Fraction review worksheet with problems on adding, subtracting, and simplifying fractions.

Let’s go through each problem one by one. I’ll solve them step by step so you can follow along easily.

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Problem 1: What is the difference between Model 1 and Model 2? Write your answer in simplest form.

Model 1 shows a rectangle divided into 8 equal parts, with 5 shaded → that’s 5/8.
Model 2 shows a rectangle divided into 6 equal parts, with 3 shaded → that’s 3/6, which simplifies to 1/2.

Now find the difference:
5/8 - 1/2

To subtract, we need a common denominator. The least common denominator of 8 and 2 is 8.

Convert 1/2 to eighths:
1/2 = 4/8

Now subtract:
5/8 - 4/8 = 1/8

✔ Final Answer for Problem 1: 1/8

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Problem 2: What are the common factors of 12 and 20?

List all factors of 12:
1, 2, 3, 4, 6, 12

List all factors of 20:
1, 2, 4, 5, 10, 20

Common factors (numbers that appear in both lists):
1, 2, 4

✔ Final Answer for Problem 2: 1, 2, 4

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Problem 3: Caryl poured 2 1/4 cups cake flour and 2/3 cup wheat flour into a mixing bowl. What is the total amount of flour in the bowl?

We need to add:
2 1/4 + 2/3

First, convert mixed number to improper fraction:
2 1/4 = (2×4 + 1)/4 = 9/4

Now add:
9/4 + 2/3

Find common denominator — LCM of 4 and 3 is 12

Convert:
9/4 = (9×3)/(4×3) = 27/12
2/3 = (2×4)/(3×4) = 8/12

Add:
27/12 + 8/12 = 35/12

Convert back to mixed number:
35 ÷ 12 = 2 with remainder 11 → 2 11/12

✔ Final Answer for Problem 3: 2 11/12 cups

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Problem 4: The difference of 5/9 and 1/3 is...

Subtract:
5/9 - 1/3

Common denominator of 9 and 3 is 9

Convert 1/3 to ninths:
1/3 = 3/9

Now subtract:
5/9 - 3/9 = 2/9

Now look at choices:

A. closest to 0 → 2/9 ≈ 0.22 → yes, close to 0
B. closest to 1/2 → 0.5 → no
C. closest to 1 → no
D. more than 1 → no

So correct choice is A

✔ Final Answer for Problem 4: A. closest to 0

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Problem 5: Look at the problem below. What number should you use as a common denominator to add the fractions? 4/7 + 1/6

Denominators are 7 and 6.

LCM of 7 and 6: since they have no common factors, multiply them:
7 × 6 = 42

✔ Final Answer for Problem 5: 42

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Problem 6: What is the sum of 4/9 and 8/7? Answer in simplest form.

Add:
4/9 + 8/7

Common denominator of 9 and 7 is 63

Convert:
4/9 = (4×7)/(9×7) = 28/63
8/7 = (8×9)/(7×9) = 72/63

Add:
28/63 + 72/63 = 100/63

Simplify: 100 ÷ 63 = 1 with remainder 37 → 1 37/63

Check if 37/63 can be simplified — 37 is prime, doesn’t divide 63 → already simplest.

✔ Final Answer for Problem 6: 1 37/63

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Problem 7: Simplify the fraction. Use digits 0, 1, 3, 6, 9 to fill boxes.

Fraction given: 6/9

Simplify: divide numerator and denominator by 3 →
6÷3=2, 9÷3=3 → 2/3

But wait — the instruction says “Use digits 0, 1, 3, 6, 9” to fill the boxes. So maybe it’s asking to write the simplified fraction using only those digits?

2/3 uses digit 2 and 3 — but 2 is NOT in the allowed set {0,1,3,6,9}. Hmm.

Wait — perhaps the fraction shown is not 6/9? Let me re-read.

Actually, looking again — the image shows a fraction bar with two boxes on top and two on bottom, and below it says “Simplify the fraction.” And then there are five digit tiles: 0,1,3,6,9.

Probably, the original fraction is made from those digits — maybe 6/9? But 6/9 simplifies to 2/3 — and 2 isn't available.

Alternative: Maybe the fraction is 3/9? That simplifies to 1/3 — and 1 and 3 ARE in the set.

Or 6/3? That’s 2 — not a fraction.

Wait — perhaps the fraction is 9/3? That’s 3 — whole number.

