Solving Proportions

Ratio and Proportion

By Marie Lorraine Gammuac

Objectives:

​At the end of the lesson, 80% of the students will be able to:

• Know what is ratio and proportion;

• Carry out solving proportion problems; and

• Easily solve missing proportional problems.

The ratio of triangles to circles is​ 2:3.

Ratio

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Examples:

What is the ratio of the figure​ below?

As you can see, there are 36 triangles and 6 circles. Then our ratio is

36 triangles: 6 circles

or

36 : 6​

Multiple Choice

What is the ratio in the figure?

• 40 : 6

• 35 : 5

• 40 : 5

• 35 : 6

Multiple Choice

What is the ratio in the figure?

• 27 : 72

• 24 : 64

• 21 : 56

• 18 : 48

Multiple Choice

What is the ratio in the figure?

• 51 : 69

• 52 : 70

• 53 : 71

• 54 : 72

Proportion

​If two ratios can be simplified into the same ratio, then the two ratios form a proportion.

find the GCF of the ratio then divide it to the ratio

Proportion

Cross Multiplication

The simplest technique to see if there is a proportion between two ratios is by cross multiplying them.

Example:

​ 4 : 6 and 8 : 12

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Multiple Choice

$$\frac{12}{7}\ and\ \frac{36}{21}$$  

• Proportion

• Not a Proportion

Multiple Choice

$$\frac{3}{11}\ and\ \frac{17}{6}$$  

• Proportion

• Not a Proportion

Multiple Choice

$$\frac{60}{55}\ and\ \frac{7}{42}$$  

• Proportion

• Not a Proportion

What if there is a missing part of ratio in proportion?

Remember: There is a proportion between two ratios if and only if the product of the means = product of the extremes

Example:

​_ : 2 = 4 : 8

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​What is the missing number?

n : 2 = 4 : 8​

Fill in the Blank

Find n:

$$\frac{n}{6}=\frac{15}{18}$$  

Fill in the Blank

$$\frac{n}{3}=\frac{16}{24}$$  

Fill in the Blank

$$\frac{3}{5}=\frac{n}{15}$$  

Fill in the Blank

$$\frac{1}{3}=\frac{3}{n}$$  

Thank you for listening!