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Video: Comparing Expressions Involving Multiplication and Division of Decimal Numbers

Tim Burnham

Calculate 947 ÷ 0.89 _ (947 ÷ 8.9) × 0.01 using <, = or >.

02:48

Video Transcript

Complete nine hundred and forty-seven divided by nought point eight nine is something to nine hundred and forty-seven divided by eight point nine times nought point nought one using the less than sign, the equal to sign, or the greater than sign.

So we’ve got two different expressions and we’ve got to decide which one is bigger than the other. Now if I can rearrange the expression on the right-hand side so that it contains exactly the same expression on the left-hand side but multiplied or divided by something, that will help me to decide which is the bigger expression.

Well in fact to make my life easier, before I start I’m going to reexpress the left-hand side: nine hundred and forty-seven divided by nought point eight nine can be rewritten as nine hundred and forty-seven over nought point eight nine.

So now let’s do a similar thing to the right-hand side: nine hundred and forty-seven divided by eight point nine can be rewritten as nine hundred and forty-seven over eight point nine, and of course that’s got to be multiplied by nought point nought one.

Now nought point nought one has got a one in the hundredths column, so that means one hundredth. So I’m going to write this as, instead of nought point nought one, I’m gonna write it as one hundredth, one over a hundred.

Now these two terms here look quite a lot like each other. We’ve got nine hundred and forty-seven over zero point eight nine, and we’ve got nine hundred and forty-seven over eight point nine. Now I’m gonna reexpress eight point nine as nought point eight nine times ten; if I multiply nought point eight nine by ten, I get eight point nine.

And because I’m multiplying two fractions together on this right-hand side over here, it doesn’t matter whether I do the multiplying by ten over here or if I move it to over here, and that’s what I’m gonna do.

And now I’ve got nine hundred and forty-seven over nought point eight nine here, and I’ve got nine hundred and forty-seven over nought point eight nine here. But in this case, I’m multiplying it by one over a hundred times ten, or one over a thousand.

So we’ve got the same expression or the same term here and here, but on the right-hand side, we’re gonna take that expression and multiply it by a thousandth or divide by a thousand; we’re gonna make it smaller. So that’s gonna be the smaller number, and this one is gonna be the bigger number.

So we can write our sign this way round: nine hundred and forty-seven divided by nought point eight nine is greater than nine hundred and forty-seven divided by eight point nine times nought point nought one. So there we have our answer.