## Thursday, October 18, 2007

### Robby's First Growing Post

Which set of fractions is larger 1/2 + 1/6 or 1/4 + 7/12?

1/4 + 7/12 > 1/2 + 1/6 by 10 minutes
1/4 + 7/12 is bigger because, visually speaking, 7/12 is more than half and 1/2 is half. 1/6 has a higher denominator than 1/4, making it larger. So 7/12 has both fractions in comparison larger than 1/6 + 1/2.

Robby's Bike Race!

The bike course is 60 kilometers long. There is also 60 minutes on a clock. Every digit on the clock stands for 5 minutes, and there are 12 of them. So 1/12 = 5 minutes. Working from there, 1/6 is double of 1/12.
So 5 minutes
x2
------
10 (1/6)

If double of 1/12 is 1/6, double of 1/6 is 1/3. So doubling it once more; 10 minutes
x2
------
20 minutes (1/3)

1/12 = 5 minutes
1/6 = 10 minutes
1/3 = 20 minutes

A pattern i noticed was that when the denominator of the fraction was cut in half, the value in minutes it held was doubled.

1 way to find a quarter of a number is cutting a number in half, then cutting the half in half, like for 16. If u cut it in half, you would get 8. If you cut it in half again, you would get 4. So 1/4 of 16 is 4.
Another way you can find a quarter of a number is if you divide the number by the numerator, in this case, 4. So for 16 again, to get it one way, you have to multiply 4 with 4. So working backwards, 16 / 4 = 4.
For 22 and 110, the best method would be the half in half method, because half these numbers are odd numbers, or unfriendly numbers.
Half of 22 is 11, half of 11 is 6.5. 6.5 = 1/4 of 22
Half of 110 is 55. Thinking of it another way, 25 x 2 = 50. 26 x 2 = 52 27 x 2 = 54. The pattern is that for every unit u go up in for the number being multiplied by 2, the answer goes up by 2 from the previous one. So if you were to half the unit that the number on the left is going up by, then the answer would be half as well. So half of 1 ( a unit ) is .5. 27 is the closest number to 55, so add .5 to 27 and you get 27.5. Half of 110 = 55. Half of 55 = 27.5.

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9.
2/5 + 5/10 DOES NOT EQUAL 8/15

What I would do first is to use the concept of the clock to help. To do so, you have to find out how much 1/10 and 1/5 is in minutes by dividing 60 (1 hour) by the denominator.
(to get division sign, hold ALT and press the numbers 0247 on the right number pad of your keyboard)
60 ÷ 10 = ?
60 and 10 both end in 0. So it would be easier to divide the simpler forms of them (6 and 1) by removing the 0.
6 ÷ 1 = 6
So 1/10 = 6 minutes. To get 5/10, multiply 6 minute by 5.
6 x 5 = 30
5/10 = 30 minutes.
(You could have also simplified 5/10 to 1/2 and see that 1/2 of an hour is 30 minutes)

You can do this strategy with 2/5 as well, or, since /5 is half of /10, making it a larger fraction, simply multiply the amount of minutes 1/10 is (6) by 2, because /5 is 2 times larger than /10.
6 x 2 = 12
(1/10) = 1/5
So 1/5 = 12 minutes. Now times it by 2 because you found that 1/5 is 12 minutes, but we need to get 2/5, which means you have to double 12 minutes.
12 x 2 = 24

2/5 = 24 minutes. Now that you have both the fractions in simple 2 digit numbers, add them up to find the total.

24 ( 2/5 )
+30(5/10)
----
54 / 60

Now 2/5 + 5/10 does not equal 8/15 because 8/15 is at the half, where clearly from the picture above, 2/5 + 5/10 is way more than half.
Or you could divide 60 by 15.
I would count by 15's till i reach 60, 15 30 45 60
There are 4 numbers, so that means 60 ÷ 15 = 4 minutes every 1/15.
Now multiply 4 by 8 because we are trying to get 8/15 and right now have 1/15.
8
x4
----
32 = 8/15 32 is a lot smaller than 54 minutes, which was 2/5 + 5/10. Thus proving that 2/5 +5/10 does not equal 8/15.

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10.

Title 1/1
Label 1/1
Question 3 5/5
Question 4/5 3/3
Question 6 5/5
Question 7 3 /3
Question 8 5/5
Question 9 5 /5
Question 10 7/7

Total 35/35

I think I should get 35/35 because I answered every question and followed all the instructions. I even used extra time and made some pictures, which I guess I had to do anyway, but its the thought that counts. I had to save this as a draft because this took longer than I expected.