Learning Goal
Part of: Apply and extend previous understandings of multiplication and division to divide fractions by fractions — 1 of 1 cluster items
Interpret and compute quotients of fractions
**6.NS.A.1**: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) / (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) / (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) / (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
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6.NS.A.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) / (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) / (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) / (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
What you'll learn
- Explain what it means to divide one fraction by another using both the measurement interpretation ("how many groups of size b fit in a?") and the partitive interpretation ("what is each share when a is split into b equal parts?")
- Use visual fraction models (number line, area model) to represent and solve fraction division problems
- Compute the quotient of two fractions using the invert-and-multiply algorithm: (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc
- Justify the invert-and-multiply procedure using the relationship between multiplication and division
- Solve word problems involving division of fractions by fractions by identifying the correct interpretation, writing the division expression, computing the quotient, and interpreting the result in context
Slides
Interactive presentations perfect for visual learners • Interactive presentation
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Exercises
Practice problems to build fluency and understanding • 1 exercises