Dividing whole numbers by decimals (hundredths) -pencils
About this video
Specialty pencils cost 27 cents each and the factory made $135, so the number sold is 135 ÷ 0.27. Multiplying the top and bottom by 100 turns this into 13,500 ÷ 27, which long division shows is 500 pencils. A gut check (27 × 1,000 = 27,000, so 27 × 500 = 13,500) confirms it.
You'll be able to
- set up a word problem as total ÷ price per item.
- multiply the top and bottom by 100 to remove a decimal in hundredths.
- use long division and a quick estimate to check my answer.
Key words
- hundredths
- Parts made by splitting one whole into 100 equal pieces; 27 cents is 27 hundredths of a dollar.
- numerator and denominator
- The top and bottom of a fraction; when division is written as a fraction, the top is divided by the bottom.
- gut check
- A quick estimate to see whether an answer is sensible.
Transcript
- [Narrator] We're told at a pencil factory, specialty pencils sell for 27 cents each. In one week, the pencil factory sold $135 worth of specialty pencils. How many pencils were sold during this week? Pause this video, try to figure that out. So let's think about it.
If we take the number sold and we multiply by the price per pencil, we're going to get the total amount. Or another way of thinking about it, if we take the total and we were to divide it by the price per pencil, then that is going to give us the number sold. So in this situation, the total amount of dollars for the sales of these pencils is $135.
So we're gonna take 135 and we're going to divide it by the price per pencil. In this case, that is 27 cents. Now, I didn't write the dollar signs here, I could have, but this simplifies it a little bit. So how do we divide 135 by 27 100ths in this case? Well, one thing we could do is multiply both the numerator and the denominator of this fraction, we've just expressed division as a fraction here so that we can get rid of these decimals.
For example, if I multiplied 27 100ths times 100, that's going to be 27. But I can't just multiply only the denominator by something, in order to not change the value of this fraction, I have to multiply both the numerator and the denominator by the same thing.
Now I'm essentially just multiplying it by a 100/100 which is the same thing as one, so I'm not changing its value. So what's this going to be equal to? Well, 135 times 100 is gonna be 135 with two zeros, or 13,500. And then if we were to take 27 100ths and multiply that times 100, as I mentioned, that is just going to be equal to 27.
And now we've been able to rewrite this exact same expression, but write it in a way that we don't have any decimals anymore. This is going to be the same thing as 13,500 divided by 27, and we know how to do that. So 13,000, lemme give myself some space. 13,500 divided by, divided by 27.
A little bit of long division now. 27 doesn't go into one, doesn't go into 13, it does go into 135. Let's see, five times 20 is 100. Five times seven is 35, oh, it looks like it goes exactly five times. Five times seven is 35. Five times two is 10, plus three is 13.
It all works out. Subtract, nothing there. Bring down another zero. 27 goes into zero, zero times, multiply it by 27. I don't necessarily have to go through all of these steps, but I will do it anyway. Bring down another zero. 27, goes into zero, zero times. Zero times 27 is zero, and we have no remainder.
So this over here is equal to 500. It's good to do a little bit of a gut check, that if I took 27 times 500, would I get 13,500? Well, if I took 27 times 1000, I would get 27,000. So it makes sense that if I multiply 27 times half of 1000 I get half of 27,000.
So this feels good, this is the number of pencils sold.
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