Addition of fractions
Addition of fractions with the same denominators
To add two fractions with the same denominators, add their numerators, and the denominators remain unchanged:
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Examples of addition of fractions with the same denominators
Example 1: Add two fractions with equal denominators: 
and 
Answer: 
Example 2: to Add two fractions with equal denominators: 
and 
Answer: 
Addition of fractions with different denominators
To add two fractions with different denominators, you need to:
- to reduce fractions to the lowest common denominator (NSC);
- add the numerators of the fractions and the denominators remain unchanged;
- reduce the resulting fraction;
- If the resulting improper fraction to turn an improper fraction into a mixed.
Examples of addition of fractions with different denominators
Example 3: to Add two fractions with different denominators: and 
Answer: 
Example 4: to Add two fractions with different denominators: 
and 
Answer: 
Adding mixed numbers
To add two mixed numbers, you need to:
- allow fractional part of these numbers to the lowest common denominator;
- separately add the whole parts and fractional parts separately;
- if adding the fractional parts were received improper fraction, to allocate the integer part of this fraction and add it to the obtained integer part;
- reduce the resulting fraction.
Examples of adding mixed numbers
Example 5: Add two mixed numbers:
and 
Answer: 
Subtraction of fractions
Subtraction of fractions with the same denominators
To subtract two fractions with the same denominators, subtract the numerator from the first fraction, the numerator of the second, and the denominator remain unchanged:
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Examples of subtraction of fractions with the same denominators
Example 1: Subtract two fractions with equal denominators: 
and 
Answer: 
Subtraction of fractions with different denominators
To subtract two fractions with different denominators, you need to:
- to reduce fractions to the lowest common denominator (NSC);
- from the first fraction numerator subtract the numerator of the second fraction multiplied by the auxiliary multipliers, respectively, and the denominators remain unchanged;
- reduce the resulting fraction
Examples of subtracting fractions with different denominators
Example 2: Subtract two fractions with different denominators: 
and 
Answer: 
Subtraction of mixed numbers
To subtract two mixed numbers, you need to:
- allow fractional part of these numbers to the lowest common denominator;
- if the fractional part of the minuend is less than the fractional part of the subtractor, to turn it into an improper fraction, reduced by one whole part;
- separately subtract whole parts and fractional parts separately;
- reduce the resulting fraction.
Examples of subtracting mixed numbers
Example 5: Add two mixed numbers:
and
Answer: 
Addition and subtraction of decimal fractions
Addition and subtraction of decimal fractions is performed bitwise. It is convenient to perform in a column.
Detailed information and examples of solving addition and subtracting decimals read here