Using Ratio Notation

Using Ratio Notation

By: Ja'Markis McCutchin

Main Objective:

• How can ratios be written mathematically?

Lesson Goals:

• Write ratios mathematically

• Recognize the relationship between the quantities

• Determine the order of the quantities in a ratio

• Write ratios in three ways: a to b, a/b, a:b

Vocabulary:

• Compare: to explain or show the similarities or differences between items or ideas

• Fraction: a ratio of two numbers a/b, where b is not zero

• Quantity: an amount of something

• Ratio: an expression that compares two or more numbers

Section 1: Writing a Ratio Symbolically

Section 1 of 8

Writing a Ratio Symbolically

• Mr. Gomez has 24 students in his class. Compare Mr. Gomez to his class

• Using the word "to": 1 teacher to 24 students, 1 to 24

• Using a colon in place of the word "to": 1:24

• Ratios can describe part-to-part relationships

Writing Ratios

• Ms. Chong has 28 students in her math class. She has 16 boys and 12 girls

• Ratios can describe part-to-part relationships

• Ratio of boys to girls: 16 to 12, 16:12, 16/12

• Ratios can describe part-to-part relationships

• Ratio of boys to Students: 16 to 28, 16:28, 16/28

Multiple Choice

Mr. Ahmed has 31 students in his class. There are 14 boys and 17 girls.

The ratio ____ describes the part-to-whole relationship for boys.

• 14:17

• 31:14

• 14:1

• 14:31

Multiple Choice

Mr. Ahmed has 31 students in his class. There are 14 boys and 17 girls.

The ratio____ describes the part-to-whole relationship for girls.

• 17:1

• 17:14

• 31:17

• 17:31

Section 2: Missing Information

Section 2 of 8

Missing Information

• A bowl of fruit contains only apples and oranges. There are 15 pieces of fruit in all. There are 4 apples.

• What is the ratio of apples to fruit: 4/15, 4:15, 4 to 15

• What is the ratio of oranges to fruit: 15-4=11, 11/15, 11:15, 11 to 15

• What is the ratio of apples to oranges: 4/11, 4:11, 4 to 11.

Multiple Select

A fruit basket contains only apples and bananas. If there are 8 apples and 13 bananas, what is the ratio of bananas to fruit? Select all that apply.

• 13:8

• 13:21

• 8/13

• 21 to 13

• 13/21

Section 3: Fractions vs. Ratios

Section 3 out of 8

Fractions vs. Ratios

• A ratio is an expression that compares two or more quantities

• A fraction is an expression that compares a part to a whole quantity

• Ratios that are fractions: Blue to whole: 3/8, Orange to whole: 5/8

• Ratios that are NOT fractions: Blue to orange: 3/5, Orange to blue: 5/3

• The top two in "Ratios that are NOT fractions" would be incorrect; The correct term is 3 to 5, and 5 to 3.

Part to Whole Relationship

• Using the word to: 1 to 2

• Using a colon: 1:2 

• Using a fraction: 1/2

• You can use all the same methods to find a ratio of an given ratio

  
  

Multiple Choice

Ben has 26 cousins. Sixteen of the cousins are female. What fraction of the cousins are male?

Step 1: Decide what comparison is being represented. You know the comparison is part-to-whole because the question is asking for a fraction to compare the number of male cousins to the total number of cousins.

Step 2: Write the correct fraction.

Which fraction represents this comparison?

• $\frac{16}{26}$

• $\frac{16}{10}$

• $\frac{26}{16}$

• $\frac{10}{26}$

Section 4: Choosing Fractions and Ratios

Section 4 of 8

Choosing Fractions and Ratios

• A class of 25 students includes 12 boys. Does the ratio of girls to students represent a fraction? Does the ratio of boys to girls represent a fraction? How do you know?

• 1: Yes, the ratio of girls to total students represents a fraction because fractions always compare part-to-whole.

• 2: No, the ratio of boys to girls does not represent a fraction.

• 3: Ratios that compare part-to-part are not represented by fractions.

Section 5: Summary

Section 5 out of 8

Lesson Goals

• Our goals for this lesson were: Write ratios mathematically; Recognize the relationship between the quantities; Determine the order of the quantities in a ratio; and Write ratios in three ways: a to b,a/b, a:b

• Ratios can be written using the word to, a colon, or a fraction bar. They can be used to compare parts and wholes

Key Concepts

• Ratios can be written in three ways-using the word to, a colon or a fraction bar.

• The order of numbers in a ratio should match the order of words.

• Ratios can describe part-to-part and part-to whole relationships

• Not all ratios are fractions

• A family of 7 includes 3 boys and 4 girls: 3 to 4, 3:4, and 3/4 are Part to Part 3/7 is part to whole