macmillanmh.com Name: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. D A B C Simplest Form Among the equivalent fractions 2 _ 3 , 4 _ 6 , and 8 _ 12 , the fraction 2 _ 3 is in simplest form because its numerator and denominator have no common factor other than 1. Fractions in Simplest Form 1 _ 2 2 _ 3 3 _ 4 3 _ 7 5 _ 8 Fractions NOT in Simplest Form 2 _ 4 4 _ 6 8 _ 10 8 _ 12 16 _ 24 Main Idea I will write a fraction in simplest form. Review Vocabulary factor New Vocabulary simplest form greatest common factor 286 Chapter 6 Relate Decimals and Fractions To change a fraction into its simplest form, you can divide both the numerator and the denominator by the greatest common factor. A greatest common factor is the greatest of the common factors of two or more numbers. Simplest Form QUIZ There are 12 questions on a quiz. Esteban got 8 out of 12 or 8 _ 12 of the questions correct. Two fractions equivalent to 8 _ 12 are 2 _ 3 and 4 _ 6 . Write 8 _ 12 in simplest form. Step 1 Find the common factors of 8 and 12. Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12 Common factors: 1, 2 and 4 Step 2 Divide by the greatest common factor, 4. 8 ÷ 4 _ 12 ÷ 4 = 2 _ 3 So, 8 _ 12 in simplest form is 2 _ 3 . ÷ 4 The numbers 2 and 3 have no common factor other than 1. 6-1 PART Fractions Multi-Part Lesson
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macmillanmh.com
C13-085A-105711.aibe
Blueprint (handwritten)
Name:1.
2.3.
4.5.
6.
7.8.
9.10.
11.12.
DA B C
Simplest FormAmong the equivalent fractions 2 _ 3 , 4 _ 6 , and 8 _ 12 , the fraction 2 _ 3 is in simplest form because its numerator and denominator have no common factor other than 1.
Fractions in Simplest Form
1 _ 2 2 _ 3 3 _ 4 3 _ 7 5 _ 8
Fractions NOT in Simplest Form
2 _ 4 4 _ 6 8 _ 10 8 _ 12 16 _ 24
Main IdeaI will write a fraction in simplest form.
Review Vocabularyfactor
New Vocabulary simplest form
greatest common factor
286 Chapter 6 Relate Decimals and Fractions
To change a fraction into its simplest form, you can divide both the numerator and the denominator by the greatest common factor. A greatest common factor is the greatest of the common factors of two or more numbers.
Simplest Form
QUIZ There are 12 questions on a quiz. Esteban got 8 out of 12 or 8 _
12 of the
questions correct. Two fractionsequivalent to 8 _
12 are 2 _ 3 and 4 _
6 .
Write 8 _ 12
in simplest form.
Step 1 Find the common factors of 8 and 12.
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Common factors: 1, 2 and 4
Step 2 Divide by the greatest common factor, 4.
8 ÷ 4 _ 12 ÷ 4 = 2 _ 3
So, 8 _ 12 in simplest form is 2 _ 3 .
÷ 4_ 4
The numbers 2 and 3 have no common factor other than 1.
6-1PART
FractionsMulti-Part Lesson
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To write a fraction in simplest form, you can also divide by common factors.
ANIMALS Koala bears sleep up to 18 hours each day. What part of a day do koalas sleep? Write the fraction in simplest form.
Step 1 Write a fraction.
18 _ 24 hours sleep each day total hours in a day
Step 2 Divide by common factors.
18 _ 24 = 18 ÷ 2 _ 24 ÷ 2 = 9 _ 12
9 _ 12 = 9 ÷ 3 _ 12 ÷ 3 = 3 _ 4
So, 18 _ 24 simplifies to 3 _ 4 . Koalas sleep up to 3 _ 4 of a day.
A common factor of 18 and 24 is 2.
A common factor of 9 and 12 is 3.
One Way Divide the numerator and denominator by the greatest common factor.
Another Way Divide the numerator and denominator by common factors until the only common factor is 1.
Simplest Form
Write each fraction in simplest form. If it is in simplest form, write simplest form. See Example 1 (p. 286)
1. 2 _ 4 1 _ 2 2. 6 _ 10 3 _
5 3. 5 _ 6 simplest form 4. 18 _ 30 3 _
5
5. Daniela read for 24 minutes. What fraction of an hour did she read? Write as a fraction in simplest form. See Example 2 (p. 287)
6. How do you know that 4 _ 5 is in simplest form?4
Lesson 6-1 Fractions 287
Divide until the
numerator and the
denominator have no
common factor other
than 1.
÷ 2_÷ 2
3_÷
2 _ 5
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29. OPEN ENDED Write three fractions that are in simplest form.
30. WHICH ONE DOESN’T BELONG? Identify the fraction that does not belong with the other three. Explain your reasoning.
2 _ 3
6 _ 15
1 _ 2 11 _ 12
31. The simplest form of 6 _ 15 is 2 _ 5 . How can you use multiplication to show that they name the same number?
Write each fraction in simplest form. If it is in simplest form, write simplest form. See Example 1 (p. 286)
7. 2 _ 10 1 _ 5 8. 3 _ 12 1 _
4 9. 7 _ 20 10. 6 _ 9 2 _
3 11. 4 _ 16 1 _
4
12. 10 _ 15 2 _ 3 13. 18 _ 27 2 _
3 14. 24 _ 40 3 _
5 15. 32 _ 42 16 _
21 16. 42 _ 56 3 _
4
Measurement What part of one day is each amount of time?Write as a fraction in simplest form. See Example 2 (p. 287)
17. 9 hours 3 _ 8 18. 16 hours 2 _
3 19. 20 hours 5 _
Algebra Find the value of x to simplify each fraction.
20. 15 _ 45 = x _ 3 1 21. 16 _ 28 = 4 _ x 22. 20 _ 36 = x _ 9
Write as a fraction in simplest form.
23. Six of the 16 marbles in a bag are yellow. What fraction of the marbles is yellow? 3 _
8
24. Adina read 12 out of 36 pages in a comic book. What fraction of the pages did she read? 1 _
3
Measurement The table lists the length of some objects in a classroom. What part of a foot is each object? Write as a fraction in simplest form. See Example 2 (p. 287)
25. pencil 1 _ 2 ft 26. crayon 1 _
4 ft
27. scissors 3 _ 4 ft 28. pencil box 2 _
3 ft
PRACTICEEXTRASee page R17.PRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEEXTRA
See page R17.
288 Chapter 6 Relate Decimals and Fractions
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