6-1 dividing fractions and whole resources...
TRANSCRIPT
4 � 4 4 � 2
4 � 1 4 � 12
Digital Resources
Launch
Find each quotient. Use a picture to represent each problem.
Reflect Which problem resulted in a quotient greater than 4? Why do you think that
happened?
Dividing Fractions and Whole Numbers
6-1
CCSS: 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.
MP1, MP4SAMPLE SOLUTIONS ARE SHOWN BELOW.
Sample: The problem 4 � 12 is equal to 8, so the quotient is
greater than 4. If you are dividing 4 by parts equal to 1, you will
get 4 parts. If you are dividing 4 by parts less than 1, then you
will get more than 4 parts.
0 1 2 3 4
4 ÷ 4 = 1 4 ÷ 2 = 2
0 1 2 3 4
4 ÷ 1 = 4
0 1 2 3 4 0 1 2 3 4
4 ÷ = 812
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Topic 6 133 Lesson 6-1
0 123
Got It?
When you divide a fraction by a whole number greater than one, how does the
quotient compare to the fraction? Explain your reasoning.
Part 1 Got It (2 of 2)
What division equation does this number line model show?
Part 1 Got It (1 of 2)
23 � 2 � 1
3
The quotient is less than the fraction. Dividing the fraction by a nonzero whole number is like dividing nonzero whole numbers. The quotient is less than the dividend.
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Topic 6 134 Lesson 6-1
0 321
Got It?
When you divide a nonzero whole number by a proper fraction, how does the
quotient compare to the whole number? Explain your reasoning.
A factory’s pipe-cutting machine cuts pieces of pipe to be threaded. The standard
length of pipe used for cutting is 8 feet. How many 23 ft long pieces of pipe can be
cut from a standard length of pipe?
Part 2 Got It (2 of 2)
What division equation does this number line model show?
Part 2 Got It (1 of 2)
Part 3 Got It
3 � 34 � 4
The quotient is greater than the whole number. Each equal segment is less than 1, so the number of equal segments is always greater than the number of whole number segments.
12
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Topic 6 135 Lesson 6-1
Close and Check
1. Use the number line to model 45 � 2.
Then write the solution.
0 1
2. Circle the division equation modeled by
the number line.
0 1 2 3 4
A. 3 �14
B. 12 �13
C. 4 �13
3. A fabric store donates 15 yards of
fabric for a community quilt project.
Each piece of fabric measures 58 yard.
How many 58-yard pieces of fabric is
the store donating?
4. Reasoning Will the quotient of a
proper fraction divided by a whole
number ever result in a whole
number? Explain.
5. Writing Explain why the first
expression can be rewritten as the
second expression.
5 �23 5 �
32
Focus QuestionHow does the relationship between multiplication and division help you to divide
fractions and whole numbers?
MP2, MP7
Sample: Multiplication and division have an inverse relationship.
Dividing is the same as multiplying by the reciprocal of the
divisor.
No. When a fraction is divided
by a whole number, the
quotient represents the value
of each lesser fractional part
of the original fraction.
Write 5 � 23 as 2
3
5 . Multiplying
by 32
32 results in a denominator
of 1. Then the numerators
can be multiplied. 5 � 3
2 5 � 32 5 � 3
223
5 23 � 3
21� � �
SAMPLE SOLUTIONS ARE SHOWN BELOW.
25
24
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Topic 6 136 Lesson 6-1