Positive and negative numbers practice
Signed numbers are the first topic of secondary-school maths and the basis of every later calculation. Master the sign rules.
Basic, Standard, Advanced: Grade 7 · Term 1
Math problem generator
Addition and subtraction
Same signs: add the absolute values and keep the sign.
Different signs: subtract the smaller absolute value from the larger and take the sign of the number with the larger absolute value.
To subtract, add the opposite: .
With many terms, drop the brackets and group the positive and negative terms:
Multiplication and division
Same signs give a positive product or quotient; different signs give a negative one. With several factors, an even number of negatives gives and an odd number gives .
Example: . Division can be written as multiplication by the reciprocal: .
Powers and mixed operations
, but . Check what the exponent applies to.
powers and brackets, then multiplication and division, then addition and subtraction
The distributive law avoids common denominators when a bracket of fractions is multiplied by an integer.
Worked examples
Calculate.
Hint
The method depends on whether the signs are the same or different.
Answer
Solution
Different signs: subtract the smaller absolute value from the larger and use the sign of the number with the larger absolute value.
Calculate.
Hint
Same signs give a positive product or quotient; different signs give a negative one.
Answer
Solution
Decide the sign, then compute with the absolute values.
Calculate.
Hint
Powers, then brackets, then × and ÷, then + and −.
Answer
Solution
Follow the order of operations.
Practice problems
Arrange the numbers from smallest to largest.
Hint
For negative numbers, the larger the absolute value, the smaller the number.
Answer
Solution
Negatives, then 0, then positives. Among negatives, the one with the larger absolute value is smaller.
Calculate.
Hint
An even number of negative factors gives +, an odd number gives −.
Answer
Solution
There are 2 negative numbers, so the sign is +.
Compute with the absolute values.
Calculate using the distributive law.
Hint
Using avoids a common denominator.
Answer
Solution
Multiply each term in the parentheses.