Practice Rational numbers
Rational numbers can be written as a ratio of two integers with a nonzero denominator.
They include fractions and terminating or repeating decimals.
Exercises with solutions
Rational numbers are all numbers that can be written as a fraction of two integers, so they include negative numbers and decimals. For calculating with signs: with the same signs you add the magnitudes, with different signs you subtract the smaller magnitude from the larger and take the sign of the larger.
Exercise 1
Calculate −8 + 3.
Show solution and working
−5
Different signs: 8 − 3 = 5. The larger magnitude belongs to −8, so the result is negative.
Exercise 2
Calculate −8 + (−3).
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−11
Same signs: the magnitudes are added. 8 + 3 = 11 and the result stays negative.
Exercise 3
Calculate −5 · (−4).
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20
Minus times minus gives plus: 5 · 4 = 20.
Exercise 4
Calculate −12 ÷ 4.
Show solution and working
−3
Minus divided by plus gives minus: 12 ÷ 4 = 3, so the result is −3.
Common mistake
Forgetting the sign rule when multiplying and dividing: minus times minus gives plus. And adding the magnitudes even though the signs differ.
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