How To Add Fractions With Like Denominators

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Adding Fractions

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

To add fractions there are Three Unproblematic Steps:

Stride i: Make certain the bottom numbers (the denominators) are the same
Stride two: Add the summit numbers (the numerators), put that reply over the denominator
Pace 3: Simplify the fraction (if possible)

Example:

i iv + ane 4

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

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

one 4 + 1 four = 1 + 1 iv = 2 4

Step 3. Simplify the fraction:

2 4 = 1 2

In picture form it looks similar this:

1 4	+	i 4	=	ii 4	=	1 2

... and do you come across how ii iv is simpler as 1 2 ? (come across Equivalent Fractions.)

Example:

1 three + 1 6

Step i: The lesser numbers are different. See how the slices are different sizes?

one 3	+	ane vi	=	?

Nosotros need to make them the same earlier we tin continue, because we tin't add together them like that.

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

× 2

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

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

The bottom numbers are at present the aforementioned, and so nosotros can get to stride 2.

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

2 6 + i 6 = 2 + one 6 = 3 half-dozen

In picture form it looks like this:

2 6	+	1 6	=	3 6

Step iii: Simplify the fraction:

iii 6 = 1 ii

In picture form the whole answer looks like this:

2 half-dozen	+	1 half-dozen	=	3 half-dozen	=	1 2

With Pen and Newspaper

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

A Rhyme To Help You Remember

♫ "If adding or subtracting is your aim,
The lesser numbers must be the same!
♫ "Change the bottom using multiply or divide,
Only the aforementioned to the summit must be applied,
♫ "And don't forget to simplify,
Before its time to say good adieu"

Example:

1 3 + 1 5

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

1 three	+	1 5	=	?

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

5 15	+	3 15

The first fraction: past multiplying the top and bottom by 5 we ended upwards with 5 15 :

× v

× five

The 2nd fraction: past multiplying the pinnacle and lesser by 3 we ended up with iii 15 :

× 3

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

5 15	+	iii 15	=	8 15

The result is already as unproblematic as it can exist, so that is the answer:

one 3 + 1 5 = viii fifteen

Making the Denominators the Same

In the previous instance how did nosotros know to cut them into ⁱ/₁₅ ths to make the denominators the same? Nosotros simply multiplied the two denominators together (3 × 5 = 15).

Read almost the two main means to make the denominators the aforementioned here:

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

They both work, use which i you prefer!

cupcakes

Example: Cupcakes

You want to make and sell cupcakes:

A friend can supply the ingredients, if you give them ¹/₃ of sales
And a marketplace stall costs ¹/_four of sales

How much is that birthday?

We need to add ¹/₃ and ¹/₄

1 3 + 1 4 = ? ?

First make the bottom numbers (the denominators) the aforementioned.

Multiply top and bottom of ¹/₃ by 4:

1×iv 3×four + 1 4 = ? ?

And multiply top and bottom of ¹/₄ by iii:

i×four iii×4 + 1×iii 4×iii = ? ?

Now practise the calculations:

4 12 + three 12 = four+three 12 = 7 12

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

Adding Mixed Fractions

We accept a special (more advanced) page on Calculation Mixed Fractions.

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