Solved Examples - Fractions Quant Notes | EduRev

Quantitative Aptitude for GMAT

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Quant : Solved Examples - Fractions Quant Notes | EduRev

The document Solved Examples - Fractions Quant Notes | EduRev is a part of the Quant Course Quantitative Aptitude for GMAT.
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Section - 1

For each of the following pairs of fractions, decide which fraction is larger.
Ques 1: Solved Examples - Fractions Quant Notes | EduRev
Ans: The denominators are the same, but the numerator of Solved Examples - Fractions Quant Notes | EduRev

Ques 2: Solved Examples - Fractions Quant Notes | EduRev
Ans: The numerators are the same, but the denominator of  Solved Examples - Fractions Quant Notes | EduRev

Ques 3: Solved Examples - Fractions Quant Notes | EduRev
Ans: In the first fraction,53/52 , the numerator is bigger than the denominator, so the fraction is greater than 1. In the second fraction, 85/16 , the denominator is bigger than the numerator, so the fraction is less than 1. Solved Examples - Fractions Quant Notes | EduRev

Section - 2
Add or subtract the following fractions. Fractions should be in their most simplified form.
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Solved Examples - Fractions Quant Notes | EduRev

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Because the denominators are the same, add the numerators and reduce.
Solved Examples - Fractions Quant Notes | EduRev

Ques 9: Solved Examples - Fractions Quant Notes | EduRev
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Find a common denominator and subtract. Because both 6 and 4 are factors of 12, 12 is the lowest common denominator.
Solved Examples - Fractions Quant Notes | EduRev

Ques 10: Solved Examples - Fractions Quant Notes | EduRev
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The common denominator of u/v and 1 is v.
Solved Examples - Fractions Quant Notes | EduRev

Section - 3
Convert the following improper fractions to mixed numbers.
Ques 11: 9/4
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Solved Examples - Fractions Quant Notes | EduRev

Ques 12: 31/7
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Ques 13: 47/15
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Solved Examples - Fractions Quant Notes | EduRev

Ques 14: 70/20.
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Solved Examples - Fractions Quant Notes | EduRev

Section - 4
Convert the following mixed numbers to improper fractions.
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Solved Examples - Fractions Quant Notes | EduRev

Section - 5
Simplify the following expressions.
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Solved Examples - Fractions Quant Notes | EduRev

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We begin by simplifying the square root in the numerator. When simplifying a square root, always look for factors that are perfect squares; in this example, we have 18 = 2 x 9 = 2 x 32. Therefore:
Solved Examples - Fractions Quant Notes | EduRev

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To begin, we simplify the square roots in the numerator and denominator by looking for factors that have pairs:
Solved Examples - Fractions Quant Notes | EduRev
Because the numbers remaining inside the square roots have a factor of 3 in common, we can simplify even further:
Solved Examples - Fractions Quant Notes | EduRev
Therefore:
Solved Examples - Fractions Quant Notes | EduRev

Ques 28: Solved Examples - Fractions Quant Notes | EduRev
Ans: 
There are several good ways to simplify a fraction with variables raised to powers. One approach is to use exponent rules to rewrite the expression so that the cancelations are more clear:
Solved Examples - Fractions Quant Notes | EduRev
Alternatively, we can consider only one variable at a time and use other exponent rules to simplify:
Solved Examples - Fractions Quant Notes | EduRev
To combine these into one fraction, we can put xand zin the numerator, Solved Examples - Fractions Quant Notes | EduRev 
Place y in the denominator.
Solved Examples - Fractions Quant Notes | EduRev

Section - 6
Multiply or divide the following fractions. Fractions should be in their most simplified form.
Ques 29: Solved Examples - Fractions Quant Notes | EduRev
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Solved Examples - Fractions Quant Notes | EduRev

Ques 32: Solved Examples - Fractions Quant Notes | EduRev
Ans: Before multiplying the fractions, look to cancel common factors.
Solved Examples - Fractions Quant Notes | EduRev

Ques 33: Solved Examples - Fractions Quant Notes | EduRev
Ans: Before multiplying the fractions, look to cancel common factors.
Solved Examples - Fractions Quant Notes | EduRev

Ques 34: Solved Examples - Fractions Quant Notes | EduRev
Ans: 
Begin by simplifying the roots.
Solved Examples - Fractions Quant Notes | EduRev
√2 can be canceled from the numerator and denominator. Also note that √5 appears twice in the denominator, and Solved Examples - Fractions Quant Notes | EduRev
Solved Examples - Fractions Quant Notes | EduRev

