Solve

[Jensi]

Hello,

Question: The amount of hot cocoa powder remaining in a can is 6 1/4 tablespoons. A single serving consists of 1 3/4 tablespoons of the powder. What is the total number of servings of the powder remaining in the can?

How do I solve it?
The answer is 3 4/7

Thanks

 

[tkhunny]

Division? Try converting to "improper" fractions.

 

[Dr.Peterson]

Hello,

Question: The amount of hot cocoa powder remaining in a can is 6 1/4 tablespoons. A single serving consists of 1 3/4 tablespoons of the powder. What is the total number of servings of the powder remaining in the can?

How do I solve it?
The answer is 3 4/7

Thanks

In order to see more easily what you need to do, you might first try solving the same problem with simpler numbers:

The amount of hot cocoa powder remaining in a can is 6 tablespoons. A single serving consists of 2 tablespoons of the powder. What is the total number of servings of the powder remaining in the can?​

Once you see what to do, do it with the actual numbers. As was pointed out, multiplication and division of mixed numbers is easiest when you convert them to improper fractions.

 

[Tamiris]

The answer is:
The remaining in a can is 6 1/4, which is an improper fraction, so you have to turn it into a proper fraction, the result is going to be 25/4, and the same you will do for the single serving.
After that you have to divide the remaining amount by the the single serving. Remember, division of a fraction equals multiplying the first one by the inverse of the second one.
After getting the result 100/28, you gotta simplify it, and you will get 25/7. The next step is turning it back into a improper fraction, when you are going to find 3 4/7.

 

[Dr.Peterson]

The answer is:
The remaining in a can is 6 1/4, which is an improper fraction, so you have to turn it into a proper fraction, the result is going to be 25/4, and the same you will do for the single serving.
After that you have to divide the remaining amount by the the single serving. Remember, division of a fraction equals multiplying the first one by the inverse of the second one.
After getting the result 100/28, you gotta simplify it, and you will get 25/7. The next step is turning it back into a improper fraction, when you are going to find 3 4/7.

Let's correct the terminology, though your work is correct.

The number 6 1/4 is not an improper fraction; it's a mixed number. It has to be converted to a single fraction, which will be an improper fraction, because a proper fraction is a number less than 1.

Now we have to divide that by 1 3/4, which is again a mixed number that we convert to an improper fraction, 7/4.

The result is [MATH]\frac{25}{4}\div\frac{7}{4}[/MATH]. We do this by multiplying [MATH]\frac{25}{4}\times\frac{4}{7}[/MATH], as you said. We can either multiply and then simplify, as you did, or we can cancel first:

[MATH]\frac{25}{\cancel{4}}\times\frac{\cancel{4}}{7} = \frac{25}{7} = 3\frac{4}{7}[/MATH].​

Here I converted it to a mixed number, because that is how a normal human expects to see an answer. We could instead just round down and say there are 3 full servings left.

 

[tkhunny]

Please note that there is nothing improper about an improper fraction. You do not have to do anything with it. Frankly, mixed numbers are substantially more cumbersome than improper fractions. It's just a name based on a convention. It should not hurt your feelings either to see or to handle an improper fraction.