Decimal

hi i need some help in these problem...

it say to express each quantity as a decimal. for example, 20 minutes = one half of an hour, or 0.5 hour. compare each quantity in the left column with the quantity on the right. then write >,< or = to show comparison. the first one is done. but i dont know the rest please help.. =(

12 inches 1/2 yard answer: 0.3 < 0.5
10 minutes 1/4 hour
4 hours 1/6 day
8 dimes 3/4 dollars
9 inches 1/4 yard
4 ounces 1/3 pound
2 digit 2/3 of an area code
4 fluid ounces 1/2 cup
15 centimeters 1 1/2 mters
8 small squares 1/4 of a checkboard
7 zodiac signs 5/6 of the zodiac
3 eggs 1/6 of a dozen

Quote:

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Originally Posted by 4thgrader

hi i need some help in these problem...

it say to express each quantity as a decimal. for example, 20 minutes = one half of an hour, or 0.5 hour. compare each quantity in the left column with the quantity on the right. then write >,< or = to show comparison. the first one is done. but i dont know the rest please help.. =(

12 inches 1/2 yard answer: 0.3 < 0.5
10 minutes 1/4 hour
4 hours 1/6 day
8 dimes 3/4 dollars
9 inches 1/4 yard
4 ounces 1/3 pound
2 digit 2/3 of an area code
4 fluid ounces 1/2 cup
15 centimeters 1 1/2 mters
8 small squares 1/4 of a checkboard
7 zodiac signs 5/6 of the zodiac
3 eggs 1/6 of a dozen

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Hello,

12 inches 1/2 yard ......... answer: 0.3 m < 0.5 m (You must add the unit. For instance use $ and your answer is wrong:) )
10 minutes 1/4 hour ......... answer: 10 min < 1/4 hour = 15 min
4 hours 1/6 day ............ answer: 4 hours = 1/6 day = 1/6 *24 hours
8 dimes 3/4 dollars ......... answer 8 dimes = 80 cts > 3/4 dollars = 75 cts

I'm not really familiar with these measure units, so please check my calculations!
9 inches 1/4 yard.........answer: 9'' = 1/4 yrd becaus 22.86 cm = 22.86 cm
(I've converted both measures into centimeters and got the same value)
4 ounces 1/3 pound.........answer: 4 oz < 1/3 lb because 113,4 g < 151,2 g
(I've converted both weights into gramms)
2 digit 2/3 of an area code
I cann#t help you here because you are refering to US postal codes which I don't know)
4 fluid ounces 1/2 cup.........answer: 4 fl oz < 1/2 cup because 118.8 cm³ < 125 cm³
I found this explanation in the internet:
cup = an informal unit of volume for coffee. The size of a cup of coffee varies according to local custom, but a typical size is about 5 fluid ounces or 150 milliliters.
15 centimeters 1 1/2 mters.........answer: 15 cm < 1.5 m = 150 cm
8 small squares 1/4 of a checkboard .........answer: 8 small squares < 1/4 checkboard = 16 small squares
7 zodiac signs 5/6 of the zodiac .........answer: 7 zodiac signs < 5/6 zodiac signs = 10 zodiac signs
3 eggs 1/6 of a dozen .........answer: 3 eggs > 1/6 of a dozen eggs = 2 eggs

Quote:

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Originally Posted by 4thgrader

hi i need some help in these problem...

it say to express each quantity as a decimal. for example, 20 minutes = one half of an hour, or 0.5 hour. compare each quantity in the left column with the quantity on the right. then write >,< or = to show comparison. the first one is done. but i dont know the rest please help.. =(

12 inches 1/2 yard answer: 0.3 < 0.5
10 minutes 1/4 hour
4 hours 1/6 day
8 dimes 3/4 dollars
9 inches 1/4 yard
4 ounces 1/3 pound
2 digit 2/3 of an area code
4 fluid ounces 1/2 cup
15 centimeters 1 1/2 mters
8 small squares 1/4 of a checkboard
7 zodiac signs 5/6 of the zodiac
3 eggs 1/6 of a dozen

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You got the answers, but not how to solve those type of questions, so here is the explanation.

You need to do three things.
First step: get both sides to have the same unit. To have a fraction, you usually want to convert to the bigger unit.
Second step: convert the fractions or numbers to decimal fractions or numbers.
Third step: compare and decide which one is bigger or are they equal.

Example: 10 minutes vs. 1/4 hour
An hour is the bigger unit. Therefore, we convert minutes to an hour.
First Step: 10 minutes = what fraction of an hour?

How to do it?

Write it as a fraction: 10minutes/1 hour
then change using 1 hour =60 minutes.
10minutes/1 hour = 10minutes/60minutes out of an hour= 1/6 hour.

Now you have 1/6 hour vs. 1/4 hour. When the numerator is the same, the fraction with the bigger denominator is the smaller fraction (to know why, you can read my Fractions book on it). Therefore, 1/4 is the bigger fraction: 1/6 hour < 1/4 hour. However, you are supposed to convert it to decimal fractions first (see complete in explanation in the Decimals book :)):
Second Step:
1/6 = 0.166 [and you should add a line over the last 6 to indicate it repeates]
1/4 = 0.25

Third Step: 0.166 < 0.25

End of Example.

In all those examples, you have to figure out how many small units are in the big units, and that number becomes the denominator.

Example: 8 dimes vs. 3/4 dollars

You want to convert dimes (small unit) to dollars (big unit).
There are 10 dimes in a dollar, and that is the denominator for the dimes side.
8 dimes /1dollar = (8dimes/10dimes) of dollars= 8/10=4/5 dollars.

I hope it helps you understand it :)