Fractions and Ratios: Partners in Proportion!

Mathematics Grades 7th Grade 3:22 Video
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Lesson Description

Explore the relationship between fractions and ratios, discovering how they represent parts of a whole and can be used to compare quantities. Learn to convert between ratio notations and fraction notations, understanding what each representation signifies.

Video Resource

Ratios as fractions | Ratios, rates, and percentages | 6th grade | Khan Academy

Khan Academy

Duration: 3:22
Watch on YouTube

Key Concepts

  • Ratio
  • Fraction
  • Proportion

Learning Objectives

  • Understand the relationship between ratios and fractions.
  • Represent ratios in fraction form.
  • Interpret fractions as ratios in context.
  • Simplify ratios and fractions.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing what ratios and fractions are separately. Ask students for examples of each and how they are used in everyday life.
  • Video Viewing (7 mins)
    Play the Khan Academy video: 'Ratios as fractions | Ratios, rates, and percentages | 6th grade | Khan Academy'. Instruct students to take notes on the different ways ratios can be represented and how they relate to fractions.
  • Guided Practice (10 mins)
    Work through examples similar to those in the video. Start with simple ratios (e.g., 3 apples to 5 bananas) and show how to write them as fractions (3/8 of the fruit are apples). Emphasize the importance of understanding what the numerator and denominator represent in the context of the problem.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing ratio problems to convert into fraction form. Include problems with different units (e.g., inches to feet, boys to girls in a class) to reinforce understanding.
  • Wrap-up and Discussion (8 mins)
    Review the key concepts learned in the lesson. Address any questions or misconceptions that students may have. Preview the next lesson on solving problems using ratios and proportions.

Interactive Exercises

  • Ratio to Fraction Conversion
    Present students with a series of ratios (e.g., 4:7, 1:3, 5:9). Have them write each ratio as a fraction, explaining what the fraction represents in each case. Use whiteboards or individual chalkboards for easy correction.
  • Real-World Ratio Scenarios
    Describe real-world scenarios involving ratios (e.g., 'In a class of 30 students, 12 are wearing glasses'). Ask students to express the ratio as a fraction and interpret its meaning (e.g., '12/30 of the students are wearing glasses').

Discussion Questions

  • How are ratios and fractions similar?
  • How are ratios and fractions different?
  • Can all ratios be written as fractions? Why or why not?
  • Why is it important to understand what the numerator and denominator represent when using a fraction to represent a ratio?

Skills Developed

  • Proportional Reasoning
  • Fraction Manipulation
  • Ratio Interpretation
  • Problem Solving

Multiple Choice Questions

Question 1:

A recipe calls for 2 cups of flour and 3 cups of sugar. What fraction of the mixture is flour?

Correct Answer: 2/5

Question 2:

Which of the following is NOT a way to represent a ratio?

Correct Answer: a - b

Question 3:

In a group of 25 students, 10 play basketball. What fraction of the students play basketball?

Correct Answer: 10/25

Question 4:

The ratio of boys to girls in a class is 3:4. What fraction of the class are boys?

Correct Answer: 3/7

Question 5:

If a store sells 5 apples for every 2 oranges, what fraction of the fruit sold are oranges?

Correct Answer: 2/7

Question 6:

A map has a scale of 1 inch = 20 miles. What fraction represents this scale?

Correct Answer: 1/20

Question 7:

In a survey, 15 out of 50 people preferred coffee. What fraction of the people preferred coffee?

Correct Answer: 15/50

Question 8:

The ratio of correct answers to total questions on a test is 9:10. What fraction of the questions were answered correctly?

Correct Answer: 9/10

Question 9:

A garden has 7 roses and 5 tulips. What fraction of the flowers are tulips?

Correct Answer: 5/12

Question 10:

If the ratio of cats to dogs in a neighborhood is 2:5, what fraction of the pets are cats?

Correct Answer: 2/7

Fill in the Blank Questions

Question 1:

A ratio of 3 apples to 7 bananas can be written as the fraction _____.

Correct Answer: 3/10

Question 2:

The fraction 2/5 represents a ratio of 2 _____ to 5 _____.

Correct Answer: to

Question 3:

If a class has 12 boys and 18 girls, the fraction of students that are girls is _____.

Correct Answer: 18/30

Question 4:

A ratio of 1 inch to 12 inches can be written as the fraction _____

Correct Answer: 1/12

Question 5:

The fraction 3/8 means that for every 3 items, there are a total of _____ items.

Correct Answer: 8

Question 6:

If a team wins 7 out of 10 games, the fraction of games won is _____.

Correct Answer: 7/10

Question 7:

A recipe uses 1 part water to 4 parts juice. The fraction of the mixture that is water is _____.

Correct Answer: 1/5

Question 8:

For a group of 50 people, if 20 like pizza, the fraction that like pizza is _____.

Correct Answer: 20/50

Question 9:

A survey shows the ratio of people who like chocolate to vanilla ice cream is 5 to 8. The fraction of the group that likes chocolate is _____.

Correct Answer: 5/13

Question 10:

The fraction representing the ratio of 4 red cars to 9 blue cars is _____.

Correct Answer: 4/13

Educational Standards

7.A.2.3:Use proportional reasoning to solve problems involving ratios. 7.N.1.2:Recognize and generate equivalent representations of rational numbers, including equivalent fractions. 7.A.2.4:Use proportional reasoning to assess the reasonableness of solutions.

Teaching Materials

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