Fractions Arithmetic

Fractions Arithmetic is an important topic of mathematics. Candidates preparing for the quantitative aptitude section must go through the terms that are related to Fractions Arithmetic such as Comparing Fractions, Equivalent Fractions and Number Line Fractions. Tricks as well as Fractions Questions and Answers are also available on this page.

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Fraction:

A fraction is a number representing a part of a whole. The whole may be a single object or a group of objects.

Consider the fraction 6/13. This fraction is read as ”six-thirteenth” which means that 6 parts out of 13 equal parts in which the whole is divided. In the fraction 6/13, 6 is called the numerator and 13 is called the denominator.

Fractions Arithmetic

 Comparing FractionsTo compare two fractions:Step 1: Compare denominators. If they are different, rewrite one or both fractions with a common denominator.Step 2: Check the numerators. If the denominators are the same, then the fraction with the greater numerator is the greater fraction. The fraction with the lesser numerator is the lesser fraction. And, as noted above, if the numerators are equal, the fractions are equivalent.

Comparing Like Fractions:

In comparing like fractions it is always easy to compare two or more because their denominators are same.

To compare two like fractions it is just enough to compare their numerators. If there are two like fractions, then the fraction with greater numerator is greater.

For Example:

⁹/₁₃ > ⁵/₁₃ or ⁵/₁₃ ⁹/₁₃ Also, ¹⁵/₇ > ¹³/₇ or ¹³/₇ < ¹⁵/₇

Three or more like fractions can be arranged in ascending or descending order by arranging their numerators in ascending or descending order.

Comparing Unlike Fractions:

In comparing unlike fractions, we first convert them into like fractions by using the following steps and then compare them.

Step I: Obtain the denominators of the fractions and find their LCM (least common multiple).

Step II: Each fractions are converted to its equivalent fraction with denominator equal to the LCM (least common multiple) obtained in Step I.

Step III: Compare the numerators of the equivalent fractions whose denominators are same.

For Example:

Which is larger ³/₄ or ⁵/₁₂ ?

Solution:

Let us first find the LCM (least common multiple) of the denominators 4 and 12.

We have,

LCM (least common multiple) of 4 and 12 is 2 × 2 × 3 = 12.

Now we convert the given fractions to equivalent fractions with denominator 12

We have,

3/4 = (3 × 3)/(4 × 3) = 9/12

5/12 = (5 × 1)/(12 × 1) = 5/12

Now we will observe the numerator, that is 9 > 5.

So, ⁹/₁₂ > ⁵/₁₂

Therefore, ³/₄ > ⁵/₁₂

 Determining Equivalent FractionsTo determine whether or not two fractions are equivalent:Step 1: Rewrite one or both of the fractions so that they have common denominators.Step 2: Compare the numerators to see if they have the same value. If so, then the fractions are equivalent.

For Example:

Equivalent fractions are the fractions having the same value.

We have,

2/4 = (1 × 2)/(2 × 2)

3/6 = (1 × 3)/(2 × 3)

4/8 = (1 × 4)/(2 × 4)

We observe that 2/4, 3/6 and 4/8 are obtained by multiplying the numerator and denominator of 1/2 by 2, 3 and 4 respectively.

Thus, an equivalent fraction of a given fraction can be obtained by multiplying its numerator and denominator by the same number (other than zero).

2/4 = (2÷ 2)/(4 ÷ 2) = 1/2

3/6 = (3÷ 3)/(6 ÷ 3) = 1/2

4/8 = (4 ÷ 4)/(8 ÷ 4) = 1/2

We observe that if we divide the numerators and denominators of 2/4, 3/6 and 4/8 each by their common factor 2, we get an equivalent fraction 1/2.

Thus, an equivalent fraction of a given fraction can be obtained by dividing its numerator and denominator by their common factor (other than 1), if any.

 Number Line FractionsIn representations of fractions on a number line we can show fractions on a number line. In order to represent 1/2 on the number line, draw the number line and mark a point A to represent 1.Now, divide the gap between O and A into two equal parts. Let T be the point of division. Then, point T represents 1/2.

Shortcuts for solving Fractions (Fractions Tricks):

Tip 1: Adding fractions without using a Least Common Multiple

Tip 2: Adding fractions without using a GCM

Tip 3: Dividing Fractions Using Keep Change Flip

Tip 4: What is the name of the bar of a fraction?

Tip 5: Use the Ladder Method to find the LCM and GCF

Tip 6: Use the Circle Method to create an Improper Fraction

Tip 7: Memorize decimal equivalents of common fractions

Question 1) In a class 3/4th of the students do not know either English or Hindi. But 1/6th of the students know English. How much students know both English and Hindi if students who know Hindi are 1/8th of total students in the class?

1. 1/24
2. 100/24
3. 10/12
4. ¼

Question 2) 2 x ? – 6 = 676/26 What will come in place of question mark?

1. 9
2. 15/26
3. 16
4. 26

Question 3) An integer is 10 more than its one-third part. The integer is

1. 15
2. 12
3. 18
4. 25

Question 4) Which is largest amongst 5/8, 2/3, 7/9, 3/5?

1. 5/8
2. 2/3
3. 7/9
4. 3/5

Question 5) Express 2/3 of 1/4 of Rs.25.20 as a fraction of 1 1/2 of Rs. 36

1. 7/90
2. 11/90
3. 5/8
4. 5/42

Check Out: Quadratic Equation | Formulas, Tricks

Question 6) A fraction is divided by reciprocal of itself. It is then multiplied by the original fraction.  What is the fraction if the answer obtained is 11(25/64)?

1. 9/4
2. 27/8
3. 9/8
4. 2/3

Question 7) Since Raj was not paying attention in class, instead of multiplying M by 2/7, he divided M by 2/7. Raj’s value was 1(13/14)  more than expected value of M. What is M?

1. 3/5
2. 6/7
3. 3/4
4. 4/3

Question 8) What is increasing order of the fractions 14/17, 10/12, 6/7, 18/22?

1. 6/7, 14/17, 10/12, 18/22
2. 6/7, 10/12, 14/17, 18/22
3. 14/17, 10/12 , 6/7, 18/22
4. 18/22, 14/17, 10/12 , 6/7

Answer: b. 6/7, 10/12, 14/17, 18/22

Question 9) In 3 fractions when the largest fraction is divided by smallest fraction, the result 5/4 is greater than the middle fraction by 1/2. If sum of the three fractions is 2(3/12) what will be the difference between largest and smallest fraction?

1. 5/12
2. 1/6
3. 7/24
4. 7/12

Get Here: Unitary Method Questions

Question 10) What is increasing order of the fractions 6/7, 8/9, 7/8,  9/10?

1. 6/7, 8/9, 7/8, 9/10
2. 9/10, 7/8, 8/9, 6/7
3. 6/7, 7/8, 8/9, 9/10
4. 9/10, 8/9, 7/8, 6/7

Answer: c. 6/7, 7/8, 8/9, 9/10

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