 # Divide Fractions by Fractions (Grade 6)

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Examples, solutions, videos, and lessons to help Grade 6 students learn to 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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Common Core: 6.NS.1

### Suggested Learning Targets

• I can compute quotients of fractions divided by fractions (including mixed numbers).
• I can interpret quotients of fractions.
• I can figure out how to solve division problems with fractions in a real-world situation.
• I can solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
 Fractions Grade 3 Develop understanding of fractions as numbers. Fractions Grade 4 Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions. Understand decimal notation for fractions, and compare decimal fractions. Fractions Grade 5 Use equivalent fractions as a strategy to add and subtract fractions. Apply and extend previous understandings of multiplication and division.
Interpret and compute quotients of fractions (Common Core Standard 6.NS.1)
6.NS.1 - Division by Fraction
How to divide a whole number by a fraction using visual models?
Even though there is an algorithm to divide fractions, using tape diagrams (bar models) to illustrate the idea behind fraction division really shows why the algorithm works.
Example:
5 ÷ 2/3
Measurement Interpretation
How many groups of 2/3 are in five?
Partitive Interpretation
2/3 of what number is 5?

6.NS.1 - Division of Whole Number by Fraction Word Problem
How to solve a word problem that involves the division of a whole number by a fraction using visual models?
Example:
Benjamin has 9 cups of sugar. If this is 3/4 of the number he needs to make cake, how many cups does he need? 6.NS.1 - Division of Fraction by Whole Number Word Problem
How to solve a division of fraction by whole number word problem using visual models?
Example:
3/4 gallons of cake batter is poured equally into 2 bowls. How many gallons are in each bowl? Dividing Fractions (6.NS.1)
Rule: Dividing by a fraction is the same as multiplying by its reciprocal.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  