Multiplying

Multiplication Basics

Multiplication is one of the four basic operations in mathematics. It’s an operation that gives the product of two numbers.
It’s often described as repeated addition. For example, 5 multiplied by 3 (5x3) is the same as adding five, three times (5+5+5).

Times Tables

Mastering times tables is the foundation to efficient multiplication. Recalling these instantly can save time.
Times tables range from 1x1 to 12x12 in your foundation syllabus.
Practice and repetition can help in memorising the tables.

Properties of Multiplication

Communitative Property: The order of numbers does not change the result i.e. 3x4 is the same as 4x3.
Associative Property: Grouping of numbers does not change the result i.e. (3x2)x4 is the same as 3x(2x4).
Distributive Property: Allows you to multiply a sum by multiplying each addend separately and then add the products. i.e. 4x(3+2) equals to (4x3)+(4x2).
Identity Property: Any number multiplied by 1 remains the same i.e. 5x1 equals 5.
Zero Property: Any number multiplied by 0 results in 0 i.e. 5x0 equals 0.

Multiplying Fractions

Multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. Simplify the fraction if needed.
For example, the product of 2/3 and 3/5 is (2x3)/(3x5) which simplifies to 6/15, and then to 2/5 when reduced.

Multiplying Decimals

First ignore the decimal points and multiply the numbers as if they were whole numbers.
Count the numbers to the right of the decimal point in the original numbers. The answer should have the same total numbers to the right of the decimal.
For example, the product of 3.2 and 2.5 would be calculated as 32x25=800. Then place the decimal point in the product so there are two digits to the right of the decimal, resulting in 8.00.

Multiplication of Negative Numbers

The product of two negative numbers is a positive number. E.g., -3 x -2 = 6.
The product of a positive number and a negative number is a negative number. E.g., 5 x -3 = -15.

Remember, understanding multiplication is the basis for further mathematical calculations, like deriving powers, finding square roots, and solving equations.