Ques 35: Solved Examples - Fractions Quant Notes | EduRev
Ans: Begin by simplifying the roots.
Solved Examples - Fractions Quant Notes | EduRev
Look to cancel common factors before multiplying. Remember you can cancel across fractions because they are being multiplied.
Solved Examples - Fractions Quant Notes | EduRev
Now we can combine the roots in the numerator.
Solved Examples - Fractions Quant Notes | EduRev

Section - 7 
Simplify the following fractions.
Ques 36: Solved Examples - Fractions Quant Notes | EduRev
Ans:  When the numerator of a fraction consists of two or more terms added together, but the denominator is a single term, we can split the fraction into two fractions with a common denominator and then simplify further:
Solved Examples - Fractions Quant Notes | EduRev
Now we need to simplify both fractions.
Solved Examples - Fractions Quant Notes | EduRev
If you left the expressions as one fraction, then you could have factored a 2 out of each term in the expression:
Solved Examples - Fractions Quant Notes | EduRev
Either version is correct.

Ques 37: Solved Examples - Fractions Quant Notes | EduRev
 Solved Examples - Fractions Quant Notes | EduRev
Ans: We can split this fraction into two fractions with a common denominator of 5xy and then simplify further:
Solved Examples - Fractions Quant Notes | EduRev
Now we have a match. The correct answer is (C).

Ques 38: Solved Examples - Fractions Quant Notes | EduRev
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We must be careful when dealing with addition or subtraction in the denominator; the best we can do is identify factors common to all terms and cancel these. Every term within the fraction contains 3a as a factor:
Solved Examples - Fractions Quant Notes | EduRev

Ques 39:  Solved Examples - Fractions Quant Notes | EduRev
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We begin by simplifying the square roots in the denominator:
Solved Examples - Fractions Quant Notes | EduRev
Because the subtraction is taking place in the denominator, we must identify common factors and cancel. These terms have a common factor of 3x√3 . Factor 3x√3 out of the denominator.
Solved Examples - Fractions Quant Notes | EduRev
Now we can cancel 3x√3 from the numerator and denominator.
Solved Examples - Fractions Quant Notes | EduRev

Section - 8
Simplify the following expressions. Final answers should be in their most simplified forms.

Ques 40: Solved Examples - Fractions Quant Notes | EduRev
Ans: Begin by simplifying each fraction.
Solved Examples - Fractions Quant Notes | EduRev
Because 3 and 7 share no common factors, the least common denominator is 3 x 7 = 21.
Solved Examples - Fractions Quant Notes | EduRev

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Solved Examples - Fractions Quant Notes | EduRev

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When subtracting fractions with more than one term in the numerator, put the subtracted term in parentheses to remind yourself to distribute the negative:
Solved Examples - Fractions Quant Notes | EduRev

Section - 9
Match the following expressions to their simplified forms.
Ques 46: Solved Examples - Fractions Quant Notes | EduRev
Solved Examples - Fractions Quant Notes | EduRev
Ans:
Begin by breaking down the fractions so that we can reduce common factors before we multiply. Remember that you can cancel across fractions because they’re multiplied.
Solved Examples - Fractions Quant Notes | EduRev
The answer is (A).

Ques 47: Solved Examples - Fractions Quant Notes | EduRev
Solved Examples - Fractions Quant Notes | EduRev
Ans:
Begin by looking for common factors to cancel before we multiply.
Solved Examples - Fractions Quant Notes | EduRev
Because (j - 2) is a factor of both the numerator and denominator, we can cancel it along with other common factors.
Solved Examples - Fractions Quant Notes | EduRev
The answer is (A).

Ques 48: Solved Examples - Fractions Quant Notes | EduRev
Solved Examples - Fractions Quant Notes | EduRev

Ans: Break down each fraction and look for common denominators.
Solved Examples - Fractions Quant Notes | EduRev
The answer is A.

Section - 10:
Simplify the following complex fractions.

Ques 49: Solved Examples - Fractions Quant Notes | EduRev 
Ans:
Begin by simplifying the denominator.
Solved Examples - Fractions Quant Notes | EduRev
Dividing by (15/4) is the same as multiplying by (4/15).
Solved Examples - Fractions Quant Notes | EduRev

Ques 50: Solved Examples - Fractions Quant Notes | EduRev
Ans:
Begin by simplifying the denominator.
Solved Examples - Fractions Quant Notes | EduRev
Now we can divide 8 by the fraction (4/3), which is the same as multiplying by (3/4).
Solved Examples - Fractions Quant Notes | EduRev

Ques 51: Solved Examples - Fractions Quant Notes | EduRev
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To begin, simplify the numerator and the denominator.
Solved Examples - Fractions Quant Notes | EduRev
Now we can divide.
Solved Examples - Fractions Quant Notes | EduRev
Simplify before you multiply.

Solved Examples - Fractions Quant Notes | EduRev

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