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In this word problem, we'll compare the weight of two objects using a ratio of integers. We'll practice simplifying a fraction, too. Created by Sal Khan.
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- is the information in the question accurate??(14 votes)
- The weight of the computers is accurate. The Mark I (1944) (Harvard University's electro-mechanical computer) weighted 4,500kg and was 16 meters in length and 2.4 meters tall. Today some laptops like the MacBook Air weight as little as 1.08kg.(41 votes)
- I don't understand what you mean as an integer is a whole number, like 1, -2, 12, -5? is there another way to explain this?(5 votes)
- Integers are zero, positive number and negative numbers, but no fractions or decimals.
so: 0, 1, 2, 3, 4, 5, 6, 7, ... etc.
and -1, -2, -3, -4, -5, -6, -7, .... etc.(7 votes)
- Every fraction a rational number but why is every rational number not a fraction?
-2 is a rational number so we can express it as -2/1 which is a fraction(4 votes)
- Every rational number can be be represented as a fraction, but not every rational number must be represented as a fraction.(6 votes)
- What's a ratio? I haven't been taught this.(3 votes)
- A ratio is a comparison between two quantities. It can written as a : b, a to b, or a/b, where a and b can be any number.(7 votes)
- So integers can ONLY be whole numbers? So does that mean decimals and fractions are NOT integers?(3 votes)
- I thought for fractions you can't have decimals for either numerator or denominator(3 votes)
- Why is the ration expressed as 5000/3 and not as 3/5000? Is there a rule?(2 votes)
- Because we were asked to give a ratio of the weight of the old computers to the weight of the new ones. If we were asked new to old, it would be 3/5000. Basically, the first case (the one in the video) shows us how much the old computers were heavier then the new ones, and the other would show how much the new ones are lighter than the old. It's essentially the same thing, just a different point of view.(2 votes)
- can ratios help with fractions(2 votes)
- I don't understand what you mean as an integer is a whole number, like 1, -2, 12, -5? is there another way to explain this?(2 votes)
- Integers will be whole numbers because by definition, integers do not contain decimals or fractions. So in this way, parts of their definition (or requirements) overlap.(1 vote)
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.