Operations with Fractions MODULE 4 - School Webmasters
Operations with Fractions
? ESSENTIAL QUESTION
How can you use operations with fractions to solve real-world problems?
4 MODULE
LESSON 4.1
Applying GCF and LCM to Fraction Operations
COMMON CORE
6.NS.4
LESSON 4.2
Dividing Fractions
COMMON CORE
6.NS.1
LESSON 4.3
Dividing Mixed Numbers
COMMON CORE
6.NS.1
LESSON 4.4
Solving Multistep Problems with Fractions and Mixed Numbers
COMMON CORE
6.NS.1
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Real-World Video
To find your average rate of speed, divide the distance
you traveled by the time you traveled. If you ride in a
twahxiicahnmd dayrivmee_12anmyioleuinwe_14rehoinuhr,eyaovuyr
rate was traffic.
2
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Go digital with your write-in student
edition, accessible on any device.
Math On the Spot
Scan with your smart phone to jump directly to the online edition, video tutor, and more.
Animated Math
Interactively explore key concepts to see how math works.
Personal Math Trainer
Get immediate feedback and help as
you work through practice sets.
75
Are YOU Ready?
Complete these exercises to review skills you will need for this module.
Write an Improper Fraction as a Mixed Number
Personal Math Trainer
Online Assessment and my. Intervention
EXAMPLE
_1_3 5
=
_ 5 5
+
_ 5 5
+
_ 3 5
=
1
+
1
+
_ 3 5
=
2
+
_ 3 5
= 2_35
Write as a sum using names for one plus a proper fraction. Write each name for one as one.
Add the ones.
Write the mixed number.
Write each improper fraction as a mixed number.
1.
_ 9 4
2.
_ 8 3
5.
_1_7 5
6.
_1_5 8
Multiplication Facts
3.
_2_3 6
7.
_3_3 10
4.
_1_1 2
8.
_2_9 12
EXAMPLE 7 ? 6 = 7 ? 6 = 42
Use a related fact you know. 6 ? 6 = 36 Think: 7 ? 6 = (6 ? 6) + 6
= 36 + 6 = 42
Multiply.
9. 6 ? 5
10. 8 ? 9
13. 9 ? 7
14. 8 ? 6
Division Facts
EXAMPLE 63 ? 7 =
11. 10 ? 11 15. 9 ? 11
12. 7 ? 8 16. 11 ? 12
Think: 7 times what number equals 63? 7 ? 9 = 63
Divide. 17. 35 ? 7 21. 36 ? 4
63 ? 7 = 9
So, 63 ? 7 = 9.
18. 56 ? 8 22. 45 ? 9
19. 28 ? 7 23. 72 ? 8
20. 48 ? 8 24. 40 ? 5
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76 Unit 2
Reading Start-Up
Visualize Vocabulary
Use the words to complete the triangle. Write the review word that fits the description in each section of the triangle.
part of a whole
top number of a fraction
Vocabulary
Review Words
area (?rea) denominator
(denominador) fraction (fracci?n)
greatest common factor (GCF) (m?ximo com?n divisor (MCD)) least common multiple (LCM) (m?nimo com?n m?ltiplo (m.c.m.)) length (longitud) numerator (numerador) product (producto) width (ancho)
bottom number of a fraction
Understand Vocabulary
In each grouping, select the choice that is described by the given vocabulary word.
1. reciprocals
A 1:15
B
_ 3 4
?
_ 1 6
2. mixed number
A
_ 1 3
-
_ 1 5
B 3_12
3. order of operations
A 5-3+2=0
B 5-3+2=4
Preview Words
mixed number (n?mero mixto)
order of operations (orden de las operaciones)
reciprocals (rec?procos)
C
_ 3 5
and
_ 5 3
C -5
C 5-3+2=6
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Active Reading
Layered Book Before beginning the module, create a layered book to help you learn the concepts in this module. Label each flap with lesson titles. As you study each lesson, write important ideas, such as vocabulary and processes, under the appropriate flap. Refer to your finished layered book as you work on exercises from this module.
Module 4 77
MODULE 4
Unpacking the Standards
Understanding the standards and the vocabulary terms in the standards will help you know exactly what you are expected to learn in this module.
6.NS.1 COMMON CORE
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.
Key Vocabulary
quotient (cociente) The result when one number is divided by another.
fraction (fracci?n) A number in the form _ba, where b 0.
What It Means to You
You will learn how to divide two fractions. You will also understand the relationship between multiplication and division.
UNPACKING EXAMPLE 6.NS.1
sZoauchpa. Hryoiws mmaakninyg1_12v-ecgueptasberlevisnoguspw. Tilhl tehreecreipceipme amkaekse6?_34 cups of
6_34 ? 1_12
=
_2_7 4
?
_ 3 2
=
_2_7 4
?
_ 2 3
=
_ 9 2
= 4_21
The recipe will make 4_12 servings.
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6 . N S . 4 COMMON CORE
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1?100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
Visit my. to see all the Common Core Standards unpacked.
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78 Unit 2
What It Means to You
You can use greatest common factors and least common multiples to simplify answers when you calculate with fractions.
UNPACKING EXAMPLE 6.NS.4
Add. Write the answer in simplest form.
_ 1 3
+
_ 1 6
=
_ 2 6
+
_ 1 6
=
_2_+__1_ 6
Use the LCM of 3 and 6 as a common denominator.
Add the numerators.
=
_ 3 6
=
_3_?__3 6 ? 3
Simplify by dividing by the GCF. The GCF of 3 and 6 is 3.
=
_ 1 2
Write the answer in simplest form.
4.1 LESSON Applying GCF and LCM to Fraction Operations
COMMON CORE
6.NS.4
Find the greatest common factor...and the least common multiple of two whole numbers...
? ESSENTIAL QUESTION How do you use the GCF and LCM when adding, subtracting, and multiplying fractions?
EXPLORE ACTIVITY
COMMON CORE
6.NS.4
Multiplying Fractions
To multiply two fractions you first multiply the numerators and then multiply the denominators.
__n_u_m__er_a_to_r_?__n_u_m_e_r_a_to_r__ denominator ? denominator
=
_n_u_m__e_ra_t_o_r_ denominator
The resulting product needs to be written in simplest form. Below are two methods for making sure that the product of two fractions is in simplest form.
EXAMPLE 1 Multiply. Write the product in simplest form.
A
_ 1 3
?
_ 3 5
Write the problem as a single fraction. Multiply numerators. Multiply denominators.
_ 1 3
?
_ 3 5
=
_1_?__3_ 3? 5
=
_____
Simplify by dividing by the GCF.
The GCF of 3 and 15 is
.
3 ? _________
15 ?
Math On the Spot
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Write the answer in simplest form.
_____
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B
_ 6 7
?
_ 2 3
Write the problem as a single fraction.
_ 6 7
?
_ 2 3
=
________
The 6 in the numerator and the 3 in the
denominator have a GCF of
. Divide
6 and 3 by 3 and write the quotients in the boxes.
6__?__2_ 7 ? 3
Use the quotients from the previous steps to multiply the numerators and denominators.
? 2
________ =
7 ?
Lesson 4.1 79
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