Rational number word problems
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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.