Ratio and Rate

Ratio, Rate & Speed

Cluster 7

08.00 - 09.00 Session 1

09.00 - 09.10 Break

09.10 - 11.00 Session 2

11.00 - 12.00 Lunch Break

12.00 - 14.00 Session 3

Objectives of the courses

• Students are able to represent the simplest form of Ratio

• Students are able to use the ratio into real world problems

Multiple Choice

Which one represents the correct example of ratio?

• Ratio of the number of boys to girls in cluster 7 is 2 : 3

• Ratio of number of students in a class to chicken in a poultry farm is 1 : 100

• Both options are correct

Concept of Ratio

The ratio of two quantities must be the same kind.
Ratio is written as a : b
Ratio can also be written as  $\frac{a}{b}$  

Example of Ratio

Example 1:

There are 17 boys and 19 girls in a class.

What is the ratio of boys to girls?

The ratio of boys to girls = 17 : 19

Why do we use Ratio?

For simplification to compare similar things inside a group / place / condition.

Multiple Choice

If the ratio of boys to girls in a class is 2:3, what does it mean?

• There are more girls than boy in a class

• For every 2 boys, there are 3 girls

• Both options are correct

Multiple Choice

There are 12 lemons and 6 pears in a basket, find the ratio of number of pears to number of lemons in the basket!

• 6 : 12

• 12 : 6

Equivalent Ratio

From the previous problem, the ratio of 6 : 12 can also be written as 2 : 4 or 1 : 4.

See the explanation in the picture!

Equivalent Ratio

Remember! The fraction is also a form of ratio.
So, the fraction of  $\frac{1}{2}$  is also the same as ratio of 1 : 2.

Thus, 6 : 12 is equivalent with 2 : 4 and 1 : 2.
See the figure for work steps.

Multiple Choice

Which one of these ratios are equivalent?

•  $\frac{1}{2}=\frac{2}{4}=\frac{8}{24}$  

• $$\frac{2}{3}=\frac{4}{6}=\frac{8}{12}$$  

Multiple Choice

Which one of these ratios is equivalent?

• 3 : 5 = 9 : 15

• 4 : 5 = 8 : 20

• Both options are correct

Simplifying Ratio

• A ratio is said to be in its simplest form (a:b) when a and b have no common factors!

• Example:

  10 : 24 is not the simplest form, because 10 and 24 have common factor of 2!

• Thus, the simple ratio is 5 : 12

Simplifying Ratio

• Before, we see the example of ratio in decimals, how do we simplify ratio of fractions?

• Example: simplify ratio of $\frac{2}{3}:\ \frac{5}{6}$  !

• First, multiply both parts by 6

•  $\frac{2}{3}\times6\ :\ \frac{5}{6}\times6$  

• Result = 4 : 5

Multiple Select

Simplify the following ratio!

$$\frac{3}{5}:\frac{8}{9}$$  


Select the correct steps! (you may choose more than 1 correct steps)

• Step 1: multiply both parts by 45

• Step 2:  $$\frac{3}{5}\times45\ :\ \frac{8}{9}\times45\$$  

• Step 3:  $$27\ :\ 40$$  

Poll

How many percent do you think you understand about ratio so far?

• 80-100%

• 50-80%

• less than 50%

• I don't understand about ratio at all!

Open Ended

What makes you don't understand about the ratio?

Self Paced Exercise

Based on the polling, you will get your own exercise.

Ratio and Fractions

• In general, using ratio to compare two quantities of the same unit is equivalent to using fraction.

• Example 1 : 5:7 is equivalent to  $\frac{5}{7}$  

• Example 2: a:b is equivalent to  $\frac{5}{3}$  . This means a = 5 and b = 3.

Multiple Choice

Given that a ratio of x:9 is equivalent to 2:3.

Calculate the value of x!

• 9

• 6

• 4

• 3

Multiple Choice

Given that a ratio of 2x:5 is equivalent to 3:5.

Calculate the value of x!

• 3/2

• 2

• 1

• 1/2

Real World Problem

Ratio involving three quantities

• Ratio can also be used to make comparisons among three or more quantities.

• Example, if x = 18, y = 27 and z= 54

• Then, the ratio is, x:y:z = 18:27:54

• After simplification,

• x:y:z = 2:3:6

Multiple Choice

If x = 14, y = 30, and z = 36, the ratio of x:y:z in the simplest form is..

• 14:30:36

• 7:30:36

• 7:15:36

• 7:15:18

Ratio Involving Three Quantities

Multiple Choice

If x:y = 5:6 and y:z = 4:9, find x:y:z !

• 10:12:27

• 20:24:54

• 5:6:9

• 5:24:9

What have we learned so far?

• Forms of ratio ( using ":" and "/" signs)

• Simplification of ratio

• Real world problems

• Ratio with three quantities.

Self Exercise

Open the text book, try to solve the problem as many as you can.