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Is the quotient of a mixed number divided by a mixed number greater than or less than...

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njacobs888 | eNotes Newbie

Posted January 27, 2010 at 6:02 AM via web

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Is the quotient of a mixed number divided by a mixed number greater than or less than 1?

This is a question on my sons math homework and I don't know how to help him.

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illegal3alien | Student , Grade 9 | eNotes Newbie

Posted January 27, 2010 at 6:16 AM (Answer #1)

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quotient is answer to a division problem

 

When dividing fractions, you multiple to first number by the reciprocal of the second (the number flipped upside down)

1   1

_ / _

2   2

Is equal to 1/2 * 2/1, which is 1 (you multiple the top across, and the bottom across. (1/4)/(1/2) (1/4*2) is (1/8)

 

A mixed number means it is greater than 1 to start with, like (3/2)/(3/2) which is 1, or (3/2)/(4/2) which is (6/8) or 3/4.

 

(100/2)/(3/2) is (200/6) which is greater than 1.

(9/8)/(50/2) is (18/400) which is less than 1.

 

Seems like it is possible to come out either way. A fraction where the numerator (top) is greater than the denominator (bottom) is the same as a mixed number. 1_1/2 == 3/2

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hermionegranger | Student , Grade 9 | Honors

Posted January 27, 2010 at 7:50 AM (Answer #2)

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try to prove this statement false. using an example, u can prove that this is false. so it is greater

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neela | High School Teacher | Valedictorian

Posted January 27, 2010 at 8:55 PM (Answer #3)

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The quotient of a mixed number dvided by a mixed number  could be greater than , or equal to, or or less than one.

Explanation:

A number is a mixed number if it is whole number exceeded by proper fraction. Example : 3 and 1/4 written like 3 1/4, 9 and7/8 equal to 9+7/8 written like 9 7/8 etc.

Quotient could be greater than one:

The quotient of  (3 and 1/2) devided by  1 and 1 /6 =(3 1/2)/(1  1/6)) = (7/2)/(7/6) = (7/2)(6/7) = 6/2 = 3. So three is the quotient of (3and1/2) divided by (1 and 1/6).

The following is the example to show that the quotient of division of two mixed numbers could be 1:

(4 and1/5)/ (4 and 1/5) = 1.

Quotient of division of two mixed number could less than 1:

(4 and 2/5)/(10 and 1/7 ) = (22/5)/(71/7) = 22*7/(71.5) =154/355) which is less than1.

So, we saw examples which shows that the quotient of two mixed numbers could greater than , equal to or less than  one according as the value of numerator is greater than, equal to or less than the the value of the denominator.

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