Download Reteach: Fractions in Simplest Form

Reteach: Fractions in Simplest Form
Name:______________________
When you write fractions in their simplest form, you are using the smallest possible
numbers to tell the amount that is being represented.
2
4
2
4
p
1
2
1
2
w
2
The fractions
and
both represent the same amount. The
4
were cut into more pieces, but the total amount is the same.
Since you want the smallest numbers when you are simplifying fractions, the shaded
portion in simplest form would be called 1 .
2
You can use pictures to help you simplify fractions, or you can use division. Fractions
with the same numerator and denominator are equal to 1, so you can simplify by
dividing both the top and bottom of the original fraction by the same number. This will
not change the actual value, since you are dividing by 1.
(You may think of this form of 1 as “Big Giant One”.)
Start by deciding which of the numbers in the original fraction is larger. Ask yourself if
the larger number can be divided evenly by the smaller number. If it can, then the
smaller number is the divisor to use in your “Big Giant One,” both as the numerator and
the denominator. If it cannot be divided evenly, next ask yourself what are the factors of
the smaller number? Can any of them divide evenly into the larger number? If so, use
the largest one that does in your “Big Giant One.” If not, the original fraction is already in
simplest form.
3 3
÷
9
Examples:
=
3
4
18
÷
2
=
2
1
3
Nine is larger, so does three divide into it evenly?
Yes, so divide both 3 and 9 by three.
Three ninths in simplest form is one third.
Eighteen is larger, so does four divide into it evenly?
No, so the factors of four are 1, 2, and 4. We know four
doesn’t work, and 1 won’t change anything. Two does
divide evenly into 18, so divide both 4 and 18 by 2.
Four eighteenths in simplest form is two ninths.
2
9
Guided Practice:
Simplify the following fractions:
1)
2)
4
4
12 ÷ 4
6
16
÷
= _____
= _____
Twelve is the largest, so can it be evenly divided by four? _______
Since it can, use 4 in “Big Giant One” and divide. Write the new
numerator and denominator to form the simplest form fraction.
Which is larger, 6 or 16? _______ Does the smaller number divide
evenly into the larger? _______ What are the factors of the smaller
number? ______________ What is the largest factor that divides
evenly into 16? _________ Put it into both parts of “Big Giant One.”
Divide. Write the new numerator and denominator to form the
simplest form fraction.
Independent Practice:
Fractions in Simplest Form
Name:________________________
Use what you have learned to simplify each of the fractions below. If it is already in simplest
form, write “simplest form” on the line.
5
1) 10 _____________________
2)
6
_____________________
14
4
_____________________
6
4)
7
_____________________
21
3)
15
5)
_____________________
20
8
6)
_____________________
12
24
7) 32 _____________________
12
8) 24 _____________________
6
9) 8
12
10) 18
_____________________
_____________________
11)
4
6
_____________________ 12)
10
22
_____________________
13)
5
7
_____________________ 14)
40
10
_____________________
9
16
15)12 _____________________ 16) 20
17)
_____________________
7
5
_____________________ 18)
_____________________
28
12
21
90
19) 36 _____________________ 20) 100 _____________________