Download Remember all numbers have decimals.

Comparing Fractions
To compare fractions, you need to make the two fractions have the same
denominator.
Step 1: Find the Lowest Common Multiple (LCM) of the denominators.
Step 2: Change each denominator into the LCM of the two
denominators.
Step 3: Finally, whatever you did to the denominator to make it into the
LCM, do the same to the numerator.
Ex.
3
7
2
5
↓
↓
15
35
14
35
Practice:
5
12
1
4
5
6
7
10
↓
↓
↓
↓
Comparing Decimals
To compare decimals, you need to put the two numbers in the same
place value.
Step 1: Find the number that has the highest decimal value.
Step 2: Change the other numbers so they are all in the same place value
by adding zeroes to the end of the number.
Ex.
Tenths
Hundredths
Thousandths
Hundredths
Tenths
0.2
0.54
0.667
0.48
0.7
0.200
0.540
0.667
0.480
0.700
Thousandths
Thousandths
Thousandths
Thousandths
Thousandths
↓
↓
↓
↓
↓
Practice:
Place each set of numbers in order from least to greatest.
0.65
0.113
0.92
0.037
0.47
Compare the two numbers. Write either > , < , or =.
0.87
0.724
0.34
0.391
Adding and Subtracting Fractions with Same
Denominators
Step 1: If the fractions have the same the denominators, you merely add
or subtract the numerators, but keep the denominators the same.
Ex.
Subtracting Fractions with Same Denominators
7
12
6
7
-
-
5
12
2
7
=
=
2
12
4
7
=
1
6
Adding Fractions with Same Denominators
5
16
1
9
+
+
3
16
4
9
=
=
8
16
5
9
=
1
2
Note: If the answer can be simplified, then you must simplify it.
Adding and Subtracting Fractions with Different
Denominators
Step 1: If the fractions have the different denominators, you must first
make the denominators the same.
Step 2: To make the denominators the same, find the Lowest Common
Multiple (LCM) of the denominators.
Step 3: Change each denominator into the LCM of the two
denominators.
Step 4: Finally, whatever you did to the denominator to make it into the
LCM, do the same to the numerator.
Step 5: Once the denominators are the same, you merely add or subtract
the numerators, but keep the denominators.
Ex.
1
2
+
1
3
↓
↓
3
6
2
6
+
4
5
=
=
5
6
-
1
2
↓
↓
8
10
5
10
-
=
=
3
10
Changing Improper Fractions to Mixed Numbers
Step 1: Divide the numerator by the denominator.
Step 2: The answer is a whole number
Step 3: If there is a remainder, place that back over the denominator and
make into a fraction.
Ex.
9
7
→
1 r2
7 )9
2
→ 1
7
Practice: Change the improper fractions to mixed numbers
18
=
5
34
=
12
24
=
4
Changing Mixed Numbers to Improper Fractions
Step 1: Multiple the whole number (the big number) and the
denominator (bottom) of the fraction.
Step 2: Add the answer from Step 1 to the numerator (top) of the
fraction.
Step 3: Place the answer from Step 2 over the denominator.
Ex.
Step 1
2
3
5
3 x 5 = 15
→
Step 2
Step 3
15 + 2 = 17
17
5
→
Practice: Change the improper fractions to mixed numbers
1
7
=
2
5
5
6
11
=
3
=
4
Improper Fractions
An improper fraction is a fraction with a numerator that is greater than the
denominator.
Ex. 1
=
7
2
Ex. 2
=
22
11
=
8
4
Mixed Numbers
A mixed number is a number written as a whole number and a fraction
Ex. 1
=
3
1
2
Ex. 2
= 2
6
3
= 2
8
4
Multiplying Fractions
Step 1: Multiply the numerators together, then multiply the denominators together.
Ex.
6
7
3
8
X
X
2
3
2
7
=
=
6×2
7×7
=
12
49
3× 2
8×3
=
6
24
=
1
4
Note: If the answer can be simplified, then you must simplify it.
Dividing Fractions
Step 1: Take the second fraction in the equation and flip it, so that the numerator
becomes the denominator, and the denominator becomes the numerator. The first
fraction does not change.
Step 2: Change the division sign to a multiplication sign.
Step 3: Then multiple the two fractions.
Ex.
1
3
5
6
÷
÷
3
4
1
2
=
=
1
2
X
3
1
5
4
X
6
3
=
=
1× 2
3 ×1
5×4
6×3
=
=
2
3
20
18
=
Note: If the answer can be simplified, then you must simplify it.
1
1
9
Multiplying and Dividing Fractions and Whole Numbers
1. When multiplying or dividing fractions with whole numbers, convert
the whole number into an improper fraction then multiply as you would
normally multiply two fractions.
2. To convert a whole number into an improper number, make the
whole number the numerator and 1 the denominator.
Example: Multiplying fractions with whole numbers.
4
5
X
4
5
X
9=
↓
↓
9
=
1
36
1
=7
5
5
Example: Dividing fractions with whole numbers.
2
3
÷ 5=
2
3
÷
2
3
X
↓
↓
↓
5
=
1
↓
1
2
=
5
15
Multiplying and Dividing Mixed Numbers
1. When multiplying mixed numbers, convert the mixed numbers into
improper fractions.
2. Then multiply as you normally would.
Example: Multiplying with mixed numbers.
1
3
X
1
3
X
↓
1
5 =
2
↓
11
11 5
=1
=
2
6
6
Example: Dividing fractions with whole numbers.
2
1
4
÷
9
2
÷
9
2
X
↓
3
=
5
↓
↓
3
=
5
↓
5
45
3
1
=
=7 =7
3
6
6
2
****Note: If you have to divide two mixed numbers, then you change
both mixed numbers to improper fractions.
Finding the Percentage of a Number
1. To find the percentage of a number, you only have to take the
percentage and convert it into a decimal.
To convert a percentage into a decimal, just move the decimal to places
to the left. Remember all numbers have decimals.
Examples:
82% .82
8% .08
233% 2.33
2. Once the percentage is converted to a decimal, multiply the decimal
and the number you are trying to find the percentage of.
Examples:
What is 15% of 325?
Step 1: 15% .15
Step 2: 325 x .15 = 48.75
Answer: 15% of 325 is 48.75
What is 6% of $67.00?
Step 1: 6% .06
Step 2: 67.00 x .06 = 4.02
Answer: 6% of $67.00 is 4.02