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Worker A picks a bucket of blueberries in `a` hours. Worker B picks a bucket of blueberries in `b` hours.
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i. `(a + b)/(ab)`
ii. `text(The reciprocal represents the number of hours it would)`
`text(take to fill one bucket, with A and B working together.)`
i. `text(In one hour:)`
COMMENT: Note that the question asks for “a fraction”.
`text(Worker A picks)\ 1/a\ text(bucket.)`
`text(Worker B picks)\ 1/b\ text(bucket.)`
`:.\ text(Fraction picked in 1 hour working together)`
`= 1/a + 1/b`
`= (a + b)/(ab)`
ii. `text(The reciprocal represents the number of hours it would)`
`text(take to fill one bucket, with A and B working together.)`
Simplify the expression `4/(y^2-16)+1/(3y-12)` (3 marks)
`(y+16)/(3(y^2-16))`
| `4/(y^2-16)+1/(3y-12)` | `=4/((y-4)(y+4))+1/(3(y-4))` | |
| `=12/(3(y-4)(y+4))+(y+4)/(3(y-4)(y+4))` | ||
| `=(y+16)/(3(y-4)(y+4))` |
Simplify the expression `(2p-1)/2+(p+1)/5` (2 marks)
`(12p-3)/10`
| `(2p-1)/2+(p+1)/5` | `=(5(2p-1))/10+(2(p+1))/10` | |
| `=(10p-5+2p+2)/10` | ||
| `=(12p-3)/10` |
Simplify the expression `(x-4)/3+(2x+1)/6` (2 marks)
`(4x-7)/6`
| `(x-4)/3+(2x+1)/6` | `=(2(x-4))/6+(2x+1)/6` | |
| `=(2x-8+2x+1)/6` | ||
| `=(4x-7)/6` |
Simplify the expression `3/(4x)+2/(5x)` (2 marks)
`23/(20x)`
| `3/(4x)+2/(5x)` | `=(3xx5)/(20x)+(2xx4)/(20x)` | |
| `=(15+8)/(20x)` | ||
| `=23/(20x)` |
Simplify the expression `(3a)/5+(a)/4` (2 marks)
`(17a)/20`
| `(3a)/5+(a)/4` | `=(12a)/20+(5a)/20` | |
| `=(17a)/20` |
Simplify the expression `x/4+(2x)/3` (2 marks)
`(11x)/12`
| `x/4+(2x)/3` | `=(3x)/12+(8x)/12` | |
| `=(11x)/12` |
Simplify the expression `p/2+p/3` (2 marks)
`(5p)/6`
| `p/2+p/3` | `=(3p)/6+(2p)/6` | |
| `=(5p)/6` |
Express `((2x-3))/2-((x-1))/5` as a single fraction in its simplest form. (2 marks)
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`(8x-13)/10`
`((2x-3))/2-((x-1))/5`
`= (5(2x-3)-2(x-1))/10`
`= (10x-15-2x + 2)/10`
`= (8x-13)/10`