Let’s solve this step by step.
We are matching equivalent equations — meaning, we need to find pairs of fraction addition or subtraction problems that give the same result.
---
Section A: Add fractions with different denominators
To add fractions with different denominators, we first convert them to have the same denominator (usually the least common denominator), then add the numerators.
Let’s go one by one on the left side and match them to the right.
---
Left Side 1:
5/8 + 1/4
Convert 1/4 to eighths:
1/4 = 2/8
So, 5/8 + 2/8 =
7/8
Now look at the right side for an equation that also equals 7/8.
Check each:
- 1/8 + 6/8 = 7/8 →
✔ Match!
- 2/8 + 6/8 = 8/8 = 1 → no
- 5/8 + 2/8 = 7/8 → already matched in example
- 1/8 + 4/8 = 5/8 → no
- 3/8 + 2/8 = 5/8 → no
Wait — the example already matched 5/8 + 1/4 with 5/8 + 2/8. That’s correct because 1/4 = 2/8.
But now we’re solving the rest.
Actually, let’s re-read: The instruction says “Match the equivalent equations.” So we’re not calculating the sum — we’re finding which two expressions are mathematically the same after converting to common denominators.
In other words, if you rewrite both fractions in each expression to have the same denominator, do they become identical?
Example given:
5/8 + 1/4 → becomes 5/8 + 2/8 → so it matches 5/8 + 2/8 on the right.
So we do the same for others.
---
Left Side 2:
1/8 + 3/4
Convert 3/4 to eighths: 3/4 = 6/8
So this becomes: 1/8 + 6/8 → which is exactly the first option on the right:
1/8 + 6/8
✔ Match: 1/8 + 3/4 ↔ 1/8 + 6/8
---
Left Side 3:
3/8 + 1/4
1/4 = 2/8 → so 3/8 + 2/8 → which is
3/8 + 2/8 on the right.
✔ Match: 3/8 + 1/4 ↔ 3/8 + 2/8
---
Left Side 4:
1/8 + 1/2
1/2 = 4/8 → so 1/8 + 4/8 → which is
1/8 + 4/8 on the right.
✔ Match: 1/8 + 1/2 ↔ 1/8 + 4/8
---
Left Side 5:
2/8 + 3/4
3/4 = 6/8 → so 2/8 + 6/8 → which is
2/8 + 6/8 on the right.
✔ Match: 2/8 + 3/4 ↔ 2/8 + 6/8
---
Now Section B: Subtract fractions with different denominators
Same idea — convert to common denominator, then see which expressions are equivalent.
Denominator here is mostly 9 and 3. Convert thirds to ninths: 1/3 = 3/9, 2/3 = 6/9
---
Left Side 1:
7/9 - 1/3
1/3 = 3/9 → so 7/9 - 3/9 → which is
7/9 - 3/9 on the right.
✔ Match: 7/9 - 1/3 ↔ 7/9 - 3/9
---
Left Side 2:
7/9 - 2/3
2/3 = 6/9 → so 7/9 - 6/9 → which is
7/9 - 6/9 on the right.
✔ Match: 7/9 - 2/3 ↔ 7/9 - 6/9
---
Left Side 3:
8/9 - 1/3
1/3 = 3/9 → so 8/9 - 3/9 → which is
8/9 - 3/9 on the right.
✔ Match: 8/9 - 1/3 ↔ 8/9 - 3/9
---
Left Side 4:
8/9 - 2/3
2/3 = 6/9 → so 8/9 - 6/9 → which is
8/9 - 6/9 on the right.
✔ Match: 8/9 - 2/3 ↔ 8/9 - 6/9
---
All matches found!
Final Answer:
Section A Matches:
- 5/8 + 1/4 ↔ 5/8 + 2/8 (given)
- 1/8 + 3/4 ↔ 1/8 + 6/8
- 3/8 + 1/4 ↔ 3/8 + 2/8
- 1/8 + 1/2 ↔ 1/8 + 4/8
- 2/8 + 3/4 ↔ 2/8 + 6/8
Section B Matches:
- 7/9 - 1/3 ↔ 7/9 - 3/9
- 7/9 - 2/3 ↔ 7/9 - 6/9
- 8/9 - 1/3 ↔ 8/9 - 3/9
- 8/9 - 2/3 ↔ 8/9 - 6/9
Parent Tip: Review the logic above to help your child master the concept of 5th grade fraction addition worksheet.
