Adding and Subtracting Fractions:
- The fractional part of a collection is determined by dividing the collection into subgroups equal to the number representing the denominator of the fraction. We then take the number of subgroups equal to the number representing the numerator of the fraction.
- A fraction can be expressed as a division and vice-versa.
- A fraction written as a combination of a whole number and a proper fraction is called a mixed number.
- To generate equivalent fractions of any given fraction, we proceed as follows:
- Multiply the numerator and denominator by the same number (other than 0) or
- Divide the numerator and denominator by their common factor (other than 1), if any.
- The two fractions are equivalent if the product of numerator of the first and denominator of the second is equal to the product of the denominator of the first and numerator of the second.
- A fraction is in its lowest term, if the numerator and denominator have no
common factor other than 1.
- Of the two fractions having the same denominator, the one with greater
numerator is greater.
- Of the two fractions having the same numerator, the one with greater
denominator is smaller.
Example: 9/4 - 3/4
- Read the problems carefully.
- If the denominators are same, add or subtract the numerators and write the answer.
- If the denominators are different, they are made common by finding LCM.
Since the denominators are same, the numerators are subtracted.
9/4 - 3/4 = 6/4
Example: 1/5 + 1/3
Since the denominators are different, find LCM of 5 and 3.
LCM of 5 and 3 is 15.
1/5 x 15/15 = 3/15
1/3 x 15/15 = 5/15
Directions: Answer the following questions. Also write at least 5 examples of your own for fraction operations: addition, subtraction, multiplication, and division of fractions.