Another idea: Maybe the fraction is 6/9, and we’re supposed to write the simplified version using the digits provided — but 2/3 requires digit 2, which isn’t allowed.

Unless... maybe the problem is to rearrange the digits to make a fraction that simplifies nicely?

Looking at the layout: There are two boxes above the line, two below — so likely a 2-digit over 2-digit fraction? But the digits given are single digits: 0,1,3,6,9 — and we have to pick four of them to make a fraction that simplifies.

Wait — actually, rereading: “Simplify the fraction.” and then there’s a visual of a fraction with blank numerator and denominator boxes, and below it are digit cards: 0,1,3,6,9.

Perhaps the fraction is already filled in as 6/9? But again, 6/9 = 2/3 — and 2 not available.

Maybe it’s 3/6? That simplifies to 1/2 — 2 not available.

What about 9/3? = 3 — not a fraction.

Wait — what if it’s 1/3? Already simplified.

I think there might be a misinterpretation.

Looking back at the original image description — it says: “Simplify the fraction.” and then shows a fraction bar with empty boxes, and below it are digit tiles: 0,1,3,6,9.

Perhaps the student is supposed to choose digits to create a fraction that can be simplified, and then simplify it? But the problem doesn’t specify which fraction.

Alternatively — maybe the fraction is implied to be 6/9, and we simplify to 2/3, but since 2 isn’t in the tile set, perhaps we leave it as 6/9? But that’s not simplified.

Wait — another thought: Maybe the fraction is 9/6? That simplifies to 3/2 — still has 2.

This is confusing.

Let me try this: Perhaps the fraction is 3/9, which simplifies to 1/3 — and 1 and 3 are in the set.

So numerator: 1, denominator: 3 → uses digits 1 and 3.

That works.

Or 6/9 → simplify to 2/3 — but 2 not available.

Unless the problem allows us to write the simplified fraction even if digits aren’t in the set? But the instruction says “use digits 0,1,3,6,9”.

Perhaps it’s 0/ something? Not meaningful.

Another idea: Maybe the fraction is 6/3 = 2, but again not a fraction.

Wait — what if it’s 1/6? Already simplified.

I think the most reasonable assumption is that the fraction to simplify is 6/9, and we simplify it to 2/3, but since 2 is not in the digit set, perhaps the problem expects us to recognize that 6/9 reduces to 2/3, and maybe the digit tiles are just distractors or for another part.

But that doesn’t fit.

Looking at the last problem — it’s separate.

Perhaps for this problem, we are to fill in the simplified fraction using the digits — so for 6/9 = 2/3, but 2 not available — so maybe it’s not 6/9.

Let’s consider: What fraction using digits 0,1,3,6,9 can be simplified?

For example: 3/6 = 1/2 — 2 not available.

9/3 = 3 — not fraction.

6/3 = 2 — same.

1/3 — already simplified.

3/9 = 1/3 — uses 1 and 3 — both in set.

So perhaps the fraction is 3/9, simplified to 1/3.

And we fill numerator box with 1, denominator with 3.

That makes sense.

Maybe 6/9 is intended, and we write 2/3, ignoring the digit constraint? But the problem says "use digits".

Another possibility: The fraction is 9/6, simplify to 3/2 — still 2.

I think the best bet is that the fraction is 3/9, simplified to 1/3, and we use digits 1 and 3.

So final answer: 1/3

✔ Final Answer for Problem 7: 1/3

*(Assuming the original fraction was 3/9 or similar that simplifies to 1/3 using available digits)*

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Problem 8: Solve the problem. 1 1/3 + 1 1/2 = ?

Convert to improper fractions:

1 1/3 = 4/3
1 1/2 = 3/2

Add: 4/3 + 3/2

Common denominator of 3 and 2 is 6

4/3 = 8/6
3/2 = 9/6

Add: 8/6 + 9/6 = 17/6

Convert to mixed number: 17 ÷ 6 = 2 with remainder 5 → 2 5/6

✔ Final Answer for Problem 8: 2 5/6

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Final Answers Summary:

1. 1/8
2. 1, 2, 4
3. 2 11/12
4. A
5. 42
6. 1 37/63
7. 1/3
8. 2 5/6

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Final Answer:
1. \frac{1}{8}
2. 1, 2, 4
3. 2\frac{11}{12}
4. A
5. 42
6. 1\frac{37}{63}
7. \frac{1}{3}
8. 2\frac{5}{6}