Math worksheet for adding fractions with instructions to simplify answers.
A worksheet titled "Factors and Fractions Worksheet #5" featuring math problems involving addition of fractions, with instructions to simplify answers to lowest form.
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Step-by-step solution for: Grade 5 Maths Resources (Factors and Fractions Printable ...
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Show Answer Key & Explanations
Step-by-step solution for: Grade 5 Maths Resources (Factors and Fractions Printable ...
Let’s solve each problem step by step. We’ll add the fractions carefully, and for Section 2, we’ll first make sure they have the same denominator before adding.
---
Section 1: Add these numbers together.
We’re just adding fractions — some are proper, some are mixed numbers. We’ll convert mixed numbers to improper fractions if needed, find common denominators when necessary, add, then simplify.
---
a) 5/7 + 4/7
Same denominator → just add numerators:
5 + 4 = 9 → 9/7
Can be written as mixed number: 1 2/7 (but since it says “simplified”, 9/7 is already simplified).
✔ Answer: 9/7
---
b) 2/3 + 11/5
Different denominators → find LCD of 3 and 5 → 15
Convert:
2/3 = (2×5)/(3×5) = 10/15
11/5 = (11×3)/(5×3) = 33/15
Add: 10/15 + 33/15 = 43/15
Simplify? 43 ÷ 15 = 2 with remainder 13 → 2 13/15
✔ Answer: 43/15 or 2 13/15
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c) 13/6 + 1/6
Same denominator → 13 + 1 = 14 → 14/6
Simplify: divide numerator and denominator by 2 → 7/3
Or as mixed number: 2 1/3
✔ Answer: 7/3 or 2 1/3
---
d) 16/3 + 5/3
Same denominator → 16 + 5 = 21 → 21/3 = 7
✔ Answer: 7
---
e) 3/4 + 7/8
LCD of 4 and 8 is 8.
3/4 = 6/8
7/8 stays
6/8 + 7/8 = 13/8 → 1 5/8
✔ Answer: 13/8 or 1 5/8
---
f) 13/3 + 5/4
LCD of 3 and 4 is 12.
13/3 = (13×4)/12 = 52/12
5/4 = (5×3)/12 = 15/12
Add: 52 + 15 = 67 → 67/12
As mixed number: 5 7/12
✔ Answer: 67/12 or 5 7/12
---
g) 19/4 + 1/12
LCD of 4 and 12 is 12.
19/4 = (19×3)/12 = 57/12
1/12 stays
57/12 + 1/12 = 58/12
Simplify: divide by 2 → 29/6
Mixed number: 4 5/6
✔ Answer: 29/6 or 4 5/6
---
h) 7/4 + 2/5
LCD of 4 and 5 is 20.
7/4 = 35/20
2/5 = 8/20
35 + 8 = 43 → 43/20
Mixed number: 2 3/20
✔ Answer: 43/20 or 2 3/20
---
Section 2: Add these numbers together. First, convert the fractions to equivalent fractions with the same denominator.
This means we must show the conversion step — even if we could do it mentally, we’ll write it out.
---
a) 2/8 + 17/8
Already same denominator → 2 + 17 = 19 → 19/8
Simplify? 19 ÷ 8 = 2 R3 → 2 3/8
✔ Answer: 19/8 or 2 3/8
---
b) 2/4 + 7/16
First, simplify 2/4 → 1/2 (optional, but let’s keep as is for now)
LCD of 4 and 16 is 16.
2/4 = (2×4)/(4×4) = 8/16
7/16 stays
8/16 + 7/16 = 15/16
✔ Answer: 15/16
---
c) 11 5/11 + 3/11
Mixed number + fraction. Convert mixed number to improper:
11 5/11 = (11×11 + 5)/11 = (121 + 5)/11 = 126/11
Now add 3/11 → 126/11 + 3/11 = 129/11
Simplify: 129 ÷ 11 = 11 R8 → 11 8/11
✔ Answer: 129/11 or 11 8/11
---
d) 6 2/5 + 2 1/2
Convert both to improper fractions.
6 2/5 = (6×5 + 2)/5 = 32/5
2 1/2 = (2×2 + 1)/2 = 5/2
LCD of 5 and 2 is 10.
