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
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?
-- Standard 6.NS.A.1
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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?
-- Standard 6.NS.A.1
What you'll learn
- Interpret a fraction division problem as either *measurement* division (how many groups of the divisor fit in the dividend) or *partitive* division (size of one group when the dividend is split equally), and identify which interpretation a word problem calls for.
- Use a visual fraction model -- number line, bar model, or area model -- to represent and find the quotient of two fractions.
- Use the relationship between multiplication and division -- *(a/b) / (c/d) = q* if and only if *q x (c/d) = a/b* -- to verify and explain a fraction quotient.
- Compute *(a/b) / (c/d) = (a/b) x (d/c) = ad/bc*, recognizing the rule as a consequence of multiplying by the reciprocal of the divisor.
- Solve word problems involving division of fractions by fractions, including the three contexts named by the standard (sharing equally, counting servings, finding a missing dimension).
- Recognize that when the divisor is between 0 and 1, the quotient is *larger* than the dividend -- and explain why using the measurement interpretation.
Slides
Interactive presentations perfect for visual learners • 2 slide decks
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Task-sets
Learning resource • 1 task-sets