Simplify Fractions Teacher Notes
Objective
Write fractions in simplest form.
Use these worksheets if students have trouble
• writing mixed numbers as improper fractions
• multiplying fractions
Vocabulary
• greatest common factor (GCF)
• simplest form
Getting Started
Write several fractions on the board, some in simplest form and some that need to be simplified.
Call on students to determine whether each fraction is in simplest form or not.
Lesson Information
Remind students that a fraction is in simplest form when the numerator and denominator of the
fraction have no other common factor than 1.
Math Challenge
Memory Game Have students write 10 pairs of fractions on index cards. Each pair will be a
fraction and its equivalent in simplest form. Two students can shuffle their cards together and
lay them facedown on the desk to play a memory game. One student chooses 2 cards. If they
are equal, he or she wins the cards. If they are not equal, the cards are placed facedown where
they were. The game is over when all the cards are gone. The student with the most cards wins.
Differentiated Instruction
Logical Learners Have students work backward to check the prime factorization. Give students
the following problem.
Which shows the prime factorization of 30?
A 3 × 10
B2×3×5
C 2 × 15
D1×5×6
Before students make their final choices, remind them that prime factorization fits two criteria:
1. It must include only prime numbers.
2. The factors must produce the correct product.
Give students similar exercises to practice.
Linguistic Learners Encourage students to summarize and write the steps for simplifying
fractions clearly and concisely in their notes. Have students work in small groups to present
concise summaries to the class. Make sure students include the following points.
Simplify a Fraction
Method 1
1. Find a common factor of the numerator and denominator.
2. Divide both the numerator and denominator by the common factor.
3. Repeat this process until there are no more common factors.
4. The fraction is in simplest form when no more common factors exist.
Method 2
1. Find the GCF of the numerator and denominator.
2. Divide the numerator and the denominator by the GCF.
Interpersonal / Auditory Learners Give student groups a fraction to simplify. Then assign
each group either the method of shading in equivalent fractions, dividing by the GCF, or using
prime factorization. Ask student groups to present their methods to the rest of the class.
Encourage those sitting to ask questions and interact with the presenters.
Assess
Step 1 Write a fraction on the board. Model how to write it in simplest form. Repeat with other
fractions, using different methods.
Step 2 Give each student three fractions. Ask them to use the three methods taught in class to
simply the fractions. They can work in pairs.
Step 3 Have students discuss their results with their partners. Have them check each other’s
work and give a new practice problem.
Step 4 Have students work alone. Tell students to write a paragraph about how they would
12
simplify 27. Ask them to include each step as well as the answer.
NAME ___________________________________________________________________ DATE _______________
Lesson
Vocabulary
and
5-6 Vocabulary
English
Language and
Development
NAME
SimplifyEnglish
FractionsLanguage
DATE
Development
Activate Prior Knowledge
Answer.
List the names of ten friends or family members. Out of the people you
listed, what fraction of them has a dog as a pet? Write your answer in simplest form.
Definition Review
Match each term with its definition.
A. any whole number greater than 1 with
exactly two factors, 1 and itself
greatest common factor
Example: GCF of 6 and 9 is 3
B. a fraction in which the numerator and the
denominator have no common factor
greater than 1
prime number
Example: 5 (factors are 1 and 5)
C. a number greater than 1 with more than
two factors
composite number
Example: 8 (factors are 1, 2, 4, 8)
D. the largest number that divides evenly into
two or more numbers
Application
Complete the graphic organizer.
Show the Prime Factorization for each
number.
Find the Greatest Common Factor for
each set of numbers.
20
20 and 75
35
35 and 42
42
42 and 20
75
75 and 42
1A116
Simplify
Fractions
Lesson
5-6
Math Triumphs
Copyright © Macmillan/McGraw-Hill, • Glencoe, a division of The McGraw-Hill Companies, Inc.
simplest form
2 = __
1
Example: __
4 2
NAME ___________________________________________________________________ DATE _______________
Lesson
NAME
DATE
Skills Practice
Skills Practice
5-6
Simplify Fractions
Write each fraction in simplest form.
1
4 in simplest form. Use models to shade an equivalent area and
Write __
6
name the simplified fraction.
=
2
4=
__
6
9
Write ___ in simplest form. Solve by finding the greatest common factor.
12
9
Factors of 9:
12
Chapter 5
Factors of 12:
Copyright © Macmillan/McGraw-Hill, • Glencoe, a division of The McGraw-Hill Companies, Inc.
