This document discusses ratios, rates, and proportions. It defines ratio as a relationship between two quantities, and rate as a comparison of two quantities with different units. It provides examples of calculating ratios, rates, and using proportions to solve problems. Key examples include calculating the ratio of melons to durians in a truck, the rate of pancakes cooked per minute, and using proportions to determine the amount of flour needed if a baker uses a dozen eggs.

1. RATE AND RATIO
RAMIL C. MANLUNAS

2. At the end of the lesson:
■ Describe the concept of ratio and
proportion
■ Compare and differentiate ration from rate

3. Ratio – a relationship between two
quantities
■
𝑎
𝑏
𝑟𝑒𝑎𝑑 𝑎𝑠 a over b
■a:b read as “a is to
b”

4. There is a large truck containing 50
large melons and 60 large durians.
■ Ratio?
■ Reduced to lowest terms?

5. 10 eggs mixed with a certain amount
of flour can make 80 pancakes
■ Ratio?
■ Reduced to lowest terms?

6. Jet plane traveled 1200 km and a train
traveled 900 km in a same amount of
time
■ Ratio?
■ Reduced to lowest terms?

7. RATE – comparison of two quantities
with different units
■ Kilometers per hour (km/hr)
■ Number of feet per second (ft/sec)
■ Amount of money per hour worked (pesos/hour)
■ Volume of water per month (cubic meter/month)

8. Karen can cook 8 pancakes in 32
minutes. What is the rate?
■ 8 pancakes : 32 minutes
■
8 𝑝𝑎𝑛𝑐𝑎𝑘𝑒𝑠
32 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
𝑜𝑟
1 𝑝𝑎𝑛𝑐𝑎𝑘𝑒
4 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
𝑜𝑟
1
4
pancake per minute

9. Daddy Bud traveled 60 km in 5 hours
using his brand new car. What is the rate
(or speed)?
■ 60 kilometers in 5 hours
■
60 𝑘𝑚
5 ℎ𝑟𝑠
𝑜𝑟
12 𝑘𝑚
ℎ𝑟
(“12 kilometers per hour”)

10. A school has 1500 students with 30
classrooms. What is the rate?
■ 1500 students per 30 classrooms
■
1500 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
30 𝑐𝑙𝑎𝑠𝑠𝑟𝑜𝑜𝑚𝑠
or
50 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
1 𝑐𝑙𝑎𝑠𝑠𝑟𝑜𝑜𝑚
or
50 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
𝑐𝑙𝑎𝑠𝑠𝑟𝑜𝑜𝑚
(50 students per
classroom)

11. PROPORTION - equality between
ratios
■ 1:2 = 8:16
1
2
=
8
16
■ 3:5 = 18:30
3
5
=
18
30
■ 100:60 = 5:3
100
60
=
5
3
a : b = c : d

12. PROPORTION - equality between
ratios
■ 1:2 = 8:16
1
2
=
8
16
■ 3:5 = 18:30
3
5
=
18
30
■ 100:60 = 5:3
100
60
=
5
3
NOT PROPORTION
■ 1:2 = 9:20
1
2
=
9
20
■ 3:5 = 18:40
3
5
=
18
40
■ 100:60 = 5:3
100
60
=
5
2

13. CHECKING the proportionality of
ratios
■ 1:2 = 8:16
1
2
=
8
16
■ 3:5 = 18:30
3
5
=
18
30
■ 100:60 = 5:3
100
60
=
5
3
NOT PROPORTION
■ 1:2 = 9:20
1
2
=
9
20
■ 3:5 = 18:40
3
5
=
18
40
■ 100:60 = 5:3
100
60
=
5
2

14. Make the statement correct:
■ 1 : 3 = 6 : N
■ N : 5 = 21 : 35
■ 2 : N = 20 : 90

15. A baker uses 1 egg for every 4 cups of
flour in a certain recipe. If he or she
uses a dozen eggs, how many cups of
flour will he or she need?
■ Given: Ratio is 1 egg : 4 cups of flour
■ Find: 1 dozen eggs : x cups
■ Solution: 1 : 4 = 12 : x
means = extremes
1 (x) = (4) (12)
x = 48 cups of flour

16. John and Jay share profits of their business
partnerships 2:3.
If John received P 30 000 000.00, how much
will Jay receive?
■ Given: John : Jay = 2 : 3
P 30 000 000.00 : x = 2 : 3
■ Solution
means = extremes
(x) (2) = P 30 000 000.00 (3)
2x = P 90 000 000.00
2𝑥
2
=
𝑃 90 000 000.00
2
x = P 45 000 000.00

17. For every 2,000 jars that a company ships,
an average of 3 jars break during transit. If
the company ships 10,000 jars, how many
jars can be expected to break during
transit?
■ Given: 2000 jars : 3 jars break = 10 000 jars : x jars break
■ Solution
means = extremes
(3 ) (10 000) = 2 000 (x)
30 000 = 2 000 x
30 000
2 000
=
2 000 𝑥
2 000
15 = x
■ Therefore, when the company ships 10 000 jars, 15 jars can be expected to break
during transit

18. Exercises
■
𝟑
𝟒
=
𝟒𝟓
𝑵
■ 3:n = 15 : 20
■ 20x = 8 : 15

19. Exercises
■ 𝑨𝒍 𝒃𝒐𝒖𝒈𝒉𝒕 𝟓 𝒅𝒐𝒛𝒆𝒏𝒔 𝒐𝒇 𝒆𝒈𝒈𝒔 𝒂𝒕 𝒂 𝒄𝒐𝒔𝒕 𝒐𝒇 𝑷 𝟑𝟎𝟎. 𝑯𝒐𝒘 𝒎𝒖𝒄𝒉 𝒘𝒊𝒍𝒍 𝟏𝟓 𝒅𝒐𝒛𝒆𝒏𝒔 𝒐𝒇 𝒆𝒈𝒈𝒔 𝒄𝒐𝒔𝒕?
Given:
Solution: means = extremes

20. END