32/5 = 64/10
5/2 = 25/10
64 + 25 = 89 → 89/10
Mixed number: 8 9/10
✔ Answer: 89/10 or 8 9/10
---
e) 5 2/3 + 2 7/12
Convert to improper:
5 2/3 = (5×3 + 2)/3 = 17/3
2 7/12 = (2×12 + 7)/12 = 31/12
LCD of 3 and 12 is 12.
17/3 = 68/12
31/12 stays
68 + 31 = 99 → 99/12
Simplify: divide by 3 → 33/4 → 8 1/4
✔ Answer: 33/4 or 8 1/4
---
f) 14 2/3 + 3 7/12
Convert:
14 2/3 = (14×3 + 2)/3 = 44/3
3 7/12 = (3×12 + 7)/12 = 43/12
LCD of 3 and 12 is 12.
44/3 = 176/12
43/12 stays
176 + 43 = 219 → 219/12
Simplify: divide by 3 → 73/4 → 18 1/4
✔ Answer: 73/4 or 18 1/4
---
g) 2 12/18 + 19 11/12
First, simplify 12/18 → 2/3 (divide by 6)
So 2 2/3 + 19 11/12
Convert to improper:
2 2/3 = 8/3
19 11/12 = (19×12 + 11)/12 = 239/12
LCD of 3 and 12 is 12.
8/3 = 32/12
239/12 stays
32 + 239 = 271 → 271/12
Mixed number: 22 7/12
✔ Answer: 271/12 or 22 7/12
---
h) 3 2/5 + 7 4/7
Convert:
3 2/5 = 17/5
7 4/7 = 53/7
LCD of 5 and 7 is 35.
17/5 = 119/35
53/7 = 265/35
119 + 265 = 384 → 384/35
Mixed number: 10 34/35
✔ Answer: 384/35 or 10 34/35
---
i) 2 2/4 + 9 5/6
Simplify 2/4 → 1/2 → so 2 1/2 + 9 5/6
Convert:
2 1/2 = 5/2
9 5/6 = 59/6
LCD of 2 and 6 is 6.
5/2 = 15/6
59/6 stays
15 + 59 = 74 → 74/6
Simplify: divide by 2 → 37/3 → 12 1/3
✔ Answer: 37/3 or 12 1/3
---
j) 5 5/12 + 3 5/12
Same denominator → add whole numbers and fractions separately.
Whole: 5 + 3 = 8
Fractions: 5/12 + 5/12 = 10/12 = 5/6
Total: 8 5/6
✔ Answer: 8 5/6
---
k) 4 1/3 + 4 5/12
Convert:
4 1/3 = 13/3
4 5/12 = 53/12
LCD of 3 and 12 is 12.
13/3 = 52/12
53/12 stays
52 + 53 = 105 → 105/12
Simplify: divide by 3 → 35/4 → 8 3/4
✔ Answer: 35/4 or 8 3/4
---
l) 6 1/2 + 5 2/3
Convert:
6 1/2 = 13/2
5 2/3 = 17/3
LCD of 2 and 3 is 6.
13/2 = 39/6
17/3 = 34/6
39 + 34 = 73 → 73/6
Mixed number: 12 1/6
✔ Answer: 73/6 or 12 1/6
---
m) 14 6/7 + 11 3/14
Convert:
14 6/7 = (14×7 + 6)/7 = 104/7
11 3/14 = (11×14 + 3)/14 = 157/14
LCD of 7 and 14 is 14.
104/7 = 208/14
157/14 stays
208 + 157 = 365 → 365/14
Mixed number: 26 1/14
✔ Answer: 365/14 or 26 1/14
---
n) 2 3/4 + 10 4/7
Convert:
2 3/4 = 11/4
10 4/7 = 74/7
LCD of 4 and 7 is 28.
11/4 = 77/28
74/7 = 296/28
77 + 296 = 373 → 373/28
Mixed number: 13 9/28
✔ Answer: 373/28 or 13 9/28
---
Final Answer:
1a) 9/7
1b) 43/15
1c) 7/3
1d) 7
1e) 13/8
1f) 67/12
1g) 29/6
1h) 43/20
2a) 19/8
2b) 15/16
2c) 129/11
2d) 89/10
2e) 33/4
2f) 73/4
2g) 271/12
2h) 384/35
2i) 37/3
2j) 8 5/6
2k) 35/4
2l) 73/6
2m) 365/14
2n) 373/28
---
Section 1: Add these numbers together.
