subtracting fractions

1.SUBTRACTING WITH LIKE DENOMINATORS
You just subtract the numerators together.
EX.4/5-1/5=3/5

2.SUBTRACTING WITH UNLIKE DENOMINATORS
You have to find the lowest common denominator for both denominators in the the times tables. You have to multiply the the numerator by how much you multiplied the denominator.
EX.5/6-4/8

6x4=24 5x4=20

8x3=24 4x3=12              

20/24-12/24=8/24

3.SUBTRACTING MIXED WITH LIKE DENOMINATORS

subtract the numerator then the whole numbers 

EX.4 4/5-2 1/5

4-1= 3

4-2=2

so 4 4/5-2 1/5= 2 3/5

4.SUBTRACTING MIXED WITH UNLIKE DENOMINATORS

You have to find the lowest common denominator for both denominators in the the times tables. You have to multiply the the numerator by how much you multiplied the denominator. subtract the numerator then the whole number.

EX.2 1/2-1 2/4

2x2=4 1x2=2

4x1=4 2x1=2 

2-2=0

2-1=1

2 1/2-1 2/4=1

Adding Fractions

There are 3 Simple Steps to add fractions:

Step 1: Make sure the bottom numbers (the denominators) are the same
Step 2: Add the top numbers (the numerators), put the answer over the denominator.
Step 3: Simplify the fraction (if needed).

Example 1:

1	+	1
4		4

Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2.

Step 2. Add the top numbers and put the answer over the same denominator:

1	+	1	=	1 + 1	=	2
4		4		4		4

Step 3. Simplify the fraction:

2	=	1
4		2

In picture form it looks like this:

1/4	+	1/4	=	2/4	=	1/2

... and do you see how ²/₄ is simpler as ¹/₂ ? (see Equivalent Fractions.)

Example 2:

1	+	1
3		6

Step 1: The bottom numbers are different. See how the slices are different sizes?

1/3	+	1/6	=	?

We need to make them the same before we can continue, because we can't add them like that.

The number "6" is twice as big as "3", so to make the bottom numbers the same we can multiply the top and bottom of the first fraction by 2, like this:

× 2

1	=	2
3		6

× 2

Important: you multiply both top and bottom by the same amount,
to keep the value of the fraction the same

Now the fractions have the same bottom number ("6"), and our question looks like this:

2/6	+	1/6

The bottom numbers are now the same, so we can go to step 2.

Step 2: Add the top numbers and put them over the same denominator:

2	+	1	=	2 + 1	=	3
6		6		6		6

In picture form it looks like this:

2/6	+	1/6	=	3/6

Step 3: Simplify the fraction:

3	=	1
6		2

In picture form the whole answer looks like this:

2/6	+	1/6	=	3/6	=	1/2

Example 3:

1	+	1
3		5

Again, the bottom numbers are different (the slices are different sizes)!

1/3	+	1/5	=	?

But let us try dividing them into smaller sizes that will each be the same:

5/15	+	3/15

The first fraction: by multiplying the top and bottom by 5 we ended up with ⁵/₁₅ :

× 5

1	=	5
3		15

× 5

The second fraction: by multiplying the top and bottom by 3 we ended up with ³/₁₅ :

× 3

1	=	3
5		15

× 3

The bottom numbers are now the same, so we can go ahead and add the top numbers:

5/15	+	3/15	=	8/15
Making the Denominators the Same In the previous example how did we know to cut them into 1/15ths to make the denominators the same? Read how to do this using either one of these methods: Common Denominator Method, or the Least Common Denominator Method They both work, use whichever you prefer! Example: Cupcakes You are going to make and sell cupcakes: A friend can supply the ingredients, if you give them 1/3 of sales And a market stall costs 1/4 of sales How much is that altogether? We need to add 1/3 and 1/4 1 + 1 = ? 3 4 ? First make the bottom numbers (the denominators) the same. Multiply top and bottom of 1/3 by 4: 1 × 4 + 1 = ? 3 × 4 4 ? And multiply top and bottom of 1/4 by 3: 1 × 4 + 1 × 3 = ? 3 × 4 4 × 3 ? Now do the calculations: 4 + 3 = 4+3 = 7 12 12 12 12 Answer: 7/12 of sales go in ingredients and market costs.

How to add fraction with like and unlike denominators
  
How to Add Fraction with like denominator

When adding fractions with like denominator it's very easy, you only have to add both numerator and you will get your answer.  

How to Add Fraction with unlike denominator

When adding fractions with unlike denominator it's not that difficult, you have to multiply both denominator to make it the same you also have to multiply the numerator too! What you used to multiply the denominator,you use the same number to multiply the numerator then you add the new fractions and you will get your answer.    

Subtracting Fractions

Subtracting Fractions

 "Proper fractions with like Denominators" 

 7/10 - 6/10 = ?

Since the denominator are alike you don't have to change it. It remains the same.

1. Subtract the numerators together and place the difference over the like denominator

                        7 - 6 = 1 

                                         7/10 - 6/10 = 1/10

"Proper fractions with unlike Denominators" 

1. If it's not like denominators, you have to find the L.C.D. (Lowest Common Denominator) by doing the times tables of both denominators. 

2.When you find the L.C.D. convert the denominator and do the same to the numerator.

4/5 - 1/3 = ?

                                4 x 3 = 12    = numerator                                     1 x 5 = 5     = numerator

                                5 x 3 = 15    = denominator                                3 x 5 = 15   = denominator   

After you converted the fractions you then subtract  the numerators to get the difference.      

                                12 - 5   = 7       

                                15   15 = 15

4/5 - 1/3 = 7/15 

"Mixed fractions with like Denominators"

2 7/8 - 1 4/8 = ?

Since the denominators are alike you don't have to change it. It remains the same.

1. Subtract the numerator's first then the whole numbers.

                                7 - 4 = 3

                                8   8 = 8

2. Subtract the whole numbers.

                                2 - 1 = 1

3. Add the remaining fraction and the remaining whole number.

                                1 + 3/8 = 1 3/8                                                      2 7/8 - 1 4/8 = 1 3/8

"Mixed fractions with unlike Denominators"

1.If it's not like denominators, you have to find the L.C.D. by doing the times tables of both denominators. 

2.When you find the L.C.D. convert the denominator and do the same to the numerator.               

             2 2/3 - 2 1/2 =?

                               2 x 2 = 4   = numerator                                           1 x 3 = 3  = numerator

                               3 x 2 = 6   = denominator                                      2 x 3 = 6  = denominator

3. After you converted you then subtract the numerators to get the difference.

                               4 - 3 = 1

                               6   6 = 6 

4. Subtract the whole numbers 

                              2 -2 = 0 

5. Add the remaining fraction and the remaining whole number

                             0 + 1/6 = 1/6 

                                                                                      2 2/3 - 2 1/2 = 1/6