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Need help with division

So im in year 9 and we were doing some division.

The question i was stuck with was 28÷35 I was pretty confused, we're not allowed to use the calculator but I check when I got home. 28÷35 is the same as 4over5 which is the same as 0.80 To get this you'd have to divide both numbers by 7. Would this always be the case? As in, would I always have to look for multiples? I know how to use the busstop method but I couldn't work it out with these numbers

Any idea on how to tackle them?
Original post by kensusan
So im in year 9 and we were doing some division.

The question i was stuck with was 28÷35 I was pretty confused, we're not allowed to use the calculator but I check when I got home. 28÷35 is the same as 4over5 which is the same as 0.80 To get this you'd have to divide both numbers by 7. Would this always be the case? As in, would I always have to look for multiples? I know how to use the busstop method but I couldn't work it out with these numbers

Any idea on how to tackle them?


Start by thinking about multiplying fractions. If I multiply a fraction by 1, it doesn't change its value e.g.

34×1=34\frac{3}{4} \times 1 = \frac{3}{4}

But I also know that if I divide any number by itself, I get 1 e.g.

1=22=33=44=⋯1 = \frac{2}{2} = \frac{3}{3} = \frac{4}{4} = \cdots

where I'm thinking of those as divisions rather than so much as fractions.

So I can write:

34×1=34×22=3×24×2=68\frac{3}{4} \times 1 = \frac{3}{4} \times \frac{2}{2} = \frac{3 \times 2}{ 4 \times 2} = \frac{6}{8}

or similarly

34×1=34×33=3×34×3=912\frac{3}{4} \times 1 = \frac{3}{4} \times \frac{3}{3} = \frac{3 \times 3}{ 4 \times 3} = \frac{9}{12}

This shows clearly that 6/8 and 3/4 and also 9/12 and 3/4 are actually the same number, with the same value.

Why is that? It's simply because I turned 3/4 into 6/8 by multiplying it by 1, which can't change its value - however, I was a bit sneaky and multiplied it by a fraction which I knew was equal to 1 (because of the division of a number by itself). So I managed to change the appearance of the fraction without changing its value. The fractions that we end up with when we do this are called "equivalent fractions".

I can turn the whole process around, though e.g.

1624=2×83×8=23×88=23×1=23\frac{16}{24} = \frac{2 \times 8}{3 \times 8} = \frac{2}{3} \times \frac{8}{8} = \frac{2}{3} \times 1 = \frac{2}{3}

This shows that 16/24 and 2/3 are equivalent fractions i.e. they have the same value, and are really the same number (i.e. they occupy the same point on the number line).

That process is called "cancelling down" - to do so, you must look for common factors in the numerator and denominator, then use the rules of fraction multiplication to extract them in the form "x/x", then note that that number is really 1, by division.

You may wish to think about why we have to use multiplication when creating equivalent fractions - why can't we use addition?

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