 7/12 is 1 step from 6/12 but 2 steps from 9/12, so closer to ½.
What other fractions serve as benchmarks?
1/3 and 2/3 are also useful benchmarks, especially for dividing things into thirds.