Write each fraction in simplest form. Use prime factorization.
3
12
___
5
27
___
7
12
___
24
81
28
4
8
___
6
10
___
8
22
___
32
45
55
Write each fraction in simplest form. Divide by the greatest common factor.
9
9
___
11
18
___
13
5
___
15
24
25
Math Triumphs
10
6
___
12
50
____
14
18
___
14
100
27
Simplify
2
LessonFractions
5-6 A117
NAME ___________________________________________________________________ DATE _______________
NAME
DATE
Problem-Solving Practice
Lesson
5-6 Fractions
Simplify
Problem-Solving Practice
Solve.
1
During the month of April, it rained on 8 days. What is the
fraction of days it rained in April in simplest form? (Hint: There are
30 days in April.)
2
Laurie is making two bracelets using heart-shaped and
triangle-shaped beads. She wants to use an equal number of beads
on each bracelet, with no beads left over. What is the greatest
number of each shape she can use on both bracelets?
3
BOOKS
RAIN
BRACELETS
Hector divided the books he read last year into four categories.
In simplest form, what fraction of the books are mystery books?
Copyright © Macmillan/McGraw-Hill, • Glencoe, a division of The McGraw-Hill Companies, Inc.
Book Categories
Category
Number
Mystery
8
Science Fiction
12
History
4
Biography
4
4
A baseball pitcher threw a total of 75 pitches in a
ballgame. Forty of those pitches were strikes. In simplest form, what
fraction of the pitches were strikes?
5
The school orchestra contains 32 musicians. There are 10
musicians in the brass section. In simplest form, what fraction of the
orchestra is the brass section?
6
A math test has a total of 100 questions. Darla got 84
questions correct. A science test has 25 questions. Darla got the
same fraction of questions correct on the science test as she did on
the math test. How many questions did Darla answer correctly on
the science test?
BASEBALL
MUSIC
TESTS
3A118
Simplify
Fractions
Lesson
5-6
Math Triumphs
NAME ___________________________________________________________________ DATE _______________
NAME
DATE
Homework Practice
Lesson
Homework
5-6
Simplify
Fractions Practice
Write each fraction in simplest form. Use models. Shade an
equivalent area and name the simplified fraction.
1
5
___
=
2
10
9
___
=
12
=
=
Write each fraction in simplest form. Use the GCF.
5
3 ___
4
50
12
___
70
6
36
18
___
Chapter 5
5
8
___
42
Copyright © Macmillan/McGraw-Hill, • Glencoe, a division of The McGraw-Hill Companies, Inc.
Write each fraction in simplest form. Use prime factorization.
15
20
7 ____
8 ___
100
30
9
54
___
81
10
8
___
44
Solve.
11
PHOTOGRAPHS Millie took 36 pictures using her digital camera. She
deleted 8 pictures. In simplest form, what fraction of the pictures
did Millie keep?
12
SURVEY A supermarket surveyed 100 people about their favorite
brand of orange juice. Thirty-five people said Sunshine State orange
juice is their favorite brand. In simplest terms, what fraction of the
people surveyed did not say Sunshine State orange juice was their
favorite brand?
Write the vocabulary word that completes each sentence.
13
A
number is any whole number greater than 1
with exactly two factors, 1 and itself.
14
A
than two factors.
Math Triumphs
number is a number greater than 1 with more
Simplify
Lesson Fractions
5-6 A1194
Simplify Fractions Answers
Vocabulary and English Language Development
1. Answers will vary.
Definition Review
B, D, A, C
Application
Skills Practice
2
1. 3
2. Factors of 9: 1, 3, 9
Factors of 12: 1, 2, 3, 4, 6, 12
9
9 3 3
12 = 12 ÷ 3 = 4
1
3. 2
1
4. 4
1
5. 3
2
6. 9
3
7. 7
2
8. 5
3
9. 5
3
10. 7
3
11. 4
1
12. 2
1
13. 5
2
14. 3
Problem-Solving Practice
4
1. 15 days
2. 9
2
3. 7 books
8
4. 15 pitches
5
5. 16 orchestra
6. 21 questions
Homework Practice
1
1. 2
3
2. 4
1
3. 10
2
4. 9
6
5. 35
3
6. 7
3
7. 20
2
8. 3
2
9. 3
2
10. 11
7
11. 9
13
12. 20
13. prime
14. composite