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Integers, Rational Numbers and Real Numbers

Chapter 2 Study Notes · O-Level 4052

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Section 6 of 8
Contents▾
Why Negative Numbers Matter2.1Negative Numbers and Ordering2.2Addition and Subtraction of Integers2.3Multiplication and Division of Integers2.4Combined Operations (BODMAS)2.5Operations on Fractions and Decimals with Negatives2.6Rational and Irrational NumbersChapter Summary

2.5Operations on Fractions and Decimals with Negatives

Recall: LCM from Chapter 1 is used to find common denominators when adding fractions.→

Adding and subtracting fractions with negatives

Find a common denominator, then add or subtract the numerators. Apply the sign rules: adding two negatives gives a negative, and subtracting a negative turns into adding, so the two signs become a plus. The result can still be negative.

Adding negative fractions

Evaluate −23+(−34)\displaystyle -\frac{2}{3} + \left(-\frac{3}{4}\right).

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−23+(−34)-\frac{2}{3} + \left(-\frac{3}{4}\right)
=−812+(−912)LCM is 12= -\frac{8}{12} + \left(-\frac{9}{12}\right) \quad \scriptsize\textit{LCM is 12}
=−1712= -\frac{17}{12}
=−1512= -1\frac{5}{12}

Multiplying and dividing fractions with negatives

Division of fractions
ab÷cd=ab×dc\displaystyle \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Dividing fractions with negatives

Evaluate (−56)÷109\displaystyle \left(-\frac{5}{6}\right) \div \frac{10}{9}.

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=(−56)×910multiply by reciprocal= \left(-\frac{5}{6}\right) \times \frac{9}{10} \quad \scriptsize\textit{multiply by reciprocal}
=−4560= -\frac{45}{60}
=−34simplify= -\frac{3}{4} \quad \scriptsize\textit{simplify}

Now you try

Evaluate −56+(−56)-\frac{5}{6} + \left(-\frac{5}{6}\right).

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Same denominator: add the numerators.
−56+(−56)\displaystyle -\frac{5}{6} + \left(-\frac{5}{6}\right)
=−106\displaystyle = -\frac{10}{6}
=−53\displaystyle = -\frac{5}{3}

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Operations on decimals with negatives

The same sign rules apply to decimals. Students are expected to use calculators for decimal arithmetic.

Combined decimal operations

Evaluate (−0.5)2×12−(−1.8)÷0.3\displaystyle (-0.5)^2 \times 12 - (-1.8) \div 0.3.

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(−0.5)2\displaystyle (-0.5)^2
=0.25\displaystyle = 0.25
0.25×12\displaystyle 0.25 \times 12
=3\displaystyle = 3
(−1.8)÷0.3\displaystyle (-1.8) \div 0.3
=−6\displaystyle = -6
3−(−6)\displaystyle 3 - (-6)
=3+6\displaystyle = 3 + 6
=9\displaystyle = 9

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Questions on Integers, Rational Numbers and Real Numbers, marked as you go, with the working shown.

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