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How to divide a fraction into an integer

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How to divide a fraction into a number the fastest? Let us analyze the theory, draw a conclusion, and see with examples how dividing a fraction by a number can be performed according to the new short rule.

Usually the division of a fraction by a number is performed according to the rule of division of fractions. The first number (fraction) is multiplied by the number inverse to the second. Since the second number is an integer, the inverse of it is a fraction whose numerator is unity and the denominator is a given number. Schematically, the division of a fraction by a natural number looks like this:

From this we conclude:

to divide a fraction by a number, you need to multiply the denominator by this number, and leave the numerator the same. The rule can be formulated even shorter:

when dividing a fraction by a number, the number goes to the denominator.

Divide the fraction by a number:

To divide the fraction into a number, we rewrite the numerator without changes, and multiply the denominator by this number. Cut 6 and 3 by 3.

When dividing the fraction by a number, we rewrite the numerator, and multiply the denominator by this number. Cut 16 and 24 by 8.

When dividing a fraction by a number, the number goes to the denominator, so we leave the numerator the same, and multiply the denominator by the divisor. Cut 21 and 35 by 7.

Rules for the division of fractions.

1. To divide 1-fraction by the second, it is necessary to multiply the dividend by the number that is inverse to the divisor.

2. To divide a fraction by a natural number, it is necessary to multiply the dividend by the number that is inverse to the divisor.

3. In other words, to divide a fraction by a natural number, you need to multiply the denominator by this number.

4. It is impossible to divide by zero.

5. It is impossible to divide into a mixed fraction.

6. When determining the result, use the basic property of fractions to reduce fractions.

For right and wrong fractions, the division rule is as follows:

To divide an ordinary fraction, it is necessary to multiply the dividend numerator by the denominator of the divisor, and multiply the denominator of the dividend by the numerator of the divisor. The first product is taken by the numerator, and the second by the denominator.

Division of a fraction into a fraction.

To divide a 1-ordinary fraction into a second, not equal to zero, you must:

  • multiply the numerator of the 1st fraction by the denominator of the 2nd fraction and write the product in the numerator of the obtained fraction,
  • multiply the denominator of the 1st fraction by the numerator of the 2nd fraction and write the product in the denominator of the obtained fraction.

In other words, the division of fractions goes to multiplication.

To divide the 1-well fraction by the second, you must multiply the dividend (1-well fraction) by the inverse fraction of the divisor.

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