Arithmetic » Sum, difference, product and quotient

Sum
Difference
Product
Quotient

Sum

The sum of two or more numbers is the outcome of adding these numbers.
Example: Calculate the sum of 13, 5 and 8.
Answer: 13 + 5 + 8 = 26

The parts you add are called terms.
Example: Which terms are in the formula y = 3x2 + 6x + 8?
Answer: Three terms, namely 3x2, 6x and 8.

Difference

The difference of two numbers is the outcome of subtracting these numbers.
Example: Calculate the difference of 80 and 14.
Answer: 80 – 14 = 66

The parts you subtrect are also called terms.
The terms in the example 80 – 14 are 80 and –14.
This is because you can write 80 – 14 as 80 + –14.
Example: Which terms are in the formula y = 5x2 – 4x – 8?
Answer: Three terms, namely 5x2, –4x and –8.

Product

The product of two or more numbers is the outcome of multiplying these numbers.
Example: Calculate the product of 12 and 7.
Answer: 12 × 7 = 84

The parts you multiply are called factors.
Example: Which factors are in the formula y = 5x(x – 4)?
Answer: Three factors, namely 5, x and x – 4.

Terms and factors

In formulas you will often come across terms within factors or factors within terms.

Example 1
Name the parts of the formula y = 7x2 – 12x.
The formula is written as the sum of terms 7x2 and –12x.
the term 7x2 consists of factors 7 and x2.
The term –12x consists of factors –12 and x.

Example 2
Name the parts of the formula y = (7x – 8)(3x + 5).
The formula is written as the product of factors 7x – 8 and 3x + 5.
The factor 7x – 8 consists of terms 7x and –8, where term 7x consists of factors 7 and x.
The factor 3x + 5 consists of terms 3x and 5, where term 3x consists of factors 3 and x.

Quotient

The quotient of two numbers is the outcome of the division of these numbers.
Example: Calculate the quotient of 20 and 4.
Answer: 20 : 4 = 5

In the example above, 20 is called the dividend and 4 the divisor.