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## Rational number word problems

Current time:0:00Total duration:2:33

# Rational number word problem: computers

CCSS.Math:

## Video transcript

In the year 1944, computers
weighed as much as 4,500 kilograms. A modern laptop weighs
around 2.7 kilograms. What is the ratio of how much
computers weighed in 1944 to how much a modern
laptop weighs? Express your answer as
a ratio of two integers. So the ratio of how much
computers weighed in 1944-- so we know that's 4,500
kilograms-- we want the ratio of that to how
much a modern laptop weighs, and that's 2.7 kilograms. So this right over
here is a ratio. But we haven't expressed it
as a ratio of two integers. In particular,
4,500 is an integer. But 2.7 is not an integer. So the easy way to
convert 2.7 to an integer is to move the decimal
place one to the right. Or another way of thinking about
it is to multiply it by 10. So we can multiply this by 10. But if we just multiplied
the denominator by 10, that would change the
value of the ratio. In order to not
change the value, we have to multiply the
numerator and the denominator by 10. This is equivalent to just
multiplying this fraction by 10/10, which is
the same thing as one. It does not change the value. So what do we get? Well, in the numerator,
4,500 times 10 is 45,000. I'll put a comma here. It makes it a little
bit easier to read. And in the
denominator-- and this is the whole point of why
we multiplied by 10-- 2.7 multiplied by 10 is 27. So we now have
expressed our answer as a ratio of two integers. So this is completely
legitimate. But we could also simplify this. Just looking at this,
it looks like 45,000 is divisible by 45,
which is divisible by 9. And 27 is also divisible by 9. So why don't we divide the
numerator and the denominator both by 9? So we're going to divide
by 9 in the numerator, and we're going to divide
by 9 in the denominator. And we are going to get
45 divided by 9 is 5. So 45,000 divided by 9 is 5,000. So we're going to get 5,000
over-- 27 divided by 9 is 3. And I think we have now
simplified this about as much as we can.