Why Turn Fraction Upside Down?

Well ... what Does a Fraction Do?

A fraction says to:
multiply by the top number divide by the bottom number

Example: 3/4 means to cut into 4 pieces, and then take 3 of those. So you: divide by 4 multiply by 3

Example: ³/₄ of 20 is:

20 divided by 4, then times 3 = (20/4) × 3 = 5 × 3 = 15

Or you could multiply before dividing:

20 times 3, then divide by 4 = (20 × 3) / 4 = 60/4 = 15

Either way gets the same result

 Dividing

But when you DIVIDE by a fraction, you are asked to do the opposite of multiply ...

So you:

• divide by the top number
• multiply by the bottom number

Example: dividing by ⁵/₂ is the same as multiplying by ²/₅

Because:

Dividing by 5, then Multiplying by 2

is the same as

Multiplying by 2, then Dividing by 5

So instead of dividing by a fraction, it is easier to turn that fraction upside down, then do a multiply.

Dividing Fractions

1	÷	1
2		6

Step 1. Turn the second fraction upside-down (it becomes a reciprocal):

1	becomes	6
6		1

Step 2. Multiply the first fraction by that reciprocal:

1	×	6	=	1 × 6	=	6
2		1		2 × 1		2

Step 3. Simplify the fraction:

6	=	3
2

Dividing Fractions Song

Let's sing together this song of dividing fractions!

I can do it, you can do it, he can do it, she can do it!

Multiplying Fractions

There are 3 simple steps to multiply fractions

1. Multiply the top numbers (the numerators).

2. Multiply the bottom numbers (the denominators).

3. Simplify the fraction if needed.

Example 1

1	×	2
2		5

Step 1. Multiply the top numbers:

1	×	2	=	1 × 2	=	2
2		5

Step 2. Multiply the bottom numbers:

1	×	2	=	1 × 2	=	2
2		5		2 × 5		10

Step 3. Simplify the fraction:

2	=	1
10		5

Example 2

1	×	9
3		16

Step 1. Multiply the top numbers:

1	×	9	=	1 × 9	=	9
3		16

Step 2. Multiply the bottom numbers:

1	×	9	=	1 × 9	=	9
3		16		3 × 16		48

Step 3. Simplify the fraction:

9	=	3
48		16

Subtracting Fractions from a Whole Number

Subtracting Fraction With The Different Denominator

1	–	1
2		6

Step 1. The bottom numbers are different. See how the slices are different sizes? We need to make them the same before we can continue, because we can't subtract them like this:

	1/2	-	1/6	=	?

To make the bottom numbers the same, multiply the top and bottom of the first fraction (¹/₂) by 3 like this:

× 3

1	=	3
2		6

× 3

And now our question looks like this:

	3/6	-	1/6

The bottom numbers (the denominators) are the same, so we can go to step 2.

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

3	–	1	=	3 – 1	=	2
6		6		6		6

In picture form it looks like this:

	3/6	-	1/6	=	2/6

Step 3. Simplify the fraction: 

2	=	1
6		3