Mixed Numbers Isolation of the whole part of an ordinary fraction

Among ordinary fractions there are two different types.

Correct and incorrect fractions

Consider fractions.

Note that in the first two fractions (3/7 and 5/7) the numerators are less than the denominators. Such fractions are called correct.

Consider the two remaining fractions.

The fraction 7/7 has a numerator equal to the denominator (such fractions are equal to one), and the fraction 11/7 has a numerator greater than the denominator. Such fractions are called incorrect.

Any wrong fraction is always more correct.

How to select the whole part

In the wrong fraction, you can select the whole part. Consider how this can be done.

To extract the whole part from an improper fraction:

1. divide with the remainder the numerator by the denominator;
2. the resulting partial quotient is written in the integer part of the fraction;
3. the remainder is recorded in the numerator of the fraction;
4. the divider is written in the denominator of the fraction.

Example. We extract the integer part of the irregular fraction 11/2.

• Divide the numerator by the denominator.
• Now write the answer.

We received a mixed number from an irregular fraction, but you can also perform the opposite action, that is, you can represent the mixed number as an improper fraction .

To represent a mixed number in the form of an improper fraction:

1. multiply its integer part by the denominator of the fractional part;
2. add the numerator of the fractional part to the resulting product;
3. write the amount from clause 2 into the numerator of the fraction, and the denominator of the fractional part remain the same.

Example. Imagine a mixed number in the form of an improper fraction.

• Multiply the integer part by the denominator.
  
  3 • 5 = 15
• We add the numerator.
  
  15 + 2 = 17
• Write the resulting amount in the numerator of the new fraction, and the denominator remains the same.

Any mixed number can be represented as the sum of the integer and fractional parts.

The quotient of dividing the numerator by the denominator of such a fraction will be equal to the given natural number.

Examples