## Lessson 2: Fractions III

October 18, 2010

### 4.2. Multiplying fractions

We do not need a common denominator when multiplying fractions.

To multiply two (or more) fractions,

 a · c b d

you have to:

• Multiply out the numerators and the result will be the numerator
• Multiply out the denominators and the result will be the denominator.
• “Tidy up” the result – simplify it if possible.

 a · c = a · c = Multiply the numerators b d b · d Multiply the denominators

Examples:

 1. Find 2 · 2 3 5

 2 · 2 = 2 · 2 = Multiply the numerators 3 5 3 · 5 Multiply the denominators = 4 15

You can learn why we multiply in this way on Descartes page. If you click on the rightarrow at the bottom of the screen you can also practise multiplication of fractions.

### 4.4. Dividing fractions

The reciprocal of a fraction (fracción inversa in Spanish) is another fraction such as the product of by its reciprocal is 1. It is obtained by interchanging the numerator and the denominator, i.e. by inverting the fraction.

Examples

When you turn the fraction upside down you have a RECIPROCAL of the original fraction.

Turning fraction upside down is also called inverting.

 A reciprocal of 3 is 4 4 3

To divide two fractions multiply the dividend by the reciprocal of the divisor.

You can do this by following few simple steps:

• Turn the second fraction (divisor) upside down.
• Change the divide sign to multiply sign and multiply the fractions.

Example

 Find 1 : 2 2 5

 1 : 2 = 1 · 5 = Change the sign to ·. 2 5 2 2 Invert (turn upside down) the divisor.

 = 1 · 5 = 5 Multiply the numerators. 2 · 2 4 Multiply the denominators.

Another way of dividing two fractions is by multiplying the terms of both fractions “crossing them”:

 a : c = a·d b d b·c

This method is very useful and we will use it most of the times. Practise on the IXL web.

### 5. Combined operations with fractions

Combined operations is an expression formed by fractions in different operations and grouped in different ways – by means of brackets, square brackets and braces {curly brackets}.

The aim of using brackets is to join or to group everything that is between them. You must respect an order to solve combined operations, the hierarchy:

1. What is inside the brackets and square brackets.
2. Powers and roots.
3. Multiplication and division from left to right.
4. Addition and subtraction from left to right

Be careful because mixed numbers appear frequently. Recall they mean an integer added to a proper fraction.

Finally, here you are a couple of videos on multiplying and dividing. Try to understand the explanation. If you have any difficulty, write to me.

### 6.1. Power of a fraction

To raise a fraction to a power you have to raise numerator and denominator to this power:

Example:

• (2/5)3 = 23 / 53 = 8 / 125

Practise on this web. You will find bases which are decimal numbers (fractions can express decimal numbers). Don’ t do those examples.

### 6.2. Root of a fraction

Square root of a fraction is the root of numerator divided by the root of denominator.

Perfect square root or exact square root of a fraction is a number whose square is equal to the fraction.