How To Add Fractions With Radicals In The Denominator

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Adding Fractions

$fraction$

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

To add fractions there are Iii Simple Steps:

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

Example:

i 4 + 1 4

Step one. The bottom numbers (the denominators) are already the same. Go straight to stride two.

Pace ii. Add the top numbers and put the respond over the aforementioned denominator:

1 4 + 1 4 = one + 1 4 = ii iv

Step 3. Simplify the fraction:

2 4 = 1 2

In picture form it looks like this:

1 4	+	1 four	=	2 4	=	1 2

... and do you see how 2 4 is simpler equally i 2 ? (run into Equivalent Fractions.)

Instance:

1 three + one 6

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

1 three	+	1 6	=	?

We need to make them the same earlier we tin can keep, considering nosotros tin can't add them similar that.

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

× 2

× two

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

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

The bottom numbers are at present the same, then we tin can become to step two.

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

2 6 + 1 half dozen = 2 + 1 6 = three vi

In picture grade it looks similar this:

2 6	+	ane vi	=	3 6

Step 3: Simplify the fraction:

3 6 = 1 2

In picture form the whole answer looks similar this:

2 6	+	1 half dozen	=	3 6	=	1 2

With Pen and Newspaper

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

A Rhyme To Assist You Remember

♫ "If adding or subtracting is your aim,
The bottom numbers must be the same!
♫ "Alter the lesser using multiply or split up,
But the aforementioned to the top must be applied,
♫ "And don't forget to simplify,
Before its time to say good goodbye"

Example:

1 iii + 1 5

Over again, the bottom numbers are different (the slices are different sizes)!

1 3	+	i v	=	?

Merely allow u.s. endeavor dividing them into smaller sizes that will each be the same:

5 15	+	3 xv

The first fraction: past multiplying the superlative and bottom by five we ended upwardly with 5 15 :

× v

× 5

The second fraction: by multiplying the top and bottom by 3 we ended upwards with three 15 :

× 3

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

v 15	+	3 15	=	8 15

The outcome is already as unproblematic as it can exist, and then that is the answer:

i 3 + ane five = 8 15

Making the Denominators the Same

In the previous example how did we know to cut them into ⁱ/₁₅ ths to make the denominators the aforementioned? We simply multiplied the two denominators together (3 × 5 = 15).

Read about the two main means to make 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

Example: Cupcakes

You lot want to make and sell cupcakes:

A friend can supply the ingredients, if you give them ⁱ/₃ of sales
And a market place stall costs ¹/₄ of sales

How much is that altogether?

We need to add ⁱ/₃ and ¹/₄

1 3 + 1 4 = ? ?

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

Multiply acme and bottom of ¹/₃ past 4:

i×iv 3×4 + 1 4 = ? ?

And multiply meridian and bottom of ^ane/₄ by 3:

1×4 3×4 + 1×iii 4×3 = ? ?

At present practice the calculations:

iv 12 + 3 12 = 4+3 12 = 7 12

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

Calculation Mixed Fractions

Nosotros have a special (more advanced) folio on Adding Mixed Fractions.

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