You're absolutely right to focus on the hint! Since all these fractions have the
same numerator, we can compare them just by looking at their
denominators.
Here's the key rule to remember:
>
When two fractions have the same numerator, the fraction with the *larger* denominator is *smaller*.
Think of it like this: If you have the same number of slices (the numerator), but you cut the whole into more pieces (a larger denominator), each individual slice is smaller.
So, for any two fractions `a/b` and `a/c` where `a` is the same:
- If `b < c`, then `a/b > a/c`
- If `b > c`, then `a/b < a/c`
- If `b = c`, then `a/b = a/c`
Let's solve each problem using this rule:
---
1) `1/2 ○ 1/3`
- Numerator is 1 for both.
- Denominator 2 vs. 3. Since 2 < 3, `1/2` is *larger* than `1/3`.
-
Answer: `>`
2) `5/9 ○ 5/6`
- Numerator is 5 for both.
- Denominator 9 vs. 6. Since 9 > 6, `5/9` is *smaller* than `5/6`.
-
Answer: `<`
3) `7/9 ○ 7/2`
- Numerator is 7 for both.
- Denominator 9 vs. 2. Since 9 > 2, `7/9` is *smaller* than `7/2`.
-
Answer: `<`
4) `4/5 ○ 4/5`
- Both fractions are identical.
-
Answer: `=`
5) `2/3 ○ 2/8`
- Numerator is 2 for both.
- Denominator 3 vs. 8. Since 3 < 8, `2/3` is *larger* than `2/8`.
-
Answer: `>`
6) `6/8 ○ 6/9`
- Numerator is 6 for both.
- Denominator 8 vs. 9. Since 8 < 9, `6/8` is *larger* than `6/9`.
-
Answer: `>`
7) `9/10 ○ 9/10`
- Both fractions are identical.
-
Answer: `=`
8) `1/9 ○ 1/2`
- Numerator is 1 for both.
- Denominator 9 vs. 2. Since 9 > 2, `1/9` is *smaller* than `1/2`.
-
Answer: `<`
9) `4/5 ○ 4/7`
- Numerator is 4 for both.
- Denominator 5 vs. 7. Since 5 < 7, `4/5` is *larger* than `4/7`.
-
Answer: `>`
10) `1/7 ○ 1/10`
- Numerator is 1 for both.
- Denominator 7 vs. 10. Since 7 < 10, `1/7` is *larger* than `1/10`.
-
Answer: `>`
---
✔ Final Answers:
1) `>`
2) `<`
3) `<`
4) `=`
5) `>`
6) `>`
7) `=`
8) `<`
9) `>`
10) `>`
Parent Tip: Review the logic above to help your child master the concept of comparing fractions with like denominators worksheet.
