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Fractions: Solved Examples | Quantitative for GMAT PDF Download

Section - 1

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

Ques 2: Fractions: Solved Examples | Quantitative for GMAT
Ans: The numerators are the same, but the denominator of  Fractions: Solved Examples | Quantitative for GMAT

Ques 3: Fractions: Solved Examples | Quantitative for GMAT
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. Fractions: Solved Examples | Quantitative for GMAT

Section - 2


Add or subtract the following fractions. Fractions should be in their most simplified form.
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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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 Fractions: Solved Examples | Quantitative for GMAT

Ques 8: Fractions: Solved Examples | Quantitative for GMAT
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Because the denominators are the same, add the numerators and reduce.
Fractions: Solved Examples | Quantitative for GMAT

Ques 9: Fractions: Solved Examples | Quantitative for GMAT
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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.
Fractions: Solved Examples | Quantitative for GMAT

Ques 10: Fractions: Solved Examples | Quantitative for GMAT
Ans:
The common denominator of u/v and 1 is v.
Fractions: Solved Examples | Quantitative for GMAT

Section - 3

Convert the following improper fractions to mixed numbers.
Ques 11: 9/4
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Fractions: Solved Examples | Quantitative for GMAT

Ques 12: 31/7
Ans: Fractions: Solved Examples | Quantitative for GMAT

Ques 13: 47/15
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Fractions: Solved Examples | Quantitative for GMAT

Ques 14: 70/20.
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Fractions: Solved Examples | Quantitative for GMAT

Section - 4

Convert the following mixed numbers to improper fractions.
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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

Section - 5

Simplify the following expressions.
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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

Ques 23: Fractions: Solved Examples | Quantitative for GMAT
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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:
Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

Ques 26: Fractions: Solved Examples | Quantitative for GMAT
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To begin, we simplify the square roots in the numerator and denominator by looking for factors that have pairs:
Fractions: Solved Examples | Quantitative for GMAT
Because the numbers remaining inside the square roots have a factor of 3 in common, we can simplify even further:
Fractions: Solved Examples | Quantitative for GMAT
Therefore:
Fractions: Solved Examples | Quantitative for GMAT

Ques 27: Fractions: Solved Examples | Quantitative for GMAT
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:
Fractions: Solved Examples | Quantitative for GMAT
Alternatively, we can consider only one variable at a time and use other exponent rules to simplify:
Fractions: Solved Examples | Quantitative for GMAT
To combine these into one fraction, we can put xand zin the numerator, Fractions: Solved Examples | Quantitative for GMAT 
Place y in the denominator.
Fractions: Solved Examples | Quantitative for GMAT

Section - 6

Multiply or divide the following fractions. Fractions should be in their most simplified form.
Ques 28: Fractions: Solved Examples | Quantitative for GMAT
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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

Ques 31: Fractions: Solved Examples | Quantitative for GMAT
Ans: Before multiplying the fractions, look to cancel common factors.
Fractions: Solved Examples | Quantitative for GMAT

Ques 32: Fractions: Solved Examples | Quantitative for GMAT
Ans: Before multiplying the fractions, look to cancel common factors.
Fractions: Solved Examples | Quantitative for GMAT

Ques 33: Fractions: Solved Examples | Quantitative for GMAT
Ans: 
Begin by simplifying the roots.
Fractions: Solved Examples | Quantitative for GMAT
√2 can be canceled from the numerator and denominator. Also note that √5 appears twice in the denominator, and Fractions: Solved Examples | Quantitative for GMAT
Fractions: Solved Examples | Quantitative for GMAT

Ques 34: Fractions: Solved Examples | Quantitative for GMAT
Ans: Begin by simplifying the roots.
Fractions: Solved Examples | Quantitative for GMAT
Look to cancel common factors before multiplying. Remember you can cancel across fractions because they are being multiplied.
Fractions: Solved Examples | Quantitative for GMAT
Now we can combine the roots in the numerator.
Fractions: Solved Examples | Quantitative for GMAT


Section - 7 

Simplify the following fractions.
Ques 35: Fractions: Solved Examples | Quantitative for GMAT
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:
Fractions: Solved Examples | Quantitative for GMAT
Now we need to simplify both fractions.
Fractions: Solved Examples | Quantitative for GMAT
If you left the expressions as one fraction, then you could have factored a 2 out of each term in the expression:
Fractions: Solved Examples | Quantitative for GMAT
Either version is correct.

Ques 36: Fractions: Solved Examples | Quantitative for GMAT
 Fractions: Solved Examples | Quantitative for GMAT
Ans: We can split this fraction into two fractions with a common denominator of 5xy and then simplify further:
Fractions: Solved Examples | Quantitative for GMAT
Now we have a match. The correct answer is (C).

