Fractions, decimals and percentages word problems | KS3 | Teachit - Free Printable

Let's solve each of these fractions, decimals, and percentages word problems step by step.

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1. Amal and Seema are planning a party...

> Seema has hired a giant bubble machine which includes $ 3 \frac{1}{2} $ bottles of bubble mixture. The party is a huge success and Amal only needed to put $ 3 \frac{1}{4} $ bottles into the machine. How many bottles of bubble mixture are left?

Step 1: Convert mixed numbers to improper fractions.

- $ 3 \frac{1}{2} = \frac{7}{2} $
- $ 3 \frac{1}{4} = \frac{13}{4} $

Step 2: Subtract the amount used from the total.

We need:
$$
\frac{7}{2} - \frac{13}{4}
$$

Convert $ \frac{7}{2} $ to fourths:
$$
\frac{7}{2} = \frac{14}{4}
$$

Now subtract:
$$
\frac{14}{4} - \frac{13}{4} = \frac{1}{4}
$$

✔ Answer: $ \boxed{\frac{1}{4}} $ bottle of bubble mixture is left.

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2. Patrick bakes 8 different cakes...

> He slices each cake into 7 pieces and takes out 2 slices from each cake for friends and family. When all the remaining slices are added together, how many cakes does he have to sell?

Step 1: Each cake has 7 slices. He takes 2 slices from each cake → so he keeps $ 7 - 2 = 5 $ slices per cake.

Step 2: He has 8 cakes, so total slices left:
$$
8 \times 5 = 40 \text{ slices}
$$

But the question asks: "How many cakes does he have to sell?"

Since each cake is sliced into 7 pieces, and he’s selling the leftover slices, we need to determine how many whole cakes' worth of slices he has.

But he’s not selling whole cakes — he’s selling individual slices. However, the question says “how many cakes does he have to sell?” — this might mean how many full cakes’ worth of slices remain.

So:

Total leftover slices = 40
Each cake = 7 slices
So number of "cakes worth" = $ \frac{40}{7} \approx 5.71 $

But since you can’t sell a fraction of a cake as a cake, maybe the question means: how many cakes' worth of slices are available to sell?

Alternatively, perhaps it's asking: how many cakes' worth of slices are left? So answer in terms of number of cakes.

But let's re-read: *"When all the remaining slices are added together how many cakes does he have to sell?"*

It likely means: how many whole cakes’ worth of slices are there to sell? But since he's selling slices, and not necessarily whole cakes, perhaps it's just asking: what is the total number of slices available for sale?

But the question says "how many cakes does he have to sell?"

Wait — maybe the key is that he sells whole cakes, but he only has slices left.

But he already took 2 slices from each cake, so each cake still has 5 slices left. He can't sell partial cakes unless he combines them.

But the problem says: *"When all the remaining slices are added together..."* — so he's combining them.

So now, he has 40 slices total.

He wants to sell whole cakes, but he only has slices. So if he's selling whole cakes, then he can’t sell any unless he reassembles them.

But the problem probably implies that he sells the slices as part of cake portions, and we’re to find how many whole cakes’ worth of slices are left.

But again, the question says: *“how many cakes does he have to sell?”* — possibly meaning how many full cakes can be made from the leftover slices?

But he can’t make new cakes — he already baked them.

Wait — perhaps the interpretation is: he has 8 cakes, each with 5 slices left. He will sell these slices, and each cake sold corresponds to 7 slices. But he doesn’t have complete cakes anymore.

So maybe the question is asking: how many whole cakes (in terms of value) can be sold from the leftover slices?

But that seems odd.

Alternative interpretation: He has 8 cakes, each with 5 slices left. So he can sell these 8 cakes, but only 5 slices per cake.

But the question says: *"when all the remaining slices are added together, how many cakes does he have to sell?"*

This is ambiguous.

But here’s a better interpretation: He originally had 8 cakes. From each, he took 2 slices for himself/family, so each cake has 5 slices left. He can now sell the remaining slices. But the question is: how many cakes' worth of slices are left?

So total slices: $ 8 \times 5 = 40 $

Each cake = 7 slices → $ \frac{40}{7} \approx 5.71 $ cakes

But since he can’t sell a fraction of a cake, maybe the answer is 5 full cakes?

But the question says “how many cakes does he have to sell?” — not “how many full cakes?”

Perhaps it’s asking: how many cakes' worth of slices are available for sale? So the answer is $ \frac{40}{7} $ cakes.

But let’s check standard interpretations.

Actually, he doesn’t have whole cakes anymore, so he can’t sell whole cakes. But the problem may mean: if he were to sell the slices as parts of cakes, how many cakes’ worth are there?

So:

Total slices left = $ 8 \times 5 = 40 $

Each cake has 7 slices → $ \frac{40}{7} = 5 \frac{5}{7} $ cakes

So he has $ 5 \frac{5}{7} $ cakes' worth of slices.

But the question says: “how many cakes does he have to sell?”

That suggests he’s selling whole cakes, but he doesn’t have any whole cakes left.

