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ladyv900's avatar

What does this mean that there are at least 2 sevens in 16 ?

Asked by ladyv900 (713points) September 16th, 2010

I’m reading about using long divison but I don’t really understand this sentence. I’m reading the solution so here this is saying ” Estimate 7(divison bar, 161 divide by 7) 161 by first estimating 7/16 and writing the result in the tens place of the quotient. Since 7 times 2 equals to 14, there are at least 2 sevens in 16. What does that last sentence mean?

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5 Answers

Vortico's avatar

The number 7 can go into 16 two times with a remainder of two. 7×2 = 14, which is less than 16.

WestRiverrat's avatar

It essentially means you can subtract 2 sevens from 16 without going into negative numbers.

Ame_Evil's avatar

When you divide 161 by 7 in long division, you start with the first 1 (representing 100), which you cannot divide so you stick the 1 in front of the 6 and then divide this number (16) by 7 which gives you the remainder 2. With this remainder you put it in front of the 1 (the third digit) to get 21. this then divides by 7 three times to leave no remainder.

If the original number was 162, at this point you would get a remainder of 1. If this is the case, to turn this into a fraction all you need to do is divide the remainder by 7 which is something like .143.

I hope that makes sense. Here is a crude representation of it. It’s hard to describe over the internet without showing you the processes that I have done, but with the above text I hope you can figure it out.

As for the final part of your question “what does this last sentence mean” I am unsure what you are referring to. If you are referring to “and writing the result in the tens place of the quotient.” this is the third step in the image where you put the 2 in front of the 1 to get the number 21 which you then divide by 7. In the first/second step what you are really dividing is 160 instead of 16, but in shorthand you just write 16 else it gets messy, especially with larger numbers.

CyanoticWasp's avatar

What the text is trying to do is help you arrive at decimal equivalents for fractions. The example given is 7/161. First you’re asked to estimate the approximate decimal value for 7/16. But I don’t understand why the author is having you estimate how many times 7 goes into 16, because the fraction indicates that the division goes the other way: 7 divided by 16.

In any case, 7 goes into 16 twice, with a remainder of 2, as others have explained.

Where the text is going to take you from there is anyone’s guess.

For the record, 7/16 is close to but less than ½, so a little bit less than 0.5. If you take the 0.5 and multiply by 1/10 (or 0.1), then you can see that the fraction 7/161 is a bit less than 0.05. When you do the final long division you should get an answer in that ballpark.

LostInParadise's avatar

The estimation process is not part of the long division. It is just a way of approximating your answer so that you can compare it to the result of the long division. In the case of 7/161, imagine dividing numerator and denominator by 7. Since 7 goes into 16 about twice, an approximation would be ½0. If you multiply your answer by 20 it should be about equal to 1.

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