Problem Overview:
The task involves comparing
unlike fractions using benchmarks. The benchmark here is
1, and we need to use the symbols `>`, `<`, or `=` to compare each pair of fractions.
Approach:
1.
Understand the Benchmark (1):
- A fraction is greater than 1 if its numerator is larger than its denominator.
- A fraction is less than 1 if its numerator is smaller than its denominator.
- A fraction is equal to 1 if its numerator equals its denominator.
2.
Compare Each Pair:
- For each pair of fractions, determine whether each fraction is greater than, less than, or equal to 1.
- Use this information to compare the two fractions in the pair.
3.
Use Symbols:
- Use `>` if the first fraction is greater than the second.
- Use `<` if the first fraction is less than the second.
- Use `=` if the two fractions are equal.
Solution:
#### Left Column:
1.
$\frac{5}{7} \quad ? \quad \frac{5}{3}$
- $\frac{5}{7} < 1$ because $5 < 7$.
- $\frac{5}{3} > 1$ because $5 > 3$.
- Therefore, $\frac{5}{7} < \frac{5}{3}$.
2.
$\frac{3}{2} \quad ? \quad \frac{1}{3}$
- $\frac{3}{2} > 1$ because $3 > 2$.
- $\frac{1}{3} < 1$ because $1 < 3$.
- Therefore, $\frac{3}{2} > \frac{1}{3}$.
3.
$\frac{9}{7} \quad ? \quad \frac{3}{5}$
- $\frac{9}{7} > 1$ because $9 > 7$.
- $\frac{3}{5} < 1$ because $3 < 5$.
- Therefore, $\frac{9}{7} > \frac{3}{5}$.
4.
$\frac{6}{5} \quad ? \quad \frac{6}{9}$
- $\frac{6}{5} > 1$ because $6 > 5$.
- $\frac{6}{9} < 1$ because $6 < 9$.
- Therefore, $\frac{6}{5} > \frac{6}{9}$.
5.
$\frac{8}{7} \quad ? \quad \frac{1}{6}$
- $\frac{8}{7} > 1$ because $8 > 7$.
- $\frac{1}{6} < 1$ because $1 < 6$.
- Therefore, $\frac{8}{7} > \frac{1}{6}$.
#### Right Column:
1.
$\frac{1}{4} \quad ? \quad \frac{6}{2}$
- $\frac{1}{4} < 1$ because $1 < 4$.
- $\frac{6}{2} = 3 > 1$ because $6 > 2$.
- Therefore, $\frac{1}{4} < \frac{6}{2}$.
2.
$\frac{9}{8} \quad ? \quad \frac{3}{7}$
- $\frac{9}{8} > 1$ because $9 > 8$.
- $\frac{3}{7} < 1$ because $3 < 7$.
- Therefore, $\frac{9}{8} > \frac{3}{7}$.
3.
$\frac{5}{15} \quad ? \quad \frac{1}{3}$
- $\frac{5}{15} = \frac{1}{3}$ (simplify by dividing numerator and denominator by 5).
- Therefore, $\frac{5}{15} = \frac{1}{3}$.
4.
$\frac{24}{6} \quad ? \quad \frac{28}{7}$
- $\frac{24}{6} = 4 > 1$.
- $\frac{28}{7} = 4 > 1$.
- Therefore, $\frac{24}{6} = \frac{28}{7}$.
5.
$\frac{10}{12} \quad ? \quad \frac{11}{10}$
- $\frac{10}{12} < 1$ because $10 < 12$.
- $\frac{11}{10} > 1$ because $11 > 10$.
- Therefore, $\frac{10}{12} < \frac{11}{10}$.
Final Answer:
\[
\boxed{
\begin{array}{cc}
\frac{5}{7} < \frac{5}{3} & \frac{1}{4} < \frac{6}{2} \\
\frac{3}{2} > \frac{1}{3} & \frac{9}{8} > \frac{3}{7} \\
\frac{9}{7} > \frac{3}{5} & \frac{5}{15} = \frac{1}{3} \\
\frac{6}{5} > \frac{6}{9} & \frac{24}{6} = \frac{28}{7} \\
\frac{8}{7} > \frac{1}{6} & \frac{10}{12} < \frac{11}{10} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of comparing fractions using benchmarks worksheet.
