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, subtracting a negative gives a positive.

Adding negative fractions

Evaluate $-\frac{2}{3} + \left(-\frac{3}{4}\right)$ .

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LCM

= 12

= -\frac{8}{12} + \left(-\frac{9}{12}\right)

= -\frac{17}{12}

= -1\frac{5}{12}

Multiplying and dividing fractions with negatives

Division of fractions

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Dividing fractions with negatives

Evaluate $\left(-\frac{5}{6}\right) \div \frac{10}{9}$ .

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= \left(-\frac{5}{6}\right) \times \frac{9}{10} \quad \scriptsize\textit{multiply by reciprocal}

= -\frac{45}{60}

= -\frac{3}{4} \quad \scriptsize\textit{simplify}

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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 $(-0.5)^2 \times 12 - (-1.8) \div 0.3$ .

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(-0.5)^2 = 0.25

0.25 \times 12 = 3

(-1.8) \div 0.3 = -6

3 - (-6) = 3 + 6 = 9

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

Practise Integers, Rational Numbers and Real Numbers