Ratio simplifying

1. Ratio and Proportion

2. Chapter # 29 : RATIO AND PROPORTION
Topic : Equivalent Rations and Simplifying Ratios
LEARNING OBJECTIVE :
• Use Knowledge of equivalence
to simplify and compare rations

3. THOUGHT FOR THE DAY
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

4. Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio
Starter
Write the ratio of green squares to blue squares.
Write each ratio in its simplest form.

5. • A ratio is a comparison of two numbers.
• Ratios can be written in three different ways:
a to b
a:b
Because a ratio is a fraction, b can not be zero
b
a
Ratios are expressed in simplest form
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio
What is a Ratio?

6. How to Use Ratios?
• The ratio of boys and girls in the class is 12 to11.
4cm
1cm
This means, for every 12 boys
you can find 11 girls to match.
• There could be just 12 boys, 11
girls.
• There could be 24 boys, 22
girls.
• There could be 120 boys, 110
girls…a huge class
What is the ratio if the
rectangle is 8cm long and
2cm wide?
Still 4 to 1, because for every
4cm, you can find 1cm to
match
• The ratio of length and width of this
rectangle
is 4 to 1.
.
How many dogs and cats do I
have? We don’t know, all we
know is if they’d start a fight,
each dog has to fight 2 cats.
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

7. Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio How to simplify ratios?
• Now I tell you I have 12 cats and 6 dogs. Can you
simplify the ratio of cats and dogs to 2 to 1?
6
12 =
6
/
6
6
/
12 =
1
2
Divide both numerator and
denominator by their
Greatest Common Factor 6.

8. Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio
A person’s arm is 80cm, he is 2m tall.
Find the ratio of the length of his arm to his total
height
m
cm
2
80

cm
cm
200
80
200
80

5
2
To compare them, we need to convert both
numbers into the same unit …either cm or m.
• Let’s try cm first!

height
arm

Once we have the
same units, we can
simplify them.
How to simplify ratios?

9. Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio
• Let’s try m now!
height
arm
m
cm
2
80

m
m
2
8
.
0

Once we have the
same units, they
simplify to 1.
20
8

5
2

To make both numbers
integers, we multiplied both
numerator and denominator by
10

10. • If the numerator and denominator do not
have the same units it may be easier to
convert to the smaller unit so we don’t
have to work with decimals…
3cm/12m = 3cm/1200cm = 1/400
2kg/15g = 2000g/15g = 400/3
5ft/70in = (5*12)in / 70 in = 60in/70in = 6/7
2g/8g = 1/4 Of course, if they are already in the same units, we
don’t have to worry about converting. Good deal
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

11. Writing & Simplifying Ratios
Your turn! Write down these ratios in the correct order and in their simplest form.
1. What is the ratio of sandwiches to muffins?
2. What is the ratio of chocolate bars to candy canes?
3. What is the ratio of tennis balls to rugby balls to soccer balls?
4:8 (HCF 2) = 1:2
10:15 (HCF 2) = 2:3
12:9:3 (HCF 3)
= 4:3:1
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

12. Task 1
Simplify these ratios.
a. 5:10:15
b. 8:10:12
c. 20:15:25
Task 2
Simplify these ratios
a. 500m:1km
b. 36 seconds:1 minute
c. 800ml:2.4l
Task 3
Ans:
a. 1:2:3
b. 4:5:6
c. 4:3:5
Ans:
a. 1:2
b. 3 : 5
c. 1 : 3
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

13. Extended Task
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio
Ans: One bag of sugar. [One bag of sugar=325g and one bag of flour=320g]

14. Plenary
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

15. Ratios in the Real World
When you’re using a concentrate of some kind to make juice or maybe mixing up
chemicals for cleaning or gardening, the instructions might say something like…
That’s a ratio!
But… get the ratio wrong and your juice or chemicals will be too strong or too weak.
The ratio really matters!
Mix up 1 part concentrate to 5 parts water.
Ratios are used all the time to represent all sorts of
things in real world situations. They’re actually all
around you, but you may not have realised that ratios
are being used.
Let’s check out some examples:
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

16. Ratios in the Real World
Here are a couple more… ratios really are used in so many different ways!
When you’re making bread, the recipe might say something like…
If you get the ratio wrong then you might end up with a loaf
that is as hard as concrete, and not soft, spongy or delicious!
Statisticians use ratios all the time to help us relate to and
understand their data.
Use 4 parts flour to 1 part water.
Here’s a headline from a 2019 news article:
Sheep outnumber New
Zealanders by just five to one
What does this mean?
Discuss with a buddy.
It means that for every 5 sheep there is 1 New Zealander. That’s a ratio of 5:1.
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

17. So Have You Got It?
Quick Quiz!
T
Q1 What is a ratio?
A ratio is a relationship or comparison between two numbers or quantities.
Q2 What does a ratio of 4:3 mean in words?
4 to 3 or 4 per 3
Q3 True or False: Ratios only compare parts to parts.
False: Ratios can also compare parts to wholes.
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

18. Q4 Give 2 examples of ratios in the real world.
Cooking, screen size, paper sizes, statistics, mixing concentrates etc.
Q5 How do you simplify a ratio?
Find the HCF of each number and divide them by it.
So Have You Got It?
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

19. SUCCESS CRITERIA
I can I am not clear
on this
I am a bit
confused
and need more
help
I can do the
tasks confiden
tly
• I can simplify ratios
when the quantities
have different units.
• I can compare ratio
when the quantities
have different units.
• I can simplify a ratio
with more than two
parts.
Lesson Outcome: Have we achieved the learning objectives?
SUCCESS CRITERIA
Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio

20. Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio
Home Assignment
Lower Secondary Mathematics Workbook 8 :
Chapter 29: Ratio
Exercise 29.1-29.2 Q1, 2, 3 and 4

21. Learning Objective: Use Knowledge of equivalence to
simplify and compare ratios.
Date:
Topic: Ratio
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