The Singing Hedgehog Guide
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Ratio and Proportion 5

This method for proportion might seem a little cumbersome

but it prevents silly errors and allows good checking.

Here is an example to show this:

We start by writing all of the question in a ratio form:

Notice that I have put a blank row in the middle.

This is deliberate and not caused by too much whisky!

Now we look to see how to turn 20 into 55;

this is not obvious so we will start with something easier!

We will first turn 20 into 1, then turn 1 into 55.

If you look at all this and say,

"but it's obvious to divide by 20 and times by 55"

then good but unfortunately there are as many who will go,

"but it's obvious to divide by 55 and times by 20"

especially if the numbers are the other way round as in the next example:
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Ratio and Proportion 5

This method for proportion might seem a little cumbersome

but it prevents silly errors and allows good checking.

Here is an example to show this:

A car travels 20km for each litre of petrol.

How many litres will it use to travel 55km in this car?

How many litres will it use to travel 55km in this car?

We start by writing all of the question in a ratio form:

travel | : | petrol |

20km | : | 1l |

: | ||

55km | : |

Notice that I have put a blank row in the middle.

This is deliberate and not caused by too much whisky!

Now we look to see how to turn 20 into 55;

this is not obvious so we will start with something easier!

We will first turn 20 into 1, then turn 1 into 55.

travel | : | petrol | |

20km | : | 1l | |

1km | : | 1/20 l | to turn 20 into 1 we divide by 20, so we also divide 1l by 20 |

55km | : | 55x1/20 l = 2.75l | to turn 1 into 55 we times by 55 so we also times the other number by 55 |

If you look at all this and say,

"but it's obvious to divide by 20 and times by 55"

then good but unfortunately there are as many who will go,

"but it's obvious to divide by 55 and times by 20"

especially if the numbers are the other way round as in the next example:

return to SHG main page