What is a Fractions?
A fraction is part of an entire object.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.
When an object is divided into a number of equal parts then each part is called a fraction.
Fractions consist of two numbers.
The top number is called the numerator. The bottom number is called the denominator.
Always remember: denominator can never be 0 (zero).
One fourth is red.
Two fourths are red. One half is red.
Three fourths are red.
Four fourths are red.
1/6 is yellow, 1/6 is blue, 1/6 is white,
1/6 is pink and 2/6 is green.
Question: For the fraction of pizza shown in the diagram, what is the numerator?
So the fraction is:
3 / 8
The numerator is the top number, and that is 3
Types of Fraction
There are 3 different types of fractions:
1) Proper Fractions
Numerator < Denominator Proper fractions have the nominator part smaller than the denominator part.
for example
See how the top number is smaller than the bottom number in each example?
Numerator > Denominator or Numerator = Denominator, Improper fractions have the nominator part greater or equal to the denominator part
for example
See how the top number is bigger than (or equal to) the bottom number?
Mixed fractions have a whole number plus a fraction
for example
See how each example is made up of a whole number and a proper fraction together? That is why it is called a "mixed" fraction (or mixed number)
CONVERTING IMPROPER FRACTIONS TO MIXED FRACTIONS
Let us convert 7/2 to the improper fraction. The fraction 7/2 (or seven halves) means "7 divided by 2".
To convert an improper fraction to a mixed fraction, follow these steps:
- Divide the numerator by the denominator.
- Write down the whole number answer
- Then write down any remainder above the denominator.
Thus 7/2, or 7 divided by 2, is 3 remainder 1, so 7/2 = 3 1/2
Example 1: Write the fraction 17/3 as a mixed fraction.
Because 17 divided by 3 is 5 remainder.
Example 2: Convert 21/5 to a mixed fraction.
CONVERTING MIXED FRACTIONS TO IMPROPER FRACTIONS
Consider the mixed fraction 1 2/5. It reads as "one whole and two fifths".
There are 5 fifths in 1 whole.
And there are 2 fifths in 2/5 , giving 5 + 2 = 7 fifths altogether.
i.e. 1 2/5 = 7/5
To convert a mixed fraction to an improper fraction, follow these steps:
- Multiply the whole number part by the fraction's denominator.
- Add that to the numerator.
- Then write the result on top of the denominator.
Example 1: Write the mixed fraction 4 2/3 as an improper fraction.
Example 2: Convert 2 3/7 to an improper fraction.
Here's More Fractions, Simplifying Fractions, Comparing Fractions, Equivalent Fractions, Adding Fractions, Subtracting Fractions, Multiplying Fractions, Dividing Fractions
Simplifying Fractions
Simplifying Fractions (Reducing Fractions)
Simplifying (or reducing) fractions means to make the fraction as simple as possible.
There are two ways to simplify a fraction:Method 1
• Find the Greatest Common Factor (GCF) of the numerator and denominator
• Divide the numerator and the denominator by the GCF
for example
Method 2
• Try dividing both the top and bottom of the fraction until you can't go any further (try dividing by 2,3,5,7,... etc)
for example
Method 3
- Factor the numerator.
- Factor the denominator.
- Find the fraction mix that equals 1.
for example
Reduce the fraction 120 / 160
Answer: Factor the numerator and factor the denominator and look for the fractions in the mix that have a value of 1.
The fraction 120 / 160 has been reduced into the equivalent fraction 3 / 4.
Now prove to yourself with your calculator that both fractions are equivalent. When you divide 120 by 160, you will get the same answer as when you divide 3 by 4.
Question: Reduce the fraction 150 / 650
Answer: Rewrite the fraction with the numerator factored and the denominator factored. The fraction 150 / 650 can be written as
Although we have reduced the fraction, we have not reduced it completely. So repeat the above steps.
The fraction 15 / 65 can be written as
The fraction 150 / 650 is equivalent to the fraction 3 / 13.
You can check the answer with your calculator. When you divide 150 by 650, you will get the same answer as when you divide 3 by 13.
Comparing Fractions
Comparing Fractions
Comparing Fractions
Comparing Fractions with the Same Denominator
If the denominators of two fractions are the same, the fraction with the largest numerator is the larger fraction.
for example
1/4 is less than 3/4 (because 1 is less than 3)
Comparing Fractions with the Same Numerator
If the numerators of two fractions are the same, the fraction with the smaller denominator is the larger fraction.
for example
Comparing Unlike Fractions
But if the denominators are not the same you need to make them the same. Multiply the numerator and denominator of one fraction by the same number so both fractions will have the same denominator.
for example;
Which is larger: 7/12 or 5/8 ?
Now we can easily see that 15/24 is the larger fraction
so 5/8 is the larger fraction
Question 1: Which one of the following fractions is the largest?
Answer 1: To compare the fractions, we need to write each of them as an equivalent fraction with a common denominator i.e. we must find the least common multiple of 4, 36, 9 and 6.
So change them all to equivalent fractions with denominator 36:
Now they all have the same denominator, we just need to find the one with the largest numerator, which is 30
Adding Fractions
Adding Fractions with the Same Denominator (Like Denominators)
There are 3 Simple Steps to add fractions:
1- Make sure the bottom numbers (the denominators) are the same
2- Add the top numbers (the numerators). Put the answer over the same denominator.
3- Simplify the fraction (if needed).
Example 1: Add the fractions
The denominators are the same, so you can skip step 1. The denominator of the answer will be 7.
Add the numerators for the numerator in the answer. 3 + 2 = 5. The answer is.
This answer is already reduced, so you can skip step 3.
All you have to do is to add the numerators.
And it is always a good idea to make your result "nice" by converting it to a mixed number and simplifying if possible.
Example 2: Add the fractions and reduce your answer.
Adding Fractions with Different Denominators (Unlike Denominators)
1- Find the Least Common Denominator (LCD) of the fractions
2- Rename the fractions to have the LCD
3- Add the numerators of the fractions
4- Simplify the Fraction (if needed).
Example 1: Add the fractions
The denominators are different, so you must build each fraction to a form where they both have the same denominator.
Since both 5 and 15 will divide evenly into 15, build both fractions to a denominator of 15.
Build the fraction 3 / 5 to an equivalent fraction whose denominator is 15.
Add the numerators to get the numerator in the answer.
This answer is already reduced, so you can skip step 4.
Example 2 : Add the fractions and reduce your answer.
The denominators are different, so you must build each fraction to a form where they both have the same denominator. Rewrite the problem with both denominators factored.
The common denominator will have to have factors 2, 5, and 7. Build each fraction so that each denominators has these three factors.
Simplify the answer.
Adding Mixed Numbers with the same Denominator
How to add two mixed numbers whose fractions have the same denominator:
- Add the numerators of the two fractions - Place that sum over the common denominator.
- If this fraction is improper (numerator larger than or equal to the denominator) then convert it to a mixed number
- Add the integer portions of the two mixed numbers
- If adding the fractional parts created a mixed number then add its integer portion to the sum.
Example 1: 4 2/3 + 7 2/3= ?
Example 2 : Add the fractions 3 4/7 + 5 6/7= ?
- Add the fractional part of the mixed numbers
- Convert 10/7 to a mixed number
- Add the integer portions of the mixed numbers
- Add the integer from the sum of the fractions
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