Addition of Fractions
Addition of Fractions with the Same Denominators:
Definition: The sum of fractions with the same denominators is called a fraction whose numerator is equal to the sum of the numerators of the original fractions, with a denominator equal to the denominator of both fractions.Formula
Let's add two fractions with the same denominators
According to the formula, we add the numerators, and keep the denominator the same
Important: If possible, we write the simplified fraction in the final answer.
Example:
When simplifying the fraction, we get the number 1/2 Addition of Fractions with Different Denominators:
Definition: To find the sum of fractions with different denominators, first bring the fractions to a common denominator, and then add them as fractions with the same denominators.Task:
Solution process:
1) We bring the fractions to a common denominator.
To do this, we find LCM - Least Common Multiple, for denominators 7 and 6, this number is 42.
Divide the number 42 by the denominators of the fractions 3/7 and 2/6
Thus, we found the additional multipliers.
Next, multiply the fractions by the additional multipliers and get the expression:
2) Add the fractions.
In our case, the fraction can be simplified by 2, and in the final answer, we write the number 16/21
Addition of a Fraction and a Whole Number:
Definition: To add a fraction to a whole number, first represent the whole number as a fraction with a denominator equal to 1.Calculation Algorithm:
1) We bring the fractions to a common denominator.
2) Add the fractions
3) If possible, simplify the resulting fraction.
4) If the result is an improper fraction, calculate the whole part from it.
Example:
Solution:
Calculate the whole part, and get the answer
Addition of Mixed Fractions:
Definition: To add mixed fractions you need to separately add the whole parts, and separately add the fractional parts.Formula
Example:
Substitute the numbers into the formula:
We get:
From the fraction, calculate the whole part as it is improper, and get the expression 7+2=9.