Ques 37: Fractions: Solved Examples | Quantitative for GMAT
Ans: 
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:
Fractions: Solved Examples | Quantitative for GMAT

Ques 38:  Fractions: Solved Examples | Quantitative for GMAT
Ans: 
We begin by simplifying the square roots in the denominator:
Fractions: Solved Examples | Quantitative for GMAT
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.
Fractions: Solved Examples | Quantitative for GMAT
Now we can cancel 3x√3 from the numerator and denominator.
Fractions: Solved Examples | Quantitative for GMAT

Section - 8

Simplify the following expressions. Final answers should be in their most simplified forms.
Ques 39: Fractions: Solved Examples | Quantitative for GMAT
Ans: Begin by simplifying each fraction.
Fractions: Solved Examples | Quantitative for GMAT
Because 3 and 7 share no common factors, the least common denominator is 3 x 7 = 21.
Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

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Fractions: Solved Examples | Quantitative for GMAT

Ques 44: Fractions: Solved Examples | Quantitative for GMAT
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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:
Fractions: Solved Examples | Quantitative for GMAT

Section - 9

Match the following expressions to their simplified forms.
Ques 45: Fractions: Solved Examples | Quantitative for GMAT
Fractions: Solved Examples | Quantitative for GMAT
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.
Fractions: Solved Examples | Quantitative for GMAT
The answer is (A).

Ques 46: Fractions: Solved Examples | Quantitative for GMAT
Fractions: Solved Examples | Quantitative for GMAT
Ans:
Begin by looking for common factors to cancel before we multiply.
Fractions: Solved Examples | Quantitative for GMAT
Because (j - 2) is a factor of both the numerator and denominator, we can cancel it along with other common factors.
Fractions: Solved Examples | Quantitative for GMAT
The answer is (A).

Ques 47: Fractions: Solved Examples | Quantitative for GMAT
Fractions: Solved Examples | Quantitative for GMAT

Ans: Break down each fraction and look for common denominators.
Fractions: Solved Examples | Quantitative for GMAT
The answer is A.

Section - 10:

Simplify the following complex fractions.
Ques 48: Fractions: Solved Examples | Quantitative for GMAT 
Ans:
Begin by simplifying the denominator.
Fractions: Solved Examples | Quantitative for GMAT
Dividing by (15/4) is the same as multiplying by (4/15).
Fractions: Solved Examples | Quantitative for GMAT

Ques 49: Fractions: Solved Examples | Quantitative for GMAT
Ans:
Begin by simplifying the denominator.
Fractions: Solved Examples | Quantitative for GMAT
Now we can divide 8 by the fraction (4/3), which is the same as multiplying by (3/4).
Fractions: Solved Examples | Quantitative for GMAT

Ques 50: Fractions: Solved Examples | Quantitative for GMAT
Ans:
To begin, simplify the numerator and the denominator.
Fractions: Solved Examples | Quantitative for GMAT
Now we can divide.
Fractions: Solved Examples | Quantitative for GMAT
Simplify before you multiply.

Fractions: Solved Examples | Quantitative for GMAT

The document Fractions: Solved Examples | Quantitative for GMAT is a part of the GMAT Course Quantitative for GMAT.
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FAQs on Fractions: Solved Examples - Quantitative for GMAT

1. What are fractions?
Ans. Fractions are numbers that represent a part of a whole. They consist of a numerator (the number on top) and a denominator (the number on the bottom), separated by a slash. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.
2. How do you add fractions?
Ans. To add fractions with the same denominator, simply add the numerators and keep the denominator the same. For example, to add 1/4 and 3/4, you add the numerators (1 + 3 = 4) and keep the denominator (4) the same. The result is 4/4, which can be simplified to 1.
3. Can fractions be added if they have different denominators?
Ans. Yes, fractions with different denominators can be added by finding a common denominator. To do this, you need to find the least common multiple (LCM) of the denominators and then convert each fraction to an equivalent fraction with the common denominator. Once the fractions have the same denominator, you can add them by adding the numerators.
4. How do you simplify fractions?
Ans. To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder. Simplifying a fraction means expressing it in its lowest terms.
5. Can fractions be multiplied and divided?
Ans. Yes, fractions can be multiplied and divided. To multiply fractions, multiply the numerators together and the denominators together. For example, to multiply 2/3 and 4/5, you multiply 2 by 4 to get 8 as the numerator, and 3 by 5 to get 15 as the denominator, resulting in 8/15. To divide fractions, you multiply the first fraction by the reciprocal of the second fraction.
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