What is fraction?
When a whole quantity is divided into parts, these parts are called fractions, a fraction is written in the
form a/b, where a and b are whole numbers but b cannot be zero. The number on top, a, is called numerator, and
the number below, b, is called denominator.
THREE CATEGORIES OF FRACTION
Categories of fractions Definitions Examples
If the numerator is less than the denominator is ½
1. Proper fraction called proper fraction. It means that the fraction ¼
names a number less than 1 unit. 3/4
If the numerator is greater than or equal to 9/8
denominator, it is called an improper fraction. It 9/5
2. Improper fraction
means that the fraction names a number greater than 5/2
or equal to 1 unit.
A mixed number is formed by combining three parts: 10 ½
3. Mixed number a whole number, a numerator, and a denominator. 8 1/3
9 1/4
Rules for changing improper fraction to mixed number or whole number and vice versa.
Rules Examples
To change a mixed number to an improper Example # 1: Change 42/3 to mixed or whole
fraction, multiply the denominator by the whole number
number and add the numerator. Write the sum over Solution
the denominator to form the improper fraction. 42÷3=14
Example # 2: Change 53/4 to a mixed or whole
Solution
53÷4=13 ¼
Example # 3: Change 4 2/3 to an improper fraction
Solution
4x3+2=14 or 14/3
FOUR OPERATIONS OF FRACTION
Addition and subtraction of fraction
Rules Examples
Add fractions only when they are like fraction. Like fractions Similar denominator
have the same denominator. Add the numerators and place the sum 7/15+4/15=11/15
over the common denominator. Simplify the result whenever
necessary.
But if fractions are unlike, determine first the least common Unlike fraction
denominator (LCD). The LCD is the least common multiple of 1/2 + 1/3
denominators of the fractions. Step 1: Find the LCD
Change each unlike fraction to an equivalent fraction with The LCD of ½ and 1/3 is 6
the LCD as a common denominator. Add the resulting fractions as Step 2:
before. 3+2 5
=
6 6
The steps are the same whether you're adding or subtracting mixed Mixed Number
numbers: 5 ¼ + 3 1/3
1. Step 1: Find the Least Common Denominator (LCD) Solution:
2. Step 2: Find the equivalent fractions. 21 10 63+40 103
+ = =
3. Step 3: Add or subtract the fractions and add or subtract the 4 3 12 12
whole numbers. =8.58
4. Step 4: Write your answer in lowest terms.
When a whole quantity is divided into parts, these parts are called fractions, a fraction is written in the
form a/b, where a and b are whole numbers but b cannot be zero. The number on top, a, is called numerator, and
the number below, b, is called denominator.
THREE CATEGORIES OF FRACTION
Categories of fractions Definitions Examples
If the numerator is less than the denominator is ½
1. Proper fraction called proper fraction. It means that the fraction ¼
names a number less than 1 unit. 3/4
If the numerator is greater than or equal to 9/8
denominator, it is called an improper fraction. It 9/5
2. Improper fraction
means that the fraction names a number greater than 5/2
or equal to 1 unit.
A mixed number is formed by combining three parts: 10 ½
3. Mixed number a whole number, a numerator, and a denominator. 8 1/3
9 1/4
Rules for changing improper fraction to mixed number or whole number and vice versa.
Rules Examples
To change a mixed number to an improper Example # 1: Change 42/3 to mixed or whole
fraction, multiply the denominator by the whole number
number and add the numerator. Write the sum over Solution
the denominator to form the improper fraction. 42÷3=14
Example # 2: Change 53/4 to a mixed or whole
Solution
53÷4=13 ¼
Example # 3: Change 4 2/3 to an improper fraction
Solution
4x3+2=14 or 14/3
FOUR OPERATIONS OF FRACTION
Addition and subtraction of fraction
Rules Examples
Add fractions only when they are like fraction. Like fractions Similar denominator
have the same denominator. Add the numerators and place the sum 7/15+4/15=11/15
over the common denominator. Simplify the result whenever
necessary.
But if fractions are unlike, determine first the least common Unlike fraction
denominator (LCD). The LCD is the least common multiple of 1/2 + 1/3
denominators of the fractions. Step 1: Find the LCD
Change each unlike fraction to an equivalent fraction with The LCD of ½ and 1/3 is 6
the LCD as a common denominator. Add the resulting fractions as Step 2:
before. 3+2 5
=
6 6
The steps are the same whether you're adding or subtracting mixed Mixed Number
numbers: 5 ¼ + 3 1/3
1. Step 1: Find the Least Common Denominator (LCD) Solution:
2. Step 2: Find the equivalent fractions. 21 10 63+40 103
+ = =
3. Step 3: Add or subtract the fractions and add or subtract the 4 3 12 12
whole numbers. =8.58
4. Step 4: Write your answer in lowest terms.
