Ratio and Proportion Worksheet / Worksheet (teacher made) - Free Printable

Let's solve each of the ratio and proportion problems from the worksheet step by step.

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Problem 1:

> For every 2 blond-haired pupils, there were 4 black-haired. There were 12 blond-haired pupils. How many black-haired pupils were there?

Step-by-step Solution:

We are given a ratio:
- Blond-haired : Black-haired = 2 : 4

This simplifies to:
- 1 : 2 (since both 2 and 4 can be divided by 2)

So for every 1 blond-haired pupil, there are 2 black-haired pupils.

Now, we're told there are 12 blond-haired pupils.

Using the ratio:
- If 1 blond → 2 black
- Then 12 blond → \( 12 \times 2 = 24 \) black

✔ Answer: 24 black-haired pupils

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Problem 2:

> On a map I am using, the scale is 1cm for every 10km. If I am mapping a 8,000km journey, how many cm is it on the map?

Step-by-step Solution:

Scale: 1 cm = 10 km

We want to find how many cm represent 8,000 km.

Set up a proportion:
\[
\frac{1 \text{ cm}}{10 \text{ km}} = \frac{x \text{ cm}}{8000 \text{ km}}
\]

Cross-multiply:
\[
x = \frac{8000}{10} = 800
\]

✔ Answer: 800 cm

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Problem 3:

> In a zoo, there were 60 lemur and 50 raccoons. What is the ratio of lemurs to raccoons?

Step-by-step Solution:

Number of lemurs = 60
Number of raccoons = 50

Ratio of lemurs to raccoons = \( 60 : 50 \)

Simplify by dividing both numbers by their greatest common divisor (GCD). GCD of 60 and 50 is 10.

\[
60 ÷ 10 = 6,\quad 50 ÷ 10 = 5
\]

So, simplified ratio = \( 6 : 5 \)

✔ Answer: 6 : 5

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Problem 4:

> I have 20 pens and 25 pencils. What is the ratio of pens to pencils?

Step-by-step Solution:

Pens = 20
Pencils = 25

Ratio = \( 20 : 25 \)

Simplify by dividing both by GCD of 20 and 25, which is 5:

\[
20 ÷ 5 = 4,\quad 25 ÷ 5 = 5
\]

So, simplified ratio = \( 4 : 5 \)

✔ Answer: 4 : 5

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✔ Final Answers:

1. 24
2. 800 cm
3. 6 : 5
4. 4 : 5

Let me know if you'd like these written in fraction form or explained further!