Mathfinity ∞

First theory lesson · Part A

Sum, difference, product and quotient

Your goal: recognise the four operations and use their mathematical names.

Operation	Name of the result	Example
Addition (+)	Sum	8 + 11 = 19
Subtraction (−)	Difference	12 − 7 = 5
Multiplication (× or ·)	Product	3 × 8 = 24
Division (÷)	Quotient	24 ÷ 3 = 8

1. Sum and terms

Adding numbers gives their sum. The numbers you add are called terms.

8 + 11 = 19

8 and 11 are the terms; 19 is their sum.

2. Difference

Subtracting one number from another gives their difference. Keep the numbers in the stated order.

12 − 7 = 5

The difference between 12 and 7 is 5.

3. Product and factors

Multiplying numbers gives their product. The numbers you multiply are called factors.

3 × 8 = 24

3 and 8 are factors; 24 is their product. Also: 3 × 8 = 8 + 8 + 8.

4. Quotient

Dividing one number by another gives their quotient. Division and multiplication are related.

24 ÷ 3 = 8 because 3 × 8 = 24

The quotient of 24 and 3 is 8.

Worked example · Turn words into a calculation

Calculate the sum of the product of 4 and 5 and the quotient of 8 and 2.

Product: 4 × 5 = 20.
Quotient: 8 ÷ 2 = 4.
Sum: 20 + 4 = 24.

In one calculation: (4 × 5) + (8 ÷ 2) = 24.

First theory lesson · Part B

Order of operations

Your goal: calculate in the correct order, including brackets.

The three rules

Brackets first. Calculate what is inside the brackets. Use these same rules inside them.
Multiply and divide from left to right. They have equal priority.
Add and subtract from left to right. They also have equal priority.

Multiplication before addition

7 + 5 · 8 = 7 + 40 = 47

The dot · means multiplication, just like ×. Multiply 5 and 8 first.

Equal priority means left to right

Multiplication does not always come before division.

48 ÷ 6 · 2 = 8 · 2 = 16

Likewise, addition does not always come before subtraction.

13 − 5 + 7 = 8 + 7 = 15

Brackets change the calculation

(7 + 5) · 8 = 12 · 8 = 96 7 + 5 · 8 = 7 + 40 = 47

With brackets, add first. Without brackets, multiply first.

Worked example · One step at a time

(20 − (20 − 8)) · 3 − 18 ÷ 9 = (20 − 12) · 3 − 18 ÷ 9 = 8 · 3 − 18 ÷ 9 = 24 − 2 = 22

Start with the inner brackets, then the outer brackets. Next multiply and divide. Finally subtract.

Avoid this mistake: 2 + 7 · 5 is 37, because 7 · 5 = 35. Adding 2 and 7 first would give 45.

Practise · A and B separately

Check your understanding

Write the calculation in your notebook, then enter the result. Use a hint or view a worked solution whenever you need help.