Download Fraction Review # 1

Name: ____________
Date: _____________
Math 9
Unit 3 ~ Operations with Fractions
Review from Grade 7 & 8
Equivalent Fractions
 Equivalent fractions have the same value.
 To find equivalent fractions, multiply or divide the numerator and denominator by
the same number.
1 2 3
4
 Example: 3, 6, 9, and 12 are equivalent fractions.
1. Write 3 equivalent fractions for each fraction.
6
a) 24 =
b)
21
c)
30
14
72
=
=
Greatest Common Factor (GCF)
 The greatest common factor is the greatest number that divides into each
number in a set.
 To find the greatest common factor, write out all of the factors of each number in
the set and then look for the greatest number that appears in all lists.
 Example: factors of 10 are 1, 2, 5, 10
greatest common factor of 10 and 15 is 5
factors of 15 are 1, 3, 5, 15
2. Determine the greatest common factor of each set of numbers.
a) 10, 40, 50
b) 4, 12, 18
c) 49, 70, 56, 21
Types of Fractions
 There are 3 types of fractions:
7
o proper fractions (numerator is smaller than denominator, like 12)
15
o improper fractions (numerator is larger than denominator, like 13)


1
o mixed number (a whole number and a proper fraction together, like 3 2)
Mixed numbers can be written as improper fractions and vice versa.
Examples
*Short cut for changing mixed to improper! Multiply denominator
by whole number then add numerator to get the new numerator.
:
ie - 8 x 3 + 5 = 29
So fraction is 29
8
3. Convert each mixed number to an improper fraction.
4
a) 3 5 =
4
b) 5 9 =
7
c) 3 20 =
1
d) 2 24 =
4. Convert each improper fraction to a mixed number.
27
a) 8 =
b)
41
c)
41
d)
29
18
15
12
=
=
=
Modelling Fractions
 We can model fractions in many ways using circles, squares, lines, etc.

5
Example: the fraction 8 can be modelled as:
5. Draw a model to represent each fraction. Use several different types of models
throughout the question.
a)
5
12
2
c) 1 3
b)
1
4
5
d) 2 6
Simplifying Fractions into Lowest Terms
 Final answers should always be left in lowest terms (smallest equivalent fraction
possible).
 To write a fraction in lowest terms, find the greatest common factor and divide
both the numerator and the denominator by this GCF.
10
 Example: to simplify 15, we divide 10 and 15 by the GCF (5);
10 ÷ 5 = 2
15 ÷ 5 = 3
10
15
2
in lowest terms is 3
6. Write the following fractions in lowest terms.
26
a) 30 =
b)
8
24
c)
50
d)
17
75
20
=
=
=
Least Common Multiple (LCM)
 The least common multiple is the lowest multiple that is the same for all numbers in
a set.
 To find the least common multiple, write out multiples of each number in the set
and look for the lowest number that appears in all lists.
 Example: multiples of 10 are 10, 20, 30, 40,...
least common multiple of 10 and 15 is 30
multiples of 15 are 15, 30, 45, 60,...
*to create a list of multiples, multiply the number first by 1, then by 2, then by 3, etc
7. Determine the least common multiple of each set of numbers.
a) 1, 4, 5
b) 2, 4, 8
c) 3, 4, 5
Adding & Subtracting Fractions
 To add or subtract fractions we must first write the fractions with a common
denominator, and then add or subtract the numerators (the denominator is not
added or subtracted).
 Mixed numbers must first be written as improper fractions.
 Examples:
= 41 – 7
8
2
= 41 – 7x4
8
2x4
= 41 – 28
8
8
= 13
8
=8+5
8 8
=1 5
8
8. Add. Write the answer in lowest terms (this includes writing improper fractions as
mixed numbers).
7
1
1
3
a) 10 + 6 =
b) 2 + 7 =
1
1
c) 3 3 + 4 2 =
5
3
d) 2 6 + 1 8 =
9. Subtract. Write the answer in lowest terms (this includes writing improper fractions
as mixed numbers).
3
3
5
1
a) 4 − 10 =
b) − =
8
1
2
c) 4 9 − 2 3 =
6
1
5
d) 7 4 − 3 6 =
3
10. Logan and Jonathan each bought a small pizza. Logan ate of his pizza and
4
7
Jonathan ate 8 of his. How much pizza did Logan and Jonathan eat together?
1
1
11. A jug holds 2 cups of liquid. A recipe for punch is 2 cup of orange juice, 4 cup of
3
5
raspberry juice, 8 of grapefruit juice, and 8 cup of lemonade. Is the jug big
enough for the punch? Explain how you know.
Multiplying and Dividing Fractions



1.
To multiply, multiply the numerators together and multiply the denominators
together. Simplify the resulting fraction if possible.
To divide, multiply by the reciprocal of the second fraction. Simplify if possible.
Example: 3 ÷ 8 = 3 x 7 = 21
5 7
5 8 40
2
3×4
3 1
a) 8 × 2
2
b) 6 × 5
4 2
c) 7  3
1
2
d) 24  35
1
2. Brett estimates he can read one chapter of a novel in 14 h.
5
Justin estimates he can read three chapters of the same novel in 26 h.
Brett read for 8 h. Justin read for 6 h. Who read more chapters?
Please show your work.
3. Divide.
2
a) 4 ÷ 3
9
÷ 3
2
c) 7 ÷ 5
b)
10
4 2
d) 7 ÷ 3
1
2
e) 4 ÷ 35