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# Division strategies for decimal quotients

There are various methods for division when the quotient is not a whole number. Different examples demonstrate how to use fractions, tenths, and reciprocals to multiply instead of divide so we can arrive at the correct answer.

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• how did you still get the anwser to 3 divieded by 2 i kept getting 5.6?
• 3/2 essentially means how many times will 2 go into three. Your answer multiplied times two should give you three. one and a half times 2 equals three. If your answer was 5.6 that would be 5.6 times two which is 11.2. So for example, try 11.2 divided by 2, the answer is 5.6 :P
• was it suposed to be 7/70 or 70/7?
• Sal's problem is 7/70 = 1/10 = 0.1 as a decimal.
• Why do we have to multiply with the reciprocal to divide?
• You don't - there are other methods of going about it. One such method is simply to divide the numerator of the first fraction by the numerator of the second fraction, and similarly for the denominators. In fact, this method helps us understand why we can simply invert and multiply in the first place!

Take the example (3/5)÷(4/7). Dividing across gives us (3÷4)/(5÷7), or (3/4)/(5/7). We can multiply by 4/4 (which is equal to 1) in order to produce a whole number for our numerator (3/(20/7), and we can multiply by 7/7 (which is also equal to 1) to give us a whole number for our denominator, producing a final result of (21/20). This is actually the same answer we get when multiplying by the reciprocal!

Here's what's going on here: after dividing 3 by 4, we then multiplied by 4 and then 7. Multiplication by 4 cancels out division by 4, so essentially all we did here is multiply by 7 (the denominator of the second fraction). Similarly, we divided 5 by 7, multiplied by 4 and then 7. The multiplication and division of 7 cancel each other out, so we essentially just multiplied by 4 - the numerator of the second fraction.

Now we can see that inverting and multiplying is actually just a shortcut to the perhaps more intuitive method of just dividing across.
• what is 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000x100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000=
• 1e+250 is the answer to the question.
• what dose 3.9875677498396545684 divdded by 68 equal
• .0586407022035 :) hope this helps!
• Wait.. How exactly does " 7 / 7 x 10 " equal " 7 / 7 /10 "?
• I've never done this myself but I think he applied the inverse property to (7 x 10) which makes it 10 / 7

So now you have 7 / 10 / 7 = 0.1
or 7 / 7 / 10 = 0.1

It seems that when it's solely division, as long as the 1st number remains the same, the order of the numbers that follow it does not matter.

3 / 5 / 1 / 2 / 6 = 0.05

3 / 1 / 2 / 6 / 5 = 0.05

I'm not sure what this property is called though. I hope someone can help us out!

Edit: looks like I'm wrong. The inverse property I was thinking of applies to fractions and I didn't apply it correctly.

It would have to be like this:
7 / 70
= 7 x 1 / 70
= 7 / 70 Which goes back to the original form lol.
= 1 / 10
= 0.1
• Why is the remainder the numerator in the mixed number?
• That's how many 'wholes' you have left. Take the mixed number 5 1/3. We have 5 wholes, and 1/3 of a whole extra, therefore the remainder will be 1 (because there is one third left).
• how do you divide decimals with a whole number do you get a whole number or a decimal?
• if you divided a decimal by a whole number you would get another decimal.