Explanation:
We need to compare each fraction with the given decimal and write the correct symbol:
<,
>, or
=.
To do this, convert the fraction to a decimal (by dividing numerator by denominator), then compare.
Let’s go one by one:
1) $\frac{7}{8} = 0.875$ → compare with 0.825 → 0.875 > 0.825 →
>
2) $\frac{4}{6} = \frac{2}{3} \approx 0.666\overline{6}$ → compare with 0.667 → 0.666... < 0.667 →
<
3) $\frac{5}{6} \approx 0.8333$ → compare with 0.708 → 0.833 > 0.708 →
>
4) $\frac{2}{3} \approx 0.666\overline{6}$ → compare with 0.667 → same as #2 →
<
5) $\frac{2}{4} = 0.5$ → compare with 0.4 → 0.5 > 0.4 →
>
6) $\frac{1}{2} = 0.5$ → compare with 0.5 → equal →
=
7) $\frac{1}{2} = 0.5$ → compare with 0.6 → 0.5 < 0.6 →
<
8) $\frac{4}{6} = \frac{2}{3} \approx 0.6667$ → compare with 0.717 → 0.6667 < 0.717 →
<
9) $\frac{4}{5} = 0.8$ → compare with 0.65 → 0.8 > 0.65 →
>
10) $\frac{2}{3} \approx 0.6667$ → compare with 0.667 → again, 0.6667 < 0.667 →
<
11) $\frac{1}{2} = 0.5$ → compare with 0.625 → 0.5 < 0.625 →
<
12) $\frac{1}{8} = 0.125$ → compare with 0.1 → 0.125 > 0.1 →
>
13) $\frac{5}{8} = 0.625$ → compare with 0.625 → equal →
=
14) $\frac{4}{5} = 0.8$ → compare with 0.95 → 0.8 < 0.95 →
<
15) $\frac{3}{4} = 0.75$ → compare with 0.875 → 0.75 < 0.875 →
<
16) $\frac{3}{4} = 0.75$ → compare with 0.625 → 0.75 > 0.625 →
>
17) $\frac{2}{5} = 0.4$ → compare with 0.4 → equal →
=
18) $\frac{6}{8} = \frac{3}{4} = 0.75$ → compare with 0.825 → 0.75 < 0.825 →
<
19) $\frac{2}{3} \approx 0.6667$ → compare with 0.592 → 0.6667 > 0.592 →
>
20) $\frac{2}{3} \approx 0.6667$ → compare with 0.692 → 0.6667 < 0.692 →
<
Let me double-check tricky ones:
- #2: 4/6 = 0.666..., and 0.667 is slightly bigger →
< ✔
- #4: same as #2 →
< ✔
- #10: same as #2 & #4 →
< ✔
- #12: 1/8 = 0.125 > 0.1 →
> ✔
- #17: 2/5 = 0.4 exactly →
= ✔
- #19: 2/3 ≈ 0.6667 > 0.592 →
> ✔
- #20: 0.6667 < 0.692 →
< ✔
All look correct.
Final Answer:
1) >
2) <
3) >
4) <
5) >
6) =
7) <
8) <
9) >
10) <
11) <
12) >
13) =
14) <
15) <
16) >
17) =
18) <
19) >
20) <
Parent Tip: Review the logic above to help your child master the concept of worksheet on converting fractions to decimals.