Improper fractions and mixed numbers - Fraction and Decimal ... - Free Printable

Let’s solve each problem one by one. We’ll take our time, think carefully, and make sure we get the right answer — especially since we need to give answers as fractions or mixed numbers, not decimals.

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Problem 1:
Four Maths Rats shared seven Twinkle Chocolate Bars between them. How many bars did they have each? No remainders, please. Give your answer as a fraction.

→ Total chocolate bars = 7
→ Number of rats = 4
→ Each rat gets: 7 ÷ 4 = 7/4

That’s already a fraction. We can leave it like that (or write as mixed number 1¾, but question says “fraction”, so 7/4 is fine).

✔ Answer for #1: 7/4

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Problem 2:
Seven chickens refreshed themselves with four litres of lemonade. They had the same amount each. How much did they have each?

→ Total lemonade = 4 litres
→ Number of chickens = 7
→ Each chicken gets: 4 ÷ 7 = 4/7

✔ Answer for #2: 4/7

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Problem 3:
A bus travelled eight miles in three hours. What was its average speed? Give your answer as a mixed number.

→ Speed = distance ÷ time = 8 ÷ 3
→ 8 ÷ 3 = 2 with remainder 2 → so 2 and 2/3

✔ Answer for #3: 2 2/3

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Problem 4:
Car factory produces seventy cars in six hours. How many is that each hour? Give your answer as a mixed number.

→ Cars per hour = 70 ÷ 6
→ Let’s divide: 6 × 11 = 66, remainder 4 → so 11 and 4/6

But simplify 4/6 → divide top and bottom by 2 → 2/3

So final answer: 11 2/3

✔ Answer for #4: 11 2/3

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Problem 5:
An oil tank is filled with 200 litres of oil in 30 seconds. How many litres of oil per second goes into the tank? Give your answer as a mixed number.

→ Litres per second = 200 ÷ 30
→ Simplify first: both divisible by 10 → 20 ÷ 3
→ 20 ÷ 3 = 6 with remainder 2 → 6 and 2/3

✔ Answer for #5: 6 2/3

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Problem 6:
Two machines made 100 tonnes of sugar in eight hours. What was the average number of tonnes of sugar made by each machine in one hour? Careful now!

This is tricky — let’s break it down.

Total sugar = 100 tonnes
Total time = 8 hours
Number of machines = 2

We want: tonnes per machine per hour.

First, find how much sugar BOTH machines make together in ONE hour:

→ 100 tonnes ÷ 8 hours = 12.5 tonnes per hour (for both machines)

Now, split that between 2 machines:

→ 12.5 ÷ 2 = 6.25 tonnes per machine per hour

BUT — we must give answer as a mixed number, NOT decimal.

So convert 6.25 to fraction:

6.25 = 6 + 0.25 = 6 + 1/4 = 6 1/4

Alternatively, do all in fractions from start:

100 ÷ 8 = 100/8 = 25/2 (simplified by dividing numerator and denominator by 4)

Then divide by 2 machines: (25/2) ÷ 2 = 25/4

25 ÷ 4 = 6 with remainder 1 → 6 1/4

✔ Answer for #6: 6 1/4

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Problem 7:
Mrs Dintre’s family has the following number of catkins on each day of the week. What was the average number of catkins per day?

Days: Mon=4, Tue=9, Wed=3, Thu=8, Fri=1, Sat=4, Sun=6

Step 1: Add up all catkins:

4 + 9 = 13
13 + 3 = 16
16 + 8 = 24
24 + 1 = 25
25 + 4 = 29
29 + 6 = 35 total catkins

Step 2: Divide by number of days = 7

→ 35 ÷ 7 = 5

That’s a whole number — which is also a fraction (5/1), but since it’s exact, we can just write 5.

The question doesn’t specify format here, but since others asked for fractions/mixed numbers, and this is a whole number, 5 is acceptable.

✔ Answer for #7: 5

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Final Answers:

1. 7/4
2. 4/7
3. 2 2/3
4. 11 2/3
5. 6 2/3
6. 6 1/4
7. 5

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Final Answer:
1. 7/4
2. 4/7
3. 2 2/3
4. 11 2/3
5. 6 2/3
6. 6 1/4
7. 5