Solve for the missing fraction
After working through the Math Now for week 10, as well as some of the problems in problem set 2, I realized I needed more work with solving for a missing fraction.
For instance, with the "Marlon Brando" problem, I did it completely differently then Dr. Dituri did, and after watching the video, I think the way he did it was much easier!
I tried to figure out how many years were spent in each phase of life.
So to find out how many years were spent as a child, I did 1/12 x 80 which came to 6.67 years.
For youth: 2/7 x 80 equaled 22.86 years.
Adult: 3/8 x 80 is 30 years.
So, he spent 59.53 years of his life in the first three stages. To find out how many years he spent as an old man, I subtracted 59.53 from 80 to get 20.47 years. Then I asked, "20.47 is what percent of 80?" That gave me 26% which I converted to a fraction of 13/50. As it turns out, this is a different fraction than what Dr. Dituri got in his answer, so I took that to mean my way wasn't correct!
It seemed much easier to set the problem up the way Dr. Dituri did. He said 1/12 + 2/7 + 3/8 + x = 1. Which of course you can then get the common denominator and represent 1 as any number over itself and solve for x. Knowing this will certainly help me when I am faced with a problem like this again.
I also watched a video at the Khan Academy that I also found helpful for solving for the missing fraction.
For instance, with the "Marlon Brando" problem, I did it completely differently then Dr. Dituri did, and after watching the video, I think the way he did it was much easier!
I tried to figure out how many years were spent in each phase of life.
So to find out how many years were spent as a child, I did 1/12 x 80 which came to 6.67 years.
For youth: 2/7 x 80 equaled 22.86 years.
Adult: 3/8 x 80 is 30 years.
So, he spent 59.53 years of his life in the first three stages. To find out how many years he spent as an old man, I subtracted 59.53 from 80 to get 20.47 years. Then I asked, "20.47 is what percent of 80?" That gave me 26% which I converted to a fraction of 13/50. As it turns out, this is a different fraction than what Dr. Dituri got in his answer, so I took that to mean my way wasn't correct!
It seemed much easier to set the problem up the way Dr. Dituri did. He said 1/12 + 2/7 + 3/8 + x = 1. Which of course you can then get the common denominator and represent 1 as any number over itself and solve for x. Knowing this will certainly help me when I am faced with a problem like this again.
I also watched a video at the Khan Academy that I also found helpful for solving for the missing fraction.
It can help to create the equation that Dr. Dituri used. The way you approached the problem is not wrong. I am wondering if your mistake happened when rounding. 26% is close to 25.59%. Fractions are more precise than rounded numbers. Great post!
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