COMMON TERMS AND EXAMPLES USED IN ARITHMETIC

ADDITION

Sum: The result of adding two or more terms or numbers.

Examples:

The sum of 3 and 4 is 7.

Find the sum of 3 and 4.

Let x = 3. If x is increased by 8, what is the result?

5 plus 2 is what number?

10 more than 50 is what?

Tom has seven more dimes than Richard. If Richard has 8 dimes, how many does Tom have altogether?

SUBTRACTION

Difference: The result obtained when one term or number is subtracted from another term or number.

Examples:

13 take away 6 is what?

6 subtracted from 13 is what number? 13 - 6 = ?

80 decreased by 8 is what? 80 - 8 = ?

If Mark is x years old and Karen is y years old, what is the difference in their ages? [Note: Here we don't know whether we need to compute x ‑ y or y ‑ x since we don't know whether x or y is larger. When comparing ages, for example, it is customary to represent the difference as a positive number.]

Caution: The order used when writing subtraction problems is important.

3 less than x is what? [Note: This is x ‑ 3 not 3 ‑ x. Plug in numbers to see this by letting x = 22: Then "3 less than 22" is 19 which implies we subtracted 3 form 22: 22 ‑ 3 = 19.]

MULTIPLICATION

Product: The result of multiplying two or more terms or numbers together.

Examples:

The product of 6 and 3 is what? 6 x 3 = ?

14 times 3 is what?

What is 6 multiplied by 0?

[Note: We can write 6 x 3 = 18,  = 18, 6(3) = 18, 6*3=18. When we use variables, we can eliminate any symbol for multiplication: = 3x, = AB.]

Note that x is a variable, or a letter that stands for a number, and 3 is a coefficient, or a number by which a variable is multiplied. The coefficient of "3x" is 3.

DIVISION

Quotient: The result obtained when one number or term or number is divided by another term or number.

Examples:

24 divided by 3 can be written 24  3 or or .

Here, 3 is the divisor, 24 is the dividend, and the quotient is 8. Since 24 is evenly divisible by 3, there is no remainder.

In this example, 24 is a multiple of 3

3 is a divisor of 24

3 is a factor of 24

24 is divisible by 3

Caution : As in subtraction, the order is important.

24 into 3 is the same as 3  24, not 24  3, and the problem would be written .