It looks like you've uploaded a worksheet titled
"Ratio and Proportion" with several problems. Since I can't view images directly, I’ll help you solve the problems based on the text you provided. Let's go through each problem step by step.
---
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:
- The ratio of
blond-haired : black-haired = 2 : 4
- Simplify the ratio: 2:4 = 1:2
- This means for every 1 blond-haired pupil, there are 2 black-haired pupils.
- But we're told there are
12 blond-haired pupils.
- So, if 1 part → 12 blond-haired, then 2 parts → ? black-haired
We can set up a proportion:
$$
\frac{1}{2} = \frac{12}{x}
$$
Cross-multiply:
$$
1 \cdot x = 2 \cdot 12 \Rightarrow x = 24
$$
✔ Answer: There were
24 black-haired pupils.
---
Problem 2:
> On a map using the scale 1 cm for every 10 km, if I am mapping a 8,000 km journey, how many cm is it on the map?
Step-by-step solution:
- Scale: 1 cm = 10 km
- So, to find how many cm represent 8,000 km:
$$
\frac{8,000 \text{ km}}{10 \text{ km/cm}} = 800 \text{ cm}
$$
✔ Answer: 800 cm on the map.
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Problem 3:
> In a zoo, there were 60 lemurs and 50 raccoons. What is the ratio of lemurs to raccoons?
Step-by-step solution:
- Lemurs : Raccoons = 60 : 50
- Simplify the ratio by dividing both numbers by their GCF (which is 10):
$$
60 ÷ 10 = 6,\quad 50 ÷ 10 = 5
$$
So, the simplified ratio is
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 : Pencils = 20 : 25
- Divide both by GCF (5):
$$
20 ÷ 5 = 4,\quad 25 ÷ 5 = 5
$$
So, the simplified ratio is
4:5
✔ Answer: 4:5
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✔ Final Answers:
1.
24 black-haired pupils
2.
800 cm on the map
3.
6:5 (lemurs to raccoons)
4.
4:5 (pens to pencils)
Let me know if you'd like help with the other side of the worksheet or any additional explanation!
Parent Tip: Review the logic above to help your child master the concept of easy ratio and proportion worksheet.
