1
Arithmetic & algebra
You use arithmetic whenever you count money or make calculations. Algebra is very useful in science because it enables us to write formulas, for example, and to write computer programs.
Arithmetic
The addition, subtraction, multiplication, and division of numbers
A sum of several numbers is their total when added together. For example, 15 is the sum of 7 and 8. A product is the result of multiplying numbers, so 15 is the product of 3 and 5. Multiples are numbers given by multiplying one number by others. The numbers 8, 12, and 16 are multiples of 4 (4x2 = 8;4x3 = 12;4x4= 16). A quotient is the whole number result of a division, and the remainder is any amount left over. When 7 is divided by 3, it gives a quotient of 2 and a remainder of 1.
Sequence
A set of numbers that have a particular relationship
The numbers 2, 4, 6, 8, 10, and so on, form a sequence of even numbers, because all are multiples of 2. A sequence is also called a series. An arithmetic progression is a series in which you add or subtract the same number each time to get the next number, such as: 4, 7, 10, 13, 16, and so on (start at 4 and add 3 each time). In a geometric progression, you multiply or divide by the same number each time to get the next number, such as: 2, 4, 8, 16, 32, and so on (start at 2 and multiply by 2 each time). In the Fibonacci series, each number is the result of adding together the two previous numbers, such as: 1, 1,2, 3,5,8, 13,21,34, 55, and so on.
Magic square
A square array of numbers in which the columns, rows, and diagonals each add up to the same total
Magic square
In this magic square, any three numbers in a straight line add up to 15.
Parentheses
The symbols ( and )
Parentheses surround any operation in arithmetic, such as adding or multiplying, that must be carried out first. So 3 + (4 x 2) = 3 + 8 = 11, but (3 + 4) x2 = 7x2 = 14.
Calculus
The use of algebra to calculate changing quantities
Calculus deals with quantities such as curving lines. It can, for example, calculate the slope of the line at any point and the area under any part of a curve.
Probability
The degree of chance that something might happen
Probability ranges from 0 (will not happen) to 1 (will happen). Throwing a die to get 5 has a probability of 1/6, as this is one result out of six possible results.
Percentage
A fraction given as a number that you have to divide by 100
4 is equal to 75 + 100, so 3/4 is often shown as 75 per cent (75%).
Ratio
A comparison between two numbers or amounts
The masses of two objects of 10 kilograms and 2 kilograms are in the ratio 5:1 (5 to 1). You divide two numbers or amounts to get their ratio. Two amounts that vary are proportional if they always have the same ratio.
Algebra
The use of letters to represent quantities in calculations
The area of a rectangle is the length multiplied by the width. If we call the length 1 and the width w, the area of any rectangle is IX ■w, or lw. The letters I and w stand for numbers - in this case, the actual length of either side in units such as inches. I and u> are variables, meaning that they can take any value. A calculation using variables, such as Iw, is called an expression. Algebra often uses x and y as variables.
Equation
A mathematical statement that two quantities or expressions are equal
In your pocket are nine coins marked 10 and 5. If the total value is 65, how many of each kind are there? You can calculate the answer using an equation. Let the number of "10" coins be x. Their value is lOx. The number of "5" coins is 9—x, and their value is 5(9-x). As the values total 65, this gives us the equation: 65 = lOx + 5(9-x). Solving this equation shows that x = 4, so there must be four coins marked 10 and five coins marked 5.
2
3