Science & Mathematics » Mathematics » How do you divide 600 by 0.75?

# How do you divide 600 by 0.75?

My calculator gets exactly 800 but when I try to do it via long division I get 8.13.

• Long division:
75 goes into 600 eight times, now multiply the 75 times 8:

5x8 = 40, put down the zero and carry the four.
7x8 = 56, plus the carried four, is 60.

So 75 x 8 is 600. Therefore 0.75 x 800 is 600.
Therefore 0.75 x 813 is NOT six hundred!
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• See cidya's answer. The position of the decimal point in your answer 8.13 says that the first mistake in your long division was not adjusting the decimal point position to account for the divisor being a fraction.

That's the "multiply by 100" step in cidyah's answer...moving the decimal place right 2 places in both numbers (divisor and dividend) so that the divisor is a whole number.

Next, it looks like you got 8 right as the first digit, but somehow multiplied 75 by 7 instead of 8 to get 725 instead of 800. That would lead to 0.13 as an approximate fraction after rounding.
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• 600 = 2 * 300

600 = 2 * 2 * 150

600 = 2 * 2 * 2 * 75

600 = 2 * 2 * 2 * 3 * 25

600 = 2 * 2 * 2 * 3 * 5 * 5

0.75 = 3 * 0.25

0.75 = 3 * (25/100)

0.75 = 3 * (5 * 5/100)

0.75 = (3 * 5 * 5)/100

= 600 / 0.75

= (2 * 2 * 2 * 3 * 5 * 5) / [(3 * 5 * 5)/100] → you can simplify by 3

= (2 * 2 * 2 * 5 * 5) / [(5 * 5)/100] → then by 5

= (2 * 2 * 2 * 5) / [5/100] → then by 5

= (2 * 2 * 2) / [1/100] → to divide by (a/b) is similar to multiply by (b/a)

= (2 * 2 * 2) / [100/1] → you know that: 100/1 = 100

= (2 * 2 * 2) / 100

= 800
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• The good Lord only knows how you are getting 8.13 by doing it manually.

600 / (3/4) is the same as 600 * 4 / 3.
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• 600 / 3/4=600 * 4/3=200 * 4=800
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• 800
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• 600/0.75=800.
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• .75 = 3/4
When you divide whole numbers by fractions, one way to do this is to rewrite the decimal as a fraction and multiply the whole number bu the fraction's reciprocal.

600/.75 = 600/(3/4) = 600 * 4/3 = 2400/3 = 800
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• 8.13 says that the first
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• 0.75 is 3/4

600/(3/4) = 600*(4/3) = 2400/3 = 800
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