Hey guys.

Can anybody explain to me how to multiply or divide whole numbers with
fractions?

Such as these?

32 1/2 / 4 1/4

or

13 1/2 X 12 1/4

Or

33 X 14 1/2

Brushing up on math and these kind stump me...

Thanks!

So 32.5/4.25= 7.65
13.5x12.25=165.375
33x14.5=478.5

Those are easy fractions to turn into decimals. Granted I used a calculator cause on a computer.

Common denominator. The bottom number.

14 1/2 is the same as 29/2. (28/2 plus 1/2, or twenty eight halves plus one half).

Do that for all numbers until you have a common denominator.  Then multiply.  Then fraction it out again.

Could u write out a whole number divided by a whole number with fraction. I am lost on those ones... I get the multiply ones now, those are easier.

Thanks!

make them both into improper fractions and multiply. for division, multiply by the inverse:

9 divided by 4.5

9/1 divided by 9/2

9/1 times 2/9

18/9

2

ETA: you only need a common denominator for addition/subraction of fractions.  multiplying and dividing is way easier

I dont get it.
















ETA just kidding I get it now. It seems harder for me on big numbers though.

One trick is that when you multiply something by a fraction, you can flip that fraction upside down and then multiply instead.

So...

A÷(B/C) = A*(C/B) = (A*C)/B

I have an old calculator I use. I can input any number, be it a fraction, or a decimal, then use which ever function I need. It will give me the answer in the simplest form. Then if I need, I can tap the button to convert from decimal to fraction. It also can input inches or feet and then use any function. It also converts decimal feet to feet/inches. Eg: 10.5' = 10' 6".

Long way:  Convert each into improper fractions, then multiply or divide (and a divide is a reciprocal and a multiply).

ex:

5 1/4 * 6 1/3
=21/4 * 19/3
=(21*19)/(4*3)
=399/12
=33 3/12
=33 1/4

division:

12 1/3 / 2 1/4
=37/3 / 9/4
=37/3 * 4/9           <---- notice flipping the second & changing to multiply, makes it easy
=(37*4) * (3/9)
=148/27
=5 13/27

Your sample problem:  (32 1/2) / (4 1/4)

My Way (with all the gory details): we are going to operate on the numerator and the denominator separately, then do the division.

Step 1:  32 1/2 = 32*(2/2) + 1/2 = (32*2)/2 + 1/2 = 64/2 + 1/2 = (64 + 1) / 2 = 65/2
a)  Convert number to a fraction.
b)  Any number divided by itself equals 1.  In this case (2/2) = 1
c)  Any number can be multiplied by 1 without affecting its value.  In this case  32*(2/2) = 32

Step 2:  65/2 = (65/2)*(2/2) = (65 *2) / (2*2) = 130/4
a)  Recognizing that 4 is the smallest common denominator, so 65/2 was converted to 130/4 using same rules stated above.
b)  Any number divided by itself equals 1.  In this case (2/2) = 1
c)  Any number can be multiplied by 1 without affecting its value.  In this case  (2/2) = 1

Step 3:  4 1/4 = 4*(4/4) + 1/4 = (4*4)/4 + 1/4 = 16/4 +1/4 = (16+1)/4 = 17/4
a)  Convert number to a fraction.
b)  Any number divided by itself equals 1.  In this case (4/4) = 1
c)  Any number can be multiplied by 1 without affecting its value.  In this case  4*(4/4) = 16

Step 4:  (130/4) = 130/4 * (1/1) = (130*1)/(1*4) = 130 * (1/4*1) = 130 * (1/4)
a)  Factor out the common denominator, (1/4).
b)  Any number divided by itself equals 1.  In this case (1/1) = 1
c)  Any number can be multiplied by 1 without affecting its value.  In this case  130/4 *(1/1) = 130/4

Step 5:  (17/4) = 17/4 * (1/1) = (17*1)/(1*4) = 17 * (1/(4*1)) = 17 *(1/4)
a)  Factor out the common denominator, (1/4).
b)  Any number divided by itself equals 1.  In this case (1/1) = 1
c)  Any number can be multiplied by 1 without affecting its value.  In this case  17/4 *(1/1) = 17/4

Step 6:  (1/4)/(1/4) = 1
a)  Recognize there is a factor of (1/4) in both the numerator and the denominator.
b)  Any number divided by itself equals 1.  In this case (1/4)/(1/4) = 1

Step 7:  130 * (1/4) / 17 *(1/4) = (130/17) * (1/4)/(1/4) = (130/17)*1 = 130/17
a)  The (1/4) fraction in the numerator cancels the (1/4) in the denominator.
b)  Any number divided by itself equals 1.  In this case (1/4)/(1/4) = 1

Step 8:  (130/17) = ~7.65
a)  The result, the answer, equals 130/17
b)  Restated the answer as a decimal fraction.


Wow!, that was a lot of typing.