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Question
Simplify each of the following and write as a rational number of the form \[\frac{p}{q}:\]
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Solution
\[\frac{- 4}{5} + \frac{- 7}{10} + \frac{- 8}{15}\]
\[ = \frac{- 24}{30} + \frac{- 21}{30} + \frac{- 16}{30}\]
\[ = \frac{( - 24) + ( - 21) + ( - 16)}{30}\]
\[ = \frac{- 24 - 21 - 16}{30}\]
\[ = \frac{- 61}{30}\]
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The table shows the portion of some common materials that are recycled.
| Material | Recycled |
| Paper | `5/11` |
| Aluminium cans | `5/8` |
| Glass | `2/5` |
| Scrap | `3/4` |
- Is the rational number expressing the amount of paper recycled more than `1/2` or less than `1/2`?
- Which items have a recycled amount less than `1/2`?
- Is the quantity of aluminium cans recycled more (or less) than half of the quantity of aluminium cans?
- Arrange the rate of recycling the materials from the greatest to the smallest.
