I'll solve this problem by comparing the fractions as instructed and explaining the solution.
First, I need to understand what's being asked. The task is to compare pairs of fractions using the symbols: greater than (>), less than (<), and equal to (=).
Let me go through each pair one by one:
1. 3/4 vs 2/4: Since both have the same denominator (4), I can compare the numerators directly. 3 > 2, so 3/4 > 2/4 ✓
2. 1/2 vs 2/4: These are equivalent fractions. 1/2 = 2/4 because if you multiply both numerator and denominator of 1/2 by 2, you get 2/4. So 1/2 = 2/4 ✓
3. 2/3 vs 1/3: Same denominator, so compare numerators. 2 > 1, so 2/3 > 1/3 ✓
4. 4/5 vs 3/5: Same denominator, compare numerators. 4 > 3, so 4/5 > 3/5 ✓
5. 2/8 vs 4/8: Same denominator, compare numerators. 2 < 4, so 2/8 < 4/8 ✓
6. 2/5 vs 1/5: Same denominator, compare numerators. 2 > 1, so 2/5 > 1/5 ✓
7. 1/3 vs 1/3: Identical fractions, so they are equal. 1/3 = 1/3 ✓
8. 3/5 vs 2/5: Same denominator, compare numerators. 3 > 2, so 3/5 > 2/5 ✓
9. 2/4 vs 3/4: Same denominator, compare numerators. 2 < 3, so 2/4 < 3/4 ✓
10. 4/7 vs 6/7: Same denominator, compare numerators. 4 < 6, so 4/7 < 6/7 ✓
11. 5/9 vs 3/9: Same denominator, compare numerators. 5 > 3, so 5/9 > 3/9 ✓
12. 3/6 vs 4/6: Same denominator, compare numerators. 3 < 4, so 3/6 < 4/6 ✓
All the comparisons in the answer key are correct. The general rule for comparing fractions with the same denominator is to compare the numerators - the fraction with the larger numerator is the larger fraction. For equivalent fractions like 1/2 and 2/4, we can simplify or find a common denominator to verify they represent the same value.
Parent Tip: Review the logic above to help your child master the concept of fractions greater than less than.
