Fractions (Recapitulation)

Fraction 

A fraction is a small part or proportion of something.

When writing a fraction there are two main parts: the numerator and the denominator.

Example:

This is read as “two-fifths”

Proper Fractions

Fraction whose numerator is less than its denominator is called Proper fraction. Proper fraction is always less than a whole.

Example:

Here, Numerator < Denominator (Numerator is smaller than Denominator)

Therefore 3/5 is a proper fraction.

Improper Fractions 

Fraction whose numerator is more than or equal to its denominator is called Improper fraction.

Example:

Here, Numerator > Denominator (Numerator is greater than Denominator)

Therefore 8/5 is an improper fraction.

Mixed Fractions

Fraction made up of a whole number and a proper number is called Mixed fraction.

Example: 

Here, 5 is a whole number and ¾ is a proper fraction.

Changing a Mixed Fraction into Improper Fraction

Step1: First multiply the whole number with denominator.

Step2: Then add product of whole number and denominator with numerator.

Step3: Write the resultant number as numerator. Also write the denominator.

Example:

5 x 4 +3 = 23

Improper Fraction = 23/4

Changing a Improper Fraction into Mixed Fraction

Step1: Divide the numerator by denominator to get quotient and remainder.

Step2: Write the mixed fraction as 

Example:

Here, Quotient = 4, Remainder = 3

Now put the values

Note:

i. If the numerator and denominator of a fraction are both multiplied by the same non-zero number, then its value does not change.

ii. If the numerator and denominator of a fraction are both divided by their common factor, then its value does not change.

Equivalent fractions

Equivalent fractions are the fraction that look different but have same value.

If product of numerator of the first fraction and denominator of second fraction is equal to product of numerator of the second fraction and denominator of first fraction, the two fractions are called equivalent.

Example:

Product 1: 5 x 3    = 15

Product 2: 1 x 15  = 15

The two products are equal. So, 5/15 and 1/3 are equivalent fractions.

Note:

i. In order to find equivalent fraction of a higher numerator or denominator, multiply the numerator and denominator of the given fraction by same number except by zero. 

ii. In order to find equivalent fraction of a lower numerator or denominator, divide the numerator and denominator of the given fraction by same number except by zero.

Like Fractions

All fractions with the same denominators (i.e. number written below the horizontal line) are called like fractions.

Example: 2/14, 3/14, 4/14, 5/14 are like fractions as all fraction have same bottom number i.e. denominator.

Unlike Fractions

All fractions with the different denominators (i.e. number written below the horizontal line) are called unlike fractions.

Example: 2/3, 5/14, 7/8, 9/13 are unlike fractions as all fraction have different bottom number i.e. denominator.

Fraction in lowest terms

A fraction is in its lowest terms if its numerator and denominator have no common factor other than 1. In order to reduce a fraction to its lowest terms, we divide its numerator and denominator by their H.C.F or common factor.

Example:

Comparing Fractions

Step1: Find the LCM of the denominators of the given fractions.

Step2: Convert each fraction to its equivalent fraction with denominator equal to the LCM obtained.

Step3: Compare and arrange the fractions. (Fraction with smaller numerator is smaller and fraction with larger numerator is larger)

Note:

i. When comparing two fractions with like denominators, the larger fraction is the one with the greater numerator.

ii. If two fractions have the same numerator but different denominators, the fraction with greater denominator is smaller.

Example:

Conversion of unlike fractions to like fractions

Step1: Find the LCM of the denominators of the given fractions.

Step2: Convert each fraction to its equivalent fraction with denominator equal to the LCM obtained.

Example:

Addition and Subtraction of like fractions

Example:

Addition and Subtraction of unlike fractions

Step1: Find the LCM of the denominators of the given fractions.

Step2: Convert each fraction to its equivalent fraction with denominator equal to the LCM obtained.

Step3: Add or subtract the fractions.

Example:

Example:

Example:

Example: Seema purchased of potatoes and onions. What is the total weight of vegetables purchased by her?

Solution:

Example: Ayush ate  of pizza and the remaining pizza was eaten by his brother Abhishek. How much part of the pizza Abhishek eat? Who ate the larger share and by how much?

Solutions:

Example: A piece of ribbon is of lengthcm. If it is cut into two pieces in such a way that the length of one piece is cm, what is the length of the other piece?

Solution:

Example: What should be added toto get 5?

Solution: