Let’s solve each problem step by step. We’re turning improper fractions into mixed numbers.
An
improper fraction is when the top number (numerator) is bigger than the bottom number (denominator).
To turn it into a
mixed number, we divide the numerator by the denominator.
The answer will be:
- The
whole number = how many times the denominator fits completely into the numerator.
- The
remainder becomes the new numerator.
- The
denominator stays the same.
We’ll go one by one.
---
1) 13 ÷ 8
8 goes into 13 once (because 8 × 1 = 8), remainder = 13 - 8 = 5
→ Mixed number:
1 5/8
---
2) 29 ÷ 5
5 × 5 = 25, remainder = 29 - 25 = 4
→
5 4/5
---
3) 11 ÷ 7
7 × 1 = 7, remainder = 11 - 7 = 4
→
1 4/7
---
4) 36 ÷ 7
7 × 5 = 35, remainder = 36 - 35 = 1
→
5 1/7
---
5) 66 ÷ 8
8 × 8 = 64, remainder = 66 - 64 = 2 → but 2/8 can simplify to 1/4
Wait — let’s check: 66 ÷ 8 = 8 with remainder 2 → so 8 2/8 → simplify 2/8 = 1/4
→
8 1/4
But wait — maybe they want unsimplified? Let’s see other problems. Actually, in most school worksheets, you simplify if possible. But let’s double-check instructions — it just says “change to mixed number”, doesn’t say simplify. Hmm.
Looking at problem 11: 72/10 → that would be 7 2/10 → which simplifies to 7 1/5. But again, unless told to simplify, sometimes they leave it. However, standard practice is to simplify the fractional part.
Actually, looking at all problems, none of them have remainders that are obvious multiples except maybe 5 and 11. Let me do them all first without simplifying, then decide.
Wait — actually, for consistency, I think we should simplify the fraction part if possible. Because otherwise, why not write 72/10 as 7 2/10? But 2/10 reduces. So yes, simplify.
So back to #5: 66 ÷ 8 = 8 R2 → 8 2/8 = 8 1/4 → correct.
---
6) 49 ÷ 8
8 × 6 = 48, remainder = 1 →
6 1/8
---
7) 53 ÷ 10
10 × 5 = 50, remainder = 3 →
5 3/10
---
8) 37 ÷ 6
6 × 6 = 36, remainder = 1 →
6 1/6
---
9) 86 ÷ 9
9 × 9 = 81, remainder = 5 →
9 5/9
---
10) 98 ÷ 12
12 × 8 = 96, remainder = 2 → 8 2/12 → simplify 2/12 = 1/6 →
8 1/6
---
11) 72 ÷ 10
10 × 7 = 70, remainder = 2 → 7 2/10 → simplify to 7 1/5 →
7 1/5
---
12) 38 ÷ 6
6 × 6 = 36, remainder = 2 → 6 2/6 → simplify to 6 1/3 →
6 1/3
---
13) 84 ÷ 11
11 × 7 = 77, remainder = 7 →
7 7/11 (can’t simplify)
---
14) 40 ÷ 9
9 × 4 = 36, remainder = 4 →
4 4/9
---
15) 52 ÷ 6
6 × 8 = 48, remainder = 4 → 8 4/6 → simplify to 8 2/3 →
8 2/3
---
Now let’s list all answers clearly:
1) 1 5/8
2) 5 4/5
3) 1 4/7
4) 5 1/7
5) 8 1/4
6) 6 1/8
7) 5 3/10
8) 6 1/6
9) 9 5/9
10) 8 1/6
11) 7 1/5
12) 6 1/3
13) 7 7/11
14) 4 4/9
15) 8 2/3
I double-checked each division and simplification. All look correct.
Final Answer:
1) 1 5/8
2) 5 4/5
3) 1 4/7
4) 5 1/7
5) 8 1/4
6) 6 1/8
7) 5 3/10
8) 6 1/6
9) 9 5/9
10) 8 1/6
11) 7 1/5
12) 6 1/3
13) 7 7/11
14) 4 4/9
15) 8 2/3
Parent Tip: Review the logic above to help your child master the concept of mixed to improper worksheet.
