The four basic arithmetic operations are addition, subtraction, multiplication, and division.
Word problems contain clue words that help determine which operation to use.
Operations Word Problems
Addition sum, together, (in) total, all, in addition, increased, give
Leslie has 3 pencils. If her teacher gives her 2 pencils, how many does she now have in total?
3 + 2 = 5 pencils
minus, less than, take away, decreased, difference, how many left, How many more/less
Sean has 12 cookies. His sister takes 2 cookies. How many cookies does Sean have left?
12 − 2 = 10 cookies
product, times, of, each/every, groups of, twice
A hospital department has 10 patient rooms. If each room holds 2 patients, how many patients can stay in the department?
10 × 2 = 20 patients
divided, per, each/every, distributed, average, How many for each
A teacher has 150 stickers to distribute to her class of 25 students. If each student gets the same number of stickers, how many stickers will each student get?
150 ÷ 25 = 6 stickers
Positive numbers are greater than zero, and negative numbers are less than zero. Use the rules in the table below to determine the sign of the answer when performing operations with positive and negative numbers.
Operations with Positive and Negative Numbers
Multiplication and Division
positive + positive = positive
4 + 5 = 9
positive × positive = positive
5 × 3 = 15
negative + negative = negative
−4 + (−5) = −9 → −4 − 5 = −9
negative × negative = positive
−6 × (−5) = 30
negative + positive = sign of the larger number
−15 + 9 = −6
negative × positive = negative
−5 × 4 = −20
Subtraction is the same as adding a negative value.
5 – 7 = 5 + (−7) = −2
A number line shows numbers increasing from left to right (usually with zero in the middle). When adding positive and negative numbers, a number line can be used to find the sign of the answer. When adding a positive number, count to the right. When adding a negative number, count to the left.
Operations in a mathematical expression are always performed in a specific order, which is described by the acronym PEMDAS:
Perform the operations within parentheses first, and then address any exponents. After those steps, perform all multiplication and division. These are carried out from left to right as they appear in the problem. Finally, do all required addition and subtraction, also from left to right as each operation appears in the problem.
Simplify the expression (32 − 2)2 + (4)53.
(32 − 2)2 + (4)53
= (9 − 2)2 + (4)53
= 72 + (4)53
= 49 + (4)125
Multiplication and division
= 49 + 500
Addition and subtraction
When working with complicated expressions, underline or highlight the operation being performed in each step to avoid confusion.
Rational numbers can be ordered from least to greatest, or greatest to least, by placing the numbers in the order in which they appear on a number line.
Order the numbers from least to greatest:
Convert each fraction to a decimal:
Plot each decimal value on a number line.
Order from least to greatest (left to right on the number line) using the original given values.
Drawing a number line can help when comparing numbers. The final list should be ordered from left to right (least to greatest) or right to left (greatest to least) on the line.