How can you divide fractions that have whole numbers?

Answer 1

If a fraction (like three and three quarters) is made up of a whole number part and a fraction part and you want to calculate with it it is usually best to change it to improper fraction".

Three and three quarters would become 15/4 because it has 15 quarters in it.

Such a fraction is sometimes called "top heavy".

If you wanted to divide 3 and 3/4 by 1 and 1/5, they would be changed to15/4 and 6/5 The rule for dividing by a fraction is to "turn it upside down and multiply" instead. So if you wanted to divide the 3 and 3/4 by the 1 and 1/5 you would then "invert" the 6/5 to 5/6 and then multiply 15/4 by 5/6. Then you can cancel the 15 and the 6 both by 3 leaving you with 5/4 x 5/6 = 25/8 which produces 3 whole ones and 1/8

If you wanted to multiply them always look for the chance to "cancel" to make numbers smaller. So starting with 3 and 3/4 multiplied by 1 and 1/5 we change the first into 15/4 and the second to 6/5. Now you can15 and the 5 by 5 giving you 3 and 1 instead. Similarly cancel the 4 and the 6 by 2 giving 2 and 3 instead. Multiplying the numerators gives9, and multiplying the denominators gives 2, so now we have 9/2 which is 9 halves which is 4 whole ones and 1/2 for the final answer.