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Station 1
Factors and GCF
List all of the factors of the following numbers.
1)
8
2)
12
3)
35
4)
28
5)
17
6)
49
Find the Greatest Common Factor (GCF) of each pair of numbers.
7)
14, 35
GCF= __________
8)
15, 16
GCF= __________
9)
27, 30
GCF= __________
10) 24, 48
GCF= __________
Station 1 Lifeline
Factors are the numbers that divide evenly into another number. The first
factor of every whole number is 1.
To list all of the factors of a number, think about what divides evenly into
that number. Each factor must pair up with another to form a factor pair.
10
1 x 10
2x5
16
1 x 16
2x8
4x4
The factors of 10 are 1, 2, 5, and 10
The factors of 16 are 1, 2, 4, 8, and 16
The Greatest Common Factor (GCF) of two or more numbers is the largest
factor that they both share.
27 - 1, 3, 9, 27
The GCF of 27 and 30 = 3
30 - 1, 2, 3, 5, 6, 10, 15, 30
18 - 1, 2, 3, 6, 9, 18
The GCF of 18 and 36 = 18
36 – 1, 2, 3, 4, 6, 9, 12, 18, 36
21 – 1, 3, 7, 21
16 – 1, 2, 4, 8, 16
The GCF of 21 and 16 = 1
Station 2
Multiples and LCM
List the first 5 multiples of the following numbers.
1)
4
2)
5
3)
8
4)
9
5)
12
6)
15
Find the Least Common Multiple (LCM) of each pair of numbers.
7)
4, 9
LCM = ___________
8)
12, 15
LCM = ___________
9)
8, 14
LCM = ___________
10) 7, 14
LCM = ___________
Station 2 Lifeline
A multiple of a number is a number that it will divide evenly into. The first
multiple of a number is that number itself.
The first 5 multiples of 5 are
5x1=5
5 x 2 = 10
5, 10, 15, 20, and 25
5 x 3 = 15
The first 5 multiples of 8 are
8x1=8
8 x 2 = 16
5 x 4 = 20
5 x 5 = 25
8, 16, 24, 32, and 40
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
The Least Common Multiple (LCM) of two or more numbers is the
smallest multiple that they share.
4 – 4, 8, 12, 16, 20
The LCM of 4 and 8 = 8
8 – 8, 16, 24, 32, 40
5 – 5, 10, 15, 20, 25, 30, 35, 40
The LCM of 5 and 8 = 40
8 – 8, 16, 24, 32, 40
6 – 6, 12, 18, 24, 30
8 – 8, 16, 24, 32, 40
The LCM of 6 and 8 = 24
Station 3
Equivalent Fractions/Simplest Form
Give two equivalent fractions for each given fraction.
1)
2
4
2)
6
7
3)
12
18
4)
3
16
5)
3
10
6)
3
9
Write each fraction in simplest form (lowest terms).
7)
4
6
8)
10
35
9)
10
20
10)
40
50
11)
15
45
12)
12
18
Station 3 Lifeline
Equivalent fractions have the same value. To find equivalent fractions, you
must either multiply or divide both the numerator and denominator by the
same number.
5 2 10
x =
6 2 12
5 10 15
, , ,
6 12 18
and
5 3 15
x =
6 3 18
50
60
5 10 50
x =
6 10 60
are all equivalent fractions
Fractions are in simplest form (lowest terms) when the numerator and
denominator cannot be divided by a common factor. To find simplest form,
both the numerator and denominator must be divisible by the same number.
4
6
÷
2 2
=
2 3
4
6
in simplest form is
2
3
9
15
÷
3 3
=
3 5
9
15
in simplest form is
3
5
20
35
÷ 5= 4
7
20
35
in simplest form is
4
7
30 10 3
÷ =
40 10 4
30
40
in simplest form is
3
4
5
Station 4
Improper Fractions to Mixed Numbers
Convert the following improper fractions to mixed numbers. Make sure your
answers are in lowest terms.
1)
17
5
2)
27
12
3)
9
4
4)
14
3
5)
23
4
6)
19
6
7)
21
14
8)
10
4
9)
16
12
Station 4 Lifeline
Fractions are improper when the numerator is larger than the denominator.
Improper fractions can be converted to mixed numbers. Mixed numbers are
a whole number with a proper fraction.
=
If
1
2
1
4
3
4
5
6
7
8
9
=
= 2 wholes +
9
4
1
1
= 2
4
4
9
1
as a mixed number is 2
4
4
To convert an improper fraction to a mixed number, divide the numerator by
the denominator.
2
4 9
9
1
=2
4
4
- 8
1
The number of times that the denominator divides into the numerator will be
the whole number.
The “remainder” will become the numerator of the
proper fraction. The denominator will remain the same.
Station 5
Mixed Numbers to Improper Fractions
Convert the following mixed numbers to an improper fraction.
1)
4
5
7
2)
3
5
6
3)
1
2
9
4)
7
1
7
5)
3
1
4
6)
1
11
12
7)
6
5
8
8)
2
3
5
9)
5
2
3
Station 5 Lifeline
To convert mixed numbers to improper fractions, follow these steps:
3
1)
5
8
Multiply the denominator times the whole number.
8 x 3 = 24
2)
Add the numerator to this product.
24 + 5 = 29
3)
This sum becomes the numerator of the improper fraction.
The denominator will remain the same as in the mixed number.
3
5
8
as an improper fraction is
29
8
Station 6
Adding and Subtracting Fractions (Like Denominators)
Add the following fractions.
Make sure your answers are in simplest form.
