How do you simplify #1.6 div 0.336#?

2 Answers
EZ as pi
Oct 3, 2016

#1.6div0.336 = 4.76#

Explanation:

When you are dividing BY a decimal, it is possible to make the decimal into a whole number by multiplying by 10, 100 or 1000. etc

#1.6/0.336 xx1000/1000 = 1600/336#

This can now be divided by long division, double division or any similar method

#color(white)(xxx..x)4.76#
#336)bar(1600.00)#
#color(white)(xx.)ul1344darr#
#color(white)(xx....)2560#
#color(white)(xx....)ul2352darr#
#color(white)(xxx....)2080#
#color(white)(xxx....)ul2016#
#color(white)(xxxxx....)64#

KillerBunny
Oct 3, 2016

#100/21#

Explanation:

Assuming you can't simply use a calculator, the only way I see to simplify this expression is translating everything to fractions: we have

#1.6 = 16/10 = 8/5#

and

#0.336 = 336/1000 = 42/125#

Now, if you want to divide by a fraction, you have to multiply for the inverse of that fraction: dividing by #3/5# is the same thing as multiplying by #5/3#, so

#1.6 : 0.336 = 8/5 : 42/125 = 8/5 * 125/42#

And now we can do cross canceling:

#8/5 * 125/42 = 4*25/21 = 100/21#

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