We’re just adding fractions — some are proper, some are mixed numbers. We’ll convert mixed numbers to improper fractions if needed, find common denominators when necessary, add, then simplify.
---
a) 5/7 + 4/7
Same denominator → just add numerators:
5 + 4 = 9 → 9/7
Can be written as mixed number: 1 2/7 (but since it says “simplified”, 9/7 is already simplified).
✔ Answer: 9/7
---
b) 2/3 + 11/5
Different denominators → find LCD of 3 and 5 → 15
Convert:
2/3 = (2×5)/(3×5) = 10/15
11/5 = (11×3)/(5×3) = 33/15
Add: 10/15 + 33/15 = 43/15
Simplify? 43 ÷ 15 = 2 with remainder 13 → 2 13/15
✔ Answer: 43/15 or 2 13/15
---
c) 13/6 + 1/6
Same denominator → 13 + 1 = 14 → 14/6
Simplify: divide numerator and denominator by 2 → 7/3
Or as mixed number: 2 1/3
✔ Answer: 7/3 or 2 1/3
---
d) 16/3 + 5/3
Same denominator → 16 + 5 = 21 → 21/3 = 7
✔ Answer: 7
---
e) 3/4 + 7/8
LCD of 4 and 8 is 8.
3/4 = 6/8
7/8 stays
6/8 + 7/8 = 13/8 → 1 5/8
✔ Answer: 13/8 or 1 5/8
---
f) 13/3 + 5/4
LCD of 3 and 4 is 12.
13/3 = (13×4)/12 = 52/12
5/4 = (5×3)/12 = 15/12
Add: 52 + 15 = 67 → 67/12
As mixed number: 5 7/12
✔ Answer: 67/12 or 5 7/12
---
g) 19/4 + 1/12
LCD of 4 and 12 is 12.
19/4 = (19×3)/12 = 57/12
1/12 stays
57/12 + 1/12 = 58/12
Simplify: divide by 2 → 29/6
Mixed number: 4 5/6
✔ Answer: 29/6 or 4 5/6
---
h) 7/4 + 2/5
LCD of 4 and 5 is 20.
7/4 = 35/20
2/5 = 8/20
35 + 8 = 43 → 43/20
Mixed number: 2 3/20
✔ Answer: 43/20 or 2 3/20
---
Section 2: Add these numbers together. First, convert the fractions to equivalent fractions with the same denominator.
This means we must show the conversion step — even if we could do it mentally, we’ll write it out.
---
a) 2/8 + 17/8
Already same denominator → 2 + 17 = 19 → 19/8
Simplify? 19 ÷ 8 = 2 R3 → 2 3/8
✔ Answer: 19/8 or 2 3/8
---
b) 2/4 + 7/16
First, simplify 2/4 → 1/2 (optional, but let’s keep as is for now)
LCD of 4 and 16 is 16.
2/4 = (2×4)/(4×4) = 8/16
7/16 stays
8/16 + 7/16 = 15/16
✔ Answer: 15/16
---
c) 11 5/11 + 3/11
Mixed number + fraction. Convert mixed number to improper:
11 5/11 = (11×11 + 5)/11 = (121 + 5)/11 = 126/11
Now add 3/11 → 126/11 + 3/11 = 129/11
Simplify: 129 ÷ 11 = 11 R8 → 11 8/11
✔ Answer: 129/11 or 11 8/11
---
d) 6 2/5 + 2 1/2
Convert both to improper fractions.
6 2/5 = (6×5 + 2)/5 = 32/5
2 1/2 = (2×2 + 1)/2 = 5/2
LCD of 5 and 2 is 10.
32/5 = 64/10
5/2 = 25/10
64 + 25 = 89 → 89/10
Mixed number: 8 9/10
✔ Answer: 89/10 or 8 9/10
---
e) 5 2/3 + 2 7/12
Convert to improper:
5 2/3 = (5×3 + 2)/3 = 17/3
2 7/12 = (2×12 + 7)/12 = 31/12
LCD of 3 and 12 is 12.