1)
4 2
+
9 9
2)
3 1
+
6 6
3)
5 1
+
12 12
4)
8 4
+
15 15
5)
4
3
+
10 10
6)
7
5
+
24 24
Subtract the following fractions.
Make sure your answers are in simplest form.
7)
7 4
9 9
8)
3 1
6 6
9)
11 5
12 12
10)
11 6
15 15
11)
17 2
20 20
12)
21 9
24 24
Station 6 Lifeline
When adding or subtracting fractions, you must make sure that they have the
same denominator. The denominator is actually the unit…
5
8
means that you have 5 units that are
1
8
each
Only add or subtract the numerators. The denominators will remain the
same.
8
5 3
+ =
11 11 11
2
5 3
- =
11 11 11
After adding or subtracting, make sure your answer is in simplest form.
5
3
8 4 2

  
12 12 12 4 3
5
3
2 2 1
   
12 12 12 2 6
Station 7
Adding and Subtracting Fractions (Unlike Denominators)
Add the following fractions.
Make sure your answers are in simplest form.
1)
2 1
+
5 3
2)
7 1
+
16 4
3)
2 1
+
3 4
4)
1 3
+
2 8
5)
4 1
+
9 6
6)
3 1
+
7 4
Subtract the following fractions.
Make sure your answers are in simplest form.
7)
2 1
5 3
8)
7 1
16 4
9)
2 1
3 4
10)
1 3
2 8
11)
4 1
9 6
12)
3 1
7 4
Station 7 Lifeline
In order to add or subtract fractions, they must have the same denominator
(common denominator). If the fractions do not already have common
denominators, you must find equivalent fractions that have the same
denominator. Make sure to put answers in simplest form when needed.
1 7 7
x =
3 7 21
1 2 2
x =
4 2 8
+ 3 ---8
3
8
+
5
8
3 3 9
x =
7 3 21
2 3 6
x =
8 3 24
+
16
21
1 4 4
x =
6 4 24
10 2 5
¸ =
24 2 12
Common denominators can also be found by simply multiplying the two
existing denominators together. Make sure your final answer is in simplest
form.
-
5 4 20
´ =
8 4 32
1 8 8
´ =
4 8 32
12 4 3
¸
32 4 8
-
3 3 9
x =
4 3 12
1 4 4
x =
3 4 12
5
12
-
2 6 12
x =
8 6 48
1 8 8
x =
6 8 48
4 4 1
¸ =
48 4 12
If you are having problems finding common denominators, please review
the lifeline on common multiples (LCM).
If you are having problems putting answers in simplest form, please review
the lifeline on simplest form (lowest terms).
Station 8
Adding Mixed Numbers
Add the following whole and mixed numbers. Make sure your answers are
in simplest form.
1)
2
2
3
+4
2)
5 + 13
3)
1
3
3 +4
7
7
4)
3
1
4 +2
8
4
5)
1
1
7 +5
3
4
6)
1
3
6 +8
6
4
7)
1
5
1 +3
2
6
8)
2
5
7 +8
3
6
9)
1
1
9 +1
6
3
8
Station 8 Lifeline
When adding mixed numbers…. add the fraction part first, then the whole
number part. Remember to always put your answers in simplest form.
6
+
5
8
1
3
8
4
2
3
4
8
3
4
+
3
6 2
7 ¸ =7
4
8 2
If needed, make equivalent fractions with like denominators.
+
1 3
3
2 x =2
4 3
12
1 2
2
5 x =5
6 2
12
7
5
12
If you get an improper fraction after adding, convert the improper fraction to
a mixed number and add the whole number part to the whole number
column.
+
5 2
10
3 x =3
6 2
12
3 3
9
5 x =5
4 3
12
8
19
12
19
7
=1
12
12
7
7
8 +1 = 9
12
12
Station 9
Subtracting Mixed Numbers
Subtract the following whole and mixed numbers. Make sure your answers
are in simplest form.
1)
5
1
7 -3
8
8
4)
4 -2
7)
1
3
9 -4
5
5
3
4
2)
3
2
12 - 4
4
4
3)
7
1
5 -2
9
3
5)
23 -19
5
8
6)
7-3
8)
1
1
4 -2
8
4
9)
1
2
6 -2
5
3
2
3
Station 9 Lifeline
When subtracting a mixed number from a whole number, you must first
change the whole number into a mixed number. You do this through
“borrowing”.
12
-
12 wholes = 11 wholes + (since 5 is our denominator)
Rewrite the problem as:
-
Always make sure that the mixed numbers have common denominators
before you subtract. If the top fraction is smaller than the bottom fraction,
again you will have to “borrow”.
-
1 5
5
7 x 7
4 5
20
3 4
12
3 x 3
5 4
20
Since you can’t subtract from , you will have to borrow from the 7.
76
20
20
so
7
5
20 5
6 
20
20 20
which equals
6
25
20
Now we can subtract.
25
20
12
3
20
6
-
3
Station 10
Applications
13
20
1)
A weather reporter recorded the rainfall as
10:00 and
7
8
3
10
inch between 9:00 and
inch between 10:00 and 11:00. What is the total rainfall
between 9:00 and 11:00?
2)
In a class,
1
6
of the students have blue eyes and
7
9
of the students have
brown eyes. How much more of the class has brown eyes than blue
eyes?
3)
If you play 12 3 minutes during the first half of a soccer game and
8
8
3
4
minutes during the second half. How many total minutes do you play?
4)
On Monday, the snowfall was 15 3 inches. On Tuesday, the snowfall
4
was 18 1 inches. What was the difference in snowfall?
2