## 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:

### 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:

### 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