Unless he recombines the slices into full cakes.

But 40 slices ÷ 7 = 5 full cakes (using 35 slices), with 5 slices left over.

So he can make 5 full cakes to sell.

But again, the problem says “when all the remaining slices are added together” — so he combines them.

So the best interpretation is: he has 40 slices, which is equivalent to $ \frac{40}{7} $ cakes.

But since the question asks “how many cakes does he have to sell”, and he’s selling the slices, perhaps it's asking for how many full cakes' worth of slices are available.

But the most logical answer is:

> He has 40 slices, which is $ \frac{40}{7} $ cakes.

But if we must give a number of cakes, and he can only sell whole cakes, then he can only sell 5 whole cakes (from 35 slices), leaving 5 slices.

But the problem doesn’t say he’s reassembling them.

Wait — let's read carefully:

> "When all the remaining slices are added together how many cakes does he have to sell?"

Ah! The key phrase: "when all the remaining slices are added together" — so he’s combining them.

Then, how many cakes does he have to sell?

Possibly: he has enough slices to make 5 full cakes and 5 extra slices, so he can sell 5 full cakes.

But again, it's unclear.

Alternatively, perhaps the question means: how many cakes’ worth of slices are left?

In that case:
Total slices = $ 8 \times 5 = 40 $
Each cake = 7 slices → $ \frac{40}{7} = 5 \frac{5}{7} $ cakes

✔ Answer: $ \boxed{5 \frac{5}{7}} $ cakes worth of slices.

But since the question says “how many cakes”, and not “how many cakes’ worth”, it's ambiguous.

But given the context, likely they want the total number of cakes’ worth.

So:
$$
\frac{40}{7} = \boxed{5 \frac{5}{7}} \text{ cakes}
$$

But let’s see if another interpretation works.

Wait — maybe “how many cakes does he have to sell?” means: how many of the original 8 cakes are still available to sell?

But he took 2 slices from each cake — so each cake still exists, but partially eaten.

So he can still sell all 8 cakes, but only 5 slices per cake.

But that doesn’t make sense — he can’t sell a cake that’s been partially eaten.

So more likely: he has 8 cakes, each with 5 slices left, so he can sell each of those 8 cakes, but only 5 slices per cake.

But the question says: “when all the remaining slices are added together” — so he’s pooling them.

So now he has 40 slices, and he’s selling them as portions.

But the question is: “how many cakes does he have to sell?”

This is poorly worded.

But in many similar problems, this means: how many whole cakes’ worth of slices are left?

So:

Total slices = $ 8 \times 5 = 40 $
Each cake = 7 slices → $ \frac{40}{7} = 5 \frac{5}{7} $ cakes

✔ Answer: $ \boxed{5 \frac{5}{7}} $ cakes

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3. Diana buys 5 pizzas and shares the pizzas equally between 10 people. What fraction of a whole pizza does each person get?

Total pizzas = 5
Number of people = 10

Each person gets:
$$
\frac{5}{10} = \frac{1}{2}
$$

✔ Answer: $ \boxed{\frac{1}{2}} $ of a pizza

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4. Fran has $ \frac{1}{4} $ a bottle of lemonade and divides it equally between 5 cups. What fraction of a whole bottle is in each cup?

She has $ \frac{1}{4} $ bottle, divided into 5 equal parts.

So each cup gets:
$$
\frac{1}{4} \div 5 = \frac{1}{4} \times \frac{1}{5} = \frac{1}{20}
$$

✔ Answer: $ \boxed{\frac{1}{20}} $ of a whole bottle

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5. Water collects at 0.6 litres per minute. How many litres after 15 minutes? After an hour?

Rate = 0.6 L/min

After 15 minutes:
$$
0.6 \times 15 = 9 \text{ litres}
$$

After 1 hour = 60 minutes:
$$
0.6 \times 60 = 36 \text{ litres}
$$

✔ Answers:
- After 15 minutes: $ \boxed{9} $ litres
- After 1 hour: $ \boxed{36} $ litres

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6. A bar of chocolate is divided into 24 squares. If I eat 0.25 of the bar, how many squares are left?

Total squares = 24
I eat 0.25 of the bar

0.25 = $ \frac{1}{4} $

So I eat:
$$
\frac{1}{4} \times 24 = 6 \text{ squares}
$$

Squares left:
$$
24 - 6 = 18
$$

✔ Answer: $ \boxed{18} $ squares

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✔ Final Answers Summary:

1. $ \boxed{\frac{1}{4}} $ bottle left
2. $ \boxed{5 \frac{5}{7}} $ cakes' worth of slices (or $ \frac{40}{7} $)
3. $ \boxed{\frac{1}{2}} $ of a pizza
4. $ \boxed{\frac{1}{20}} $ of a bottle
5. After 15 min: $ \boxed{9} $ L; After 1 hour: $ \boxed{36} $ L
6. $ \boxed{18} $ squares left

Let me know if you'd like explanations in simpler language or visual representations!