Name ———————————————————————
SECTION
2
Date ————————————
Fractions
CA Standards
G6 NS 2.4
Lesson 2: GCF and Fractions in Simplest Form
To write a fraction in simplest form, first list all factors of both the numerator and the
denominator. Look for common factors. Divide both the numerator and the denominator
by the greatest common factor (GCF), which is also known as the greatest common divisor.
EXAMPLE 1
Find the greatest common factor (GCF) of 4 and 12.
List all the factors of each number.
Factors of 12: 1, 2, 3, 4, 6, 12
The greatest factor that appears in both lists is 4, so the GCF is 4.
EXAMPLE 2
4
Write the fraction }
in simplest form.
12
Find the GCF of the numerator and the denominator: 4. Write the numerator and the
denominator as a product, using the GCF as a factor. Then simplify.
4
12
431
433
1
3
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
}5}5}
1
Simplest form is }3 .
2. FRACTIONS
2. GCF and Fractions
HINT
The GCF is always
at least 1.
Factors of 4: 1, 2, 4
Practice: First Try
Find the greatest common factor of the numbers.
1. 3, 6
2. 3, 8
3. 2, 14
4.
8, 12
5. 4, 18
6. 12, 15
7. 6, 9
8.
9, 15
11. 4, 12
12.
8, 10
9. 5, 13
10. 6, 16
Write the fraction in simplest form.
8
13. }
12
2
14. }
12
3
15. }
15
16.
}
5
20
6
17. }
21
6
18. }
10
16
19. }
24
20.
}
4
21. }
18
12
22. }
20
9
23. }
15
24.
}
14
21
6
16
Remediation Book Lesson 2.2
41
Name ———————————————————————
Date ————————————
Practice: Second Try
Find the greatest common factor of the numbers.
1. 2, 4
2.
4, 10
3. 6, 27
4.
12, 30
5. 3, 7
6.
5, 25
7. 36, 42
8.
8, 22
9. 3, 6
10.
10, 15
11. 16, 24
12.
7, 28
13. 15, 27
14.
22, 33
15. 18, 48
16.
14, 35
4
17. }
8
18.
}
10
16
9
19. }
12
20.
}
3
21. }
9
22.
}
5
15
4
23. }
6
24.
}
10
25. }
20
26.
}
4
30
8
27. }
20
28.
}
12
29. }
18
30.
}
9
24
5
31. }
35
32.
}
18
33. }
81
34.
}
36
48
14
35. }
49
36.
}
Extend Your Skills
For exercises 37–39, find the GCF for each list of numbers.
37. 12, 20, 32
38. 9, 15, 24, 36
39. 15, 35, 60, 75
40. For the numbers in exercise 39, would the GCF be different if the number 35 were
removed from the list? Explain your answer.
Puzzle
Three friends draw the fraction cards shown. In simplest form, whose card has a
prime number in both the numerator and the denominator?
42
}
65
50
}
50
125
}
Alex
Ben
Greg
Remediation Book Lesson 2.2
24
64
8
14
10
35
14
28
16
28
24
42
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
2. FRACTIONS
2. GCF and Fractions
Write the fraction in simplest form.