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## 7th grade

### Course: 7th grade > Unit 3

Lesson 4: Rational number word problems- Rational number word problem: school report
- Rational number word problem: cosmetics
- Rational number word problem: cab
- Rational number word problem: ice
- Rational number word problem: computers
- Rational number word problem: stock
- Rational number word problem: checking account
- Rational number word problems

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# Rational number word problem: computers

CCSS.Math:

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.

## Want to join the conversation?

- is the information in the question accurate??(16 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.(44 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?(6 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.(9 votes)

- What's a ratio? I haven't been taught this.(4 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.(9 votes)

- Every fraction a rational number but why is every rational number not a fraction?

example

-2 is a rational number so we can express it as -2/1 which is a fraction(5 votes)- Every rational number
**can**be be represented as a fraction, but not every rational number**must**be represented as a fraction.(7 votes)

- So integers can ONLY be whole numbers? So does that mean decimals and fractions are NOT integers?(5 votes)
- Yep, decimals and fractions are forbidden from being an integer.(5 votes)

- I thought for fractions you can't have decimals for either numerator or denominator(3 votes)
- you can have decimals in the numerator and the denominator(4 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)
- a fraction can be the way of writing a ratio. ex. 2 girls to 1 boy can be written as 2 girls/1 boy(2 votes)

- Couldn't you also do 45,000 by 27 and 27 by 45,000 to find another ratio?(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)

## 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.