Subtracting Fractions

Subtracting Fractions with the Same Denominator (Like Denominators)

There are 3 Simple Steps to Subtract fractions:

1- Make sure the bottom numbers (the denominators) are the same 2- Subtract the top numbers (the numerators). Put the answer over the same denominator. 3- Simplify the fraction (if needed).

Example 1: Subtract the fractions

The denominators are the same, so you can skip step1. The denominator of the answer will be 7. Subtract the numerators for the numerator in the answer. 3 - 2 = 1. The answer is. This answer is already reduced, so you can skip step 3.

All you have to do is to subtract 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: Subtract the fractions and reduce your answer.



Subtracting 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- Subtract the numerators of the fractions

4- Simplify the Fraction (if needed).


Example 1: Subtract 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.

Subtract the numerators to get the numerator in the answer.

This answer is already reduced, so you can skip step 4.

Example 2 : Subtract 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.


Subtracting Mixed Numbers with the same Denominator

How to subtract two mixed numbers whose fractions have the same denominator:

- Subtract the numerators of the two fractions

- Place that difference over the common denominator.

- Subtract the integer portions of the two mixed numbers

- If subtracting the fractional parts created a mixed number then subtract its integer portion to the difference.


Example 1: 6 4/5 - 2 2/5= ?



Example 2: Subtract the fractions 6 6/7 - 3 5/7= ?


- Subtract the fractional part of the mixed numbers
- Subtract the integer portions of the mixed numbers
- Subtract the integer from the difference of the fractions

Equivalent Fractions

Equivalent fractions
What Equivalent fractions means?

Equivalent fractions are fractions that name the same amount.

a fraction can have many different appearances, these are called equivalent fractions

The word EQUIVALENT means the same as EQUAL or, more precisely, of equal value.

In the following picture we have ½ of a cake because the whole cake is divided into two congruent parts and we have only one of those parts.

But if we cut the cake into smaller congruent pieces, we can see that Or we can cut the original cake into 6 congruent pieces,

Now we have 3 pieces out of 6 equal pieces, but the total amount we have is still the same. Therefore,

If you don’t like this, we can cut the original cake into 8 congruent pieces,

Then we have 4 pieces out of 8 equal pieces, but the total amount we have is still the same. Therefore,

By looking at the pictures, each box has the same portion (or fraction)
filled, so these portions are called equivalent fractions.

We can generalize this to
 

Are they equivalent fractions?
 
Yes!
These fractions are equal. They are equivalent fractions.



1) To raise fractions make the denominator larger.

2) Multiply numerator and denominator (top and bottom) of the fraction by the same number.

3) This is the same thing as multiplying by 1.



Are sometimes called equal fractions: two or more fractions that name the same number.
Equivalent Fraction Models




To compare 1/2 and 3/7 we would multiply 1/2 by 3/3 to produce 3/6. Since 3/6 is not the same as 3/7, the fractions are not equivalent.

Fractions equivalent to 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12 ...

Fractions equivalent to 1/3 are 2/6, 3/9, 4/12, 5/15, ...

Fractions equivalent to 1/4 are 2/8, 3/12, 4/16, 5/20, ...

Fractions equivalent to 1/5 are 2/10, 3/15, 4/20, 5/25, ...

Fractions equivalent to 2/5 are 4/10, 6/15, 8/20, 10/25, ...

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 2/5 + 7 4/5= ?

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

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?

2) Improper Fractions
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?

3) Mixed Fractions

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

Fractions

Content: Fractions, Types of Fraction, Proper fraction, Improper fraction, Mixed Fraction, Simplifying Fractions, Comparing Fractions, Equivalent Fractions, Adding Fractions, Subtracting Fractions, Multiplying Fractions, Dividing Fractions
What is a Fractions?

A fraction is part of an entire object.

We call the top number the Numerator, it is the number of parts you have.

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?

Answer: The diagram shows 3 slices of pizza left on the plate out of eight slices altogether.

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?

2) Improper Fractions
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?

3) Mixed Fractions

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.

Since 4, 9 and 6 are all factors of 36, the least common multiple is 36

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