1. how many multiple of 7 that are between 100 and 1000
Solution:
`100/7` is `14` with a remainder of `2`
Smallest multiple of 7 greater than 100 is 15, `(7xx15=105)`
`1000/7` is `142` with a remainder of `6`
Largest multiple of 7 less than 1000 is 142, `(7xx142=994)`
So number of multiples of 7`=142-15+1=128`
2. how many multiple of 8 between 100 and 500
Solution:
`100/8` is `12` with a remainder of `4`
Smallest multiple of 8 greater than 100 is 13, `(8xx13=104)`
`500/8` is `62` with a remainder of `4`
Largest multiple of 8 less than 500 is 62, `(8xx62=496)`
So number of multiples of 8`=62-13+1=50`
3. how many multiple of 12 that are less than 100
Solution:
Smallest multiple of 12 greater than 1 is 1, `(12xx1=12)`
`100/12` is `8` with a remainder of `4`
Largest multiple of 12 less than 100 is 8, `(12xx8=96)`
So number of multiples of 12`=8`
Multiples of 12 less than 100
| 12 | `xx` | 1 | = | 12 |
| 12 | `xx` | 2 | = | 24 |
| 12 | `xx` | 3 | = | 36 |
| 12 | `xx` | 4 | = | 48 |
| 12 | `xx` | 5 | = | 60 |
| 12 | `xx` | 6 | = | 72 |
| 12 | `xx` | 7 | = | 84 |
| 12 | `xx` | 8 | = | 96 |
Multiples of 12 are `12,24,36,48,60,72,84,96`
This material is intended as a summary. Use your textbook for detail explanation.
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