## More Number Work This topic contains material that is usually studied in later years, but continues on from the topics covered previously.

### Standard Form

Very large numbers, such 148 800 000 km the distance from the Earth to the Sun and very small numbers such as 0.000 000 23 can be written in a shorter way by using standard form.

Standard form, sometimes called scientific notation, is often used in science to show very large or very small numbers.

Numbers written in standard form are shown as the product of a number between 1 and 10 and a power of 10.

e.g. 327 = 3.27 × 102

0.46 = 4.6 × 10 -1

So in our examples above, the distance from the Earth to the Sun becomes 1.488 × 108 and 0.000 000 23 becomes 2.3 × 10-7

### Operations with Fractions

In the earlier topic on fractions we learnt what a fraction was and how to convert it to a decimal and percentage. In this section the addition, subtraction, multiplication and division of fractions will be covered.

When doing any fraction calculation always begin by changing any mixed numbers into improper fractions. If the calculation is very simple then the integers can be added together first, followed by the fractions.

e.g. 314 + 712 = 1034

• Step 1 If the denominators are different, change them to equivalent fractions with the same denominator.
• Step 2 Add or subtract the top lines only − never add or subtract the bottom lines!
• Step 3 Simplify where possible.

 Examples Answers Calculate: 3⁄5 + 4⁄5 3⁄5 + 4⁄5 = 7⁄5 = 12⁄5 8⁄9 − 5⁄6 8⁄9 − 5⁄6 = 16⁄18 − 15⁄18 = 1⁄18 13⁄4 + 22⁄5 13⁄4 + 22⁄5 = 65⁄20 + 88⁄20 = 153⁄20 = 713⁄20

Multiplication of fractions

• Step 1: Simplify by cancelling common factors between top and bottom lines.
• Step 2: Multiply the numerators together and then multiply the denominators together.

 Examples Answers Calculate: 3⁄9 × 4⁄8 = 1⁄3 × 1⁄2  = 1⁄6 (by cancelling) 31⁄2 × 13⁄7 31⁄2 × 13⁄7 = 7⁄2 × 10⁄7 =  1⁄1 × 5⁄1 = 5

Division of fractions

• Step 1 Turn the second fraction upside down (to make it into the reciprocal)
• Step 2 Change the operation sign to multiply,

 Examples Answers Calculate: 5⁄6 ÷ 5⁄12 5⁄6 ÷ 5⁄12 = 5⁄6 × 12⁄5 = 1⁄1 × 2⁄1 = 2 51⁄4 ÷ 13⁄5 51⁄4 ÷ 13⁄5 = 21⁄4 × 5⁄8 = 105⁄32 = 39⁄32

### Percentage Calculations

Increasing a quantity by a percentage:

To increase a quantity by x percent. Calculate: Example Answer Increase 50 by 8% Decreasing a quantity by a percentage:

To decrease a quantity by x percent. Calculate: Example Answers Decrease 50 by 8% 