978-1-4730-1185-4 (.epub)

Prefix | Symbol | Meaning | Factor |
---|---|---|---|

micro- | μ | one millionth | 0.000001 |

milli- | m | one thousandth | 0.001 |

centi- | c | one hundredth | 0.01 |

deci- | d | one tenth | 0.1 |

kilo- | k | thousand | 1000 |

mega- | M | million | 1 000 000 |

giga- | G | thousand million | 1 000 000 000 |

1 ml = 1 cm ^{3}

Isaac | 1.098 |

Jasmine | 1.120 |

Kim | 1.100 |

To multiply by 0.4, multiply by 4 and shift the digits one place to the right, 52 × 4 = 208. So 52 × 0.4 = 20.8. So the hair will grow 20.8 cm in a year. (0.4 is just under a half and half of 52 is 26, so the answer is sensible.)

10÷ 0.4 = = (multiply top and bottom by 10). Now carry out the division: 100 ÷ 4 = 25. So it would take 25 weeks to grow 10 cm. (Check: 10 cm is about half of the previous answer of 20.8 cm which took a year, so will take about half a year. 25 weeks is near enough half a year, so the answer is sensible.)

Carrying out the division gives 7.5. Alternatively you might do it more informally: it grows 4 cm in 10 weeks, and 3 cm is three-quarters of 4 cm, so the answer is three-quarters of 10 weeks, i.e. × 10 = 7.5 weeks. Therefore it would take 7.5 weeks to grow 3 cm. (Check: 3 cm is a bit less than a third of 10 cm which takes 25 weeks, so will take a bit less than a third of 25 weeks. 7.5 weeks is near enough a third of 25 weeks, so the answer is sensible.)

‘First look at the bottom number of each fraction. If these are the same, then this is also the bottom number of the answer. To get the top number in the answer, add the two top numbers in the given fractions. ‘If the bottom numbers are different, multiply the topandbottomof the first fraction by thebottom numberof the second. Then multiply thetopandbottomof the second fraction by thebottomnumber of thefirst. Now the two fractions have thesame bottom numberso they can be added as above.’

‘To multiply two fractions, multiply the top two numbers together (the numerators) and multiply the bottom two numbers together (the denominators). To give the answer in its simplest form, check whether top and bottom numbers have a factor in common and, if so, divide through by it.’

‘To multiply two fractions by cancelling, find a number that goes into (divides) a number on the top and a number on the bottom i.e. cancel. Repeat this until there are no numbers left which will cancel with each other. Then multiply together the top two numbers (the numerators) and the bottom two numbers (the denominators). This fraction should be in its simplest form.’

Discussion 2020051800