Download Equivalent Fractions - Avon School District

Fraction Review
Benchmark Assessment: Thursday, February 14th
Fractions
- Denominator represents the total number of equal pieces
- Numerator represent the number of equal pieces you are looking for
- Fraction bar represents division
7÷9=
7
9
7 is the numerator
9 is the denominator
7
This picture represents the fraction of a region.
9
7 boxes are shaded out of 9 boxes
7
This picture represents the fraction of a set.
9
7 circles are blue out of the 9 circles
Represent the fractions as division. Draw a picture to represent the fraction as a
region and a set.
5
3
7
6
4
11
Equivalent Fractions
- To find an equivalent fraction multiple or divide the numerator and
denominator by the same number.
8
12
5
8
2
4
4
2
6
6
÷ =
is equivalent to
3
15
15
3
24
24
x =
8
12
is equivalent to
5
8
Write two equivalent fractions for each fraction given.
5
6
9
9
24
54
Compare Fractions
- If fractions have a common denominator compare the numerators. The
greater the numerator the greater the fraction.
- If fractions do not have a common denominator, find a common
denominator by finding a common multiple or multiply the denominators
together.
5
2
>9
9
These fractions have a common denominator of 9. The numerator 5 is
5
2
9
9
greater than 2 therefore is greater than
3
5
2
<3
.
These fractions do not have a common denominator. A common multiple of
5 and 3 is fifteen because 5 x 3 =15.
Rename the fractions with the common denominator.
3
5
2
3
3
9
3
5
15
10
5
15
x =
x =
Common the numerators. 9 is less than 10.
Therefore
9
15
is less than
10
15
3
2
5
3
, and is less than .
Compare the fractions using <, >, or =.
4
7
9
12
8
9
8
8
18
24
9
12
Mixed Numbers and Improper Fractions
- Mixed numbers include a whole number and a fraction.
- An improper fraction has a numerator that is greater than or equal to the
denominator.
To write a mixed number as an improper fraction, multiply the denominator by the
whole number and add the numerator. Put it over the same denominator
2
5
3
3
1 =
3x1=3+2=5
To write an improper fraction as a mixed number, divide the numerator by the
denominator and put the remainder over the denominator.
9
6
=1
3
6
9÷6=1r3
Change to a mixed number or improper fraction.
15
18
7
15
5
2
6
2
5
7
Greatest Common Factor.
- To find the GCF, list the factors of the two numbers, identify the GCF
- To find the GCF, find the prime factorization of the two numbers, identify
the common prime factors, and multiply the common prime factors
together
20: 1, 2, 4, 5, 10, 20
GCF is 4
16: 1, 2, 4, 8, 16
Prime Factorization Using a Factor Tree
20 = 2 x 2 x 5
16 = 2 x 2 x 2 x 2
GCF = 2 x 2 = 4
Find the GCF of each pair of numbers.
24, 56
36, 108
112, 72
Simplest Form
- A fraction is in simplest form when the numerator and denominator have
no common factors except for 1.
- To write a fraction in simplest form, divide the numerator and denominator
by a common factor or GCF until the numerator and denominator have no
common factors except for 1
16
20
4
4
4
4
5
5
÷ =
is in simplest form because 4 and 5 have no common
factors except for 1.
Write each fraction in simplest form.
15
80
25
36
30
100
75
92