Hello Math Central,

I have a question to ask you. I really hope you can help me with these questions. PLEASE!! :)

Mr. Bob has 3/4 of a bottle of medicine left. He takes the medicine three times a day. Each dose is 1/16 of the bottle. How many days will it take for Mr. Bob to finish the bottle?

My friend gave me a problem to solve and it is so hard. Can you help me solve it? Here it is: If g- 4.8 = 9.66 and e-1/3 = 1/8, what is the sum of g and e?

Mariko's mother used ribbon to wrap 3 birthday gifts. She had 3 ribbons and each was 72 inches long. She used 8/9 of the first ribbon, 2/3 of the second ribbon, and 5/6 of the the third ribbon. How many feet did she use?

Lady Bird


I would mimic what bob does and keep track of how much medicine he uses.

dosemedicine used
21/16 + 1/16 = 2/16 = 1/8
31/16 + 1/16 + 1/16 = 3/16
Keep filling in the table until the amount of medicine used is 3/4. When you see how many days it takes can you find a quicker way to get the answer?

Her is one approach.

The first step to finding out how many days it will take for Mr. Bob to finish the bottle, you need to find out how much he uses each day. You are told he uses 1/16 of the bottle each dose, and has 3 doses each day. So he uses 3 * (1/16) = 3/16 of the bottle each day. The next step is to use the information that he has only 3/4 of the bottle left. It is probably clearer to see the answer if you convert 3/4 to a fraction with the same denominator as 3/16, or you can write out the equation as (3/4)/(3/16) which is the same as (3/4) * (16/3)

For the second problem, since one of the equations is written in decimal form I would write them both in decimal form.

g - 4.8 = 9.66
e - 0.333 = 0.125
I find that, at times, it helps to think of an equation as a balance. For your first equation you have g - 4.8 an one side of the balance and 9.66 on the other. Since they are balanced, they will remain so if 4.8 is added to each side. That is g - 4.8 + 4.8 = 9.66 + 4.8 or g = 14.46 Use the same procedure to find e and then calculate g + e.

For your third problem, you need to add up the three fractions that represent the lengths of ribbon she used. If she used 8/9 of one of the 72 inch ribbons, then she used (8/9) * 72 inches. If we write this as an improper fraction and display the numerator in a factored form we see that (8*9*8)/9 can be reduced by eliminating the factor of 9 from both the numerator and denominator. We are left with 8*8 = 64.

The other two lengths are found in a similar fashion.

Leeanne and Penny
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