Mixed Numbers Isolation of the whole part of an ordinary fraction

Lecture



Among ordinary fractions there are two different types.

Correct and incorrect fractions

Consider fractions.

Mixed Numbers Isolation of the whole part of an ordinary fraction

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

The correct fraction has a numerator less than the denominator. Therefore, the correct fraction is always less than one.

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.

A wrong fraction has a numerator equal to or greater than the denominator. Therefore, an improper fraction is either equal to one or greater than one.

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. Mixed Numbers Isolation of the whole part of an ordinary fraction
  • Now write the answer. Mixed Numbers Isolation of the whole part of an ordinary fraction

The resulting number above, containing the integer and fractional part, is called a mixed number .

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. Mixed Numbers Isolation of the whole part of an ordinary fraction

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

Mixed Numbers Isolation of the whole part of an ordinary fraction

Any natural number can be written with a fraction with any natural denominator.

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

Examples

Mixed Numbers Isolation of the whole part of an ordinary fraction

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Arithmetic

Terms: Arithmetic