We've already learned how to add, subtract, multiply and divide fractions. Similarly, we've looked at each of these operations with negative numbers.
The process is just the same when we have questions with negative fractions - we'll just combine these two skills and their rules to complete the operation.
Using the number line or zero pairs may be helpful with working positive and negative fractions.
Calculate: $3+4-\left(-\frac{4}{5}\right)$3+4−(−45).
Think: We will evaluate the addition and subtraction, working from left to right.
Do:
$3+4-\left(-\frac{4}{5}\right)$3+4−(−45) | $=$= | $7-\left(-\frac{4}{5}\right)$7−(−45) |
$=$= | $7+\frac{4}{5}$7+45 | |
$=$= | $7\frac{4}{5}$745 |
Reflect: What if this problem were written as a decimal? Is $3+4-\left(-0.8\right)$3+4−(−0.8) easier to compute? Do you still end up with the same solution when you convert the decimal back to a mixed number?
Evaluate $-10\times\left(-2\frac{1}{4}\right)$−10×(−214), giving your answer as a mixed number in simplest form.
Evaluate $-8\frac{4}{7}+3\frac{3}{7}$−847+337, writing your answer as a mixed number in its simplest form.
Evaluate $4\frac{2}{3}\div\left(-1\frac{2}{5}\right)$423÷(−125), giving your answer as a mixed number in simplest form.
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Represent addition and subtraction on a horizontal or vertical number line.
(d) Apply properties of operations as strategies to add and subtract rational numbers.
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
(c) Apply properties of operations as strategies to multiply and divide rational numbers.