17/3 = 68/12
31/12 stays
68 + 31 = 99 → 99/12
Simplify: divide by 3 → 33/4 → 8 1/4
✔ Answer: 33/4 or 8 1/4
---
f) 14 2/3 + 3 7/12
Convert:
14 2/3 = (14×3 + 2)/3 = 44/3
3 7/12 = (3×12 + 7)/12 = 43/12
LCD of 3 and 12 is 12.
44/3 = 176/12
43/12 stays
176 + 43 = 219 → 219/12
Simplify: divide by 3 → 73/4 → 18 1/4
✔ Answer: 73/4 or 18 1/4
---
g) 2 12/18 + 19 11/12
First, simplify 12/18 → 2/3 (divide by 6)
So 2 2/3 + 19 11/12
Convert to improper:
2 2/3 = 8/3
19 11/12 = (19×12 + 11)/12 = 239/12
LCD of 3 and 12 is 12.
8/3 = 32/12
239/12 stays
32 + 239 = 271 → 271/12
Mixed number: 22 7/12
✔ Answer: 271/12 or 22 7/12
---
h) 3 2/5 + 7 4/7
Convert:
3 2/5 = 17/5
7 4/7 = 53/7
LCD of 5 and 7 is 35.
17/5 = 119/35
53/7 = 265/35
119 + 265 = 384 → 384/35
Mixed number: 10 34/35
✔ Answer: 384/35 or 10 34/35
---
i) 2 2/4 + 9 5/6
Simplify 2/4 → 1/2 → so 2 1/2 + 9 5/6
Convert:
2 1/2 = 5/2
9 5/6 = 59/6
LCD of 2 and 6 is 6.
5/2 = 15/6
59/6 stays
15 + 59 = 74 → 74/6
Simplify: divide by 2 → 37/3 → 12 1/3
✔ Answer: 37/3 or 12 1/3
---
j) 5 5/12 + 3 5/12
Same denominator → add whole numbers and fractions separately.
Whole: 5 + 3 = 8
Fractions: 5/12 + 5/12 = 10/12 = 5/6
Total: 8 5/6
✔ Answer: 8 5/6
---
k) 4 1/3 + 4 5/12
Convert:
4 1/3 = 13/3
4 5/12 = 53/12
LCD of 3 and 12 is 12.
13/3 = 52/12
53/12 stays
52 + 53 = 105 → 105/12
Simplify: divide by 3 → 35/4 → 8 3/4
✔ Answer: 35/4 or 8 3/4
---
l) 6 1/2 + 5 2/3
Convert:
6 1/2 = 13/2
5 2/3 = 17/3
LCD of 2 and 3 is 6.
13/2 = 39/6
17/3 = 34/6
39 + 34 = 73 → 73/6
Mixed number: 12 1/6
✔ Answer: 73/6 or 12 1/6
---
m) 14 6/7 + 11 3/14
Convert:
14 6/7 = (14×7 + 6)/7 = 104/7
11 3/14 = (11×14 + 3)/14 = 157/14
LCD of 7 and 14 is 14.
104/7 = 208/14
157/14 stays
208 + 157 = 365 → 365/14
Mixed number: 26 1/14
✔ Answer: 365/14 or 26 1/14
---
n) 2 3/4 + 10 4/7
Convert:
2 3/4 = 11/4
10 4/7 = 74/7
LCD of 4 and 7 is 28.
11/4 = 77/28
74/7 = 296/28
77 + 296 = 373 → 373/28
Mixed number: 13 9/28
✔ Answer: 373/28 or 13 9/28
---
Final Answer:
1a) 9/7
1b) 43/15
1c) 7/3
1d) 7
1e) 13/8
1f) 67/12
1g) 29/6
1h) 43/20
2a) 19/8
2b) 15/16
2c) 129/11
2d) 89/10
2e) 33/4
2f) 73/4
2g) 271/12
2h) 384/35
2i) 37/3
2j) 8 5/6
2k) 35/4
2l) 73/6
2m) 365/14
2n) 373/28
Parent Tip: Review the logic above to help your child master the concept of fractions grade 5 worksheet.
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