Brian W. answered • 08/29/19
Struggling Elementary Math Student Extraordinaire
Jamie divided 6 2/5 ounces of candy into equal amounts. He put the candy into containers that hold 2 2/3 ounces each. How many containers will be filled?
This is a very complex problem that has a LOT of steps to it. So to solve it, we will break it down, 1 step at a time.
The problem gives you the operation as division so we know we are dealing with a division of fractions.
6 2/5 ÷ 2 2/3
We cannot divide mixed numbers as we have here so first we must convert the mixed numbers into improper fractions. To do this, we must multiply the whole number by the denominator, and add the numerator in each mixed number. Then we put that answer over the denominator.
6 2/5 --> 6X5+2 = 30+2 = 32/5 2 2/3--> 2X3+2 = 6+2 = 8/3
Now we have 32/5 ÷ 8/3
To divide fractions, we actually do something called KEEP, CHANGE, FLIP
We KEEP the first fraction (32/5), CHANGE the sign (÷ becomes X) and FLIP the last fraction (3/8)
Now we have 32/5 X 3/8
Now we simply multiply straight across, numerators and denominators.
Multiplying the numerators, we get 32X3 to get 96
Multiplying the denominators, we get 5X8 to get 40
Now we have an answer to the original problem of 96/40, an improper fraction.
We must convert this to a mixed number by dividing the numerator by the denominator. 96 ÷ 40, we get the answer of 2, with a remainder of 16. When written as a fraction, this would be 2 16/40, and reduced down, this would become 2 2/5
So the final answer to the MATH would be 2 2/5. You would be tempted to make this your answer to the problem. But let's go back and look at the original question. What does it ask us?
How many containers will be filled?
Looking at the final answer, we see a whole number part and a fraction part. We know a fraction is a PART of a whole, not a whole. Filled containers implies WHOLE containers. How many would be FILLED? 2. The rest would only be a partial container.
