How To Add Fractions How To Subtract Fractions

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Adding Fractions

$fraction$

A fraction like 3 4 says we have 3 out of the 4 parts the whole is divided into.

To add together fractions there are Iii Simple Steps:

Footstep 1: Make sure the bottom numbers (the denominators) are the same
Pace 2: Add the top numbers (the numerators), put that answer over the denominator
Pace 3: Simplify the fraction (if possible)

Example:

ane iv + 1 4

Step 1. The bottom numbers (the denominators) are already the aforementioned. Get straight to stride 2.

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

i 4 + 1 iv = 1 + ane 4 = 2 iv

Pace 3. Simplify the fraction:

2 4 = 1 2

In motion-picture show class it looks like this:

1 four	+	1 iv	=	two 4	=	1 2

... and do you see how 2 4 is simpler equally 1 2 ? (come across Equivalent Fractions.)

Example:

1 3 + i vi

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

one 3	+	1 6	=	?

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

The number "6" is twice as large as "three", so to make the bottom numbers the same we can multiply the top and lesser of the first fraction by 2, similar this:

× 2

Of import: you multiply both top and bottom by the aforementioned corporeality,
to keep the value of the fraction the same

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

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

Pace 2: Add the acme numbers and put them over the aforementioned denominator:

two six + 1 six = 2 + ane half dozen = three 6

In flick form it looks similar this:

two half-dozen	+	1 6	=	3 vi

Step 3: Simplify the fraction:

3 6 = 1 ii

In picture form the whole answer looks similar this:

2 half-dozen	+	1 6	=	three 6	=	ane 2

With Pen and Paper

And here is how to do information technology with a pen and paper (press the play button):

A Rhyme To Help You Recall

♫ "If adding or subtracting is your aim,
The bottom numbers must exist the aforementioned!
♫ "Alter the bottom using multiply or divide,
Simply the same to the elevation must be applied,
♫ "And don't forget to simplify,
Before its fourth dimension to say good bye"

Instance:

1 3 + 1 5

Once again, the lesser numbers are dissimilar (the slices are different sizes)!

one three	+	1 5	=	?

But permit united states try dividing them into smaller sizes that will each exist the aforementioned:

v 15	+	three 15

The get-go fraction: by multiplying the pinnacle and lesser by 5 nosotros ended up with v 15 :

× 5

× v

The 2d fraction: by multiplying the top and bottom by 3 we ended upwards with 3 fifteen :

× iii

× three

The bottom numbers are now the aforementioned, so nosotros can go ahead and add the top numbers:

five xv	+	3 15	=	8 xv

The result is already as elementary as it can be, then that is the answer:

ane 3 + 1 5 = 8 xv

Making the Denominators the Same

In the previous example how did we know to cut them into ¹/₁₅ ths to make the denominators the same? Nosotros only multiplied the two denominators together (3 × 5 = fifteen).

Read about the ii main ways to brand the denominators the same here:

Common Denominator Method, or the
To the lowest degree Mutual Denominator Method

They both work, use which one you prefer!

cupcakes

Instance: Cupcakes

Yous want to brand and sell cupcakes:

A friend can supply the ingredients, if you give them ⁱ/_iii of sales
And a market stall costs ¹/₄ of sales

How much is that altogether?

We need to add ¹/₃ and ⁱ/₄

1 3 + ane four = ? ?

First brand the bottom numbers (the denominators) the same.

Multiply top and bottom of ¹/₃ past four:

1×4 3×4 + i 4 = ? ?

And multiply superlative and lesser of ^ane/_four by 3:

ane×4 iii×4 + i×3 4×3 = ? ?

Now practice the calculations:

4 12 + iii 12 = 4+3 12 = 7 12

Reply: 7 12 of sales go in ingredients and market place costs.

Adding Mixed Fractions

Nosotros accept a special (more advanced) page on Adding Mixed Fractions.

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