How to divide a fraction into a fraction

It is not difficult to divide a fraction into a fraction - you just need to multiply the first fraction by the "inverted" second. However, there are some nuances here that you still need to consider.

Instruction manual

one

When dividing ordinary fractions, it is necessary to multiply the first fraction (divisible) by the inverted second fraction (divisor). Such a fraction, where the numerator and denominator are reversed, is called the inverse (to the original).

When dividing fractions, it is necessary to ensure that the second fraction and the denominators of both fractions are not equal to zero (or do not take zero values ​​for certain values ​​of parameters / variables / unknowns). Sometimes, due to the cumbersome appearance of the fraction, it is very unobvious. All values ​​of variables (parameters) that vanish the divisor (second fraction) or denominators of fractions must be indicated in the answer.

Example 1: divide 1/2 to 2/3

1/2: 2/3 = 1/2 * 3/2 = (1 * 3) / (2 * 2) = 3/4, or

Example 2: divide a / s by x / s

a / s: x / s = a / s * s / x = (a * s) / (s * x) = a / x, where s? 0 x? 0.

2

To separate mixed fractions, you need to bring them to their normal form. Next, we proceed as in paragraph 1.

To convert a mixed fraction to an ordinary form, you need to multiply its integer part by the denominator, and then add this product to the numerator.

Example 3: convert a mixed fraction 2 2/3 to ordinary:

2 2/3 = (2 + 2 * 3) / 3 = 8/3

Example 4: divide the fraction 3 4/5 by 3/10:

3 4/5: 3/10 = (3 * 5 + 4) / 5: 3/10 = 19/5: 3/10 = 19/5 * 10/3 = (19 * 10) / (5 * 3) = 38/3 = 12 2/3

3

When dividing fractions of different types (mixed, decimal, ordinary), all fractions are preliminarily reduced to an ordinary form. Further, according to paragraph 1. The decimal fraction is converted to an ordinary fraction very simply: the decimal fraction is written in the numerator and the decimal fraction is written in the denominator (ten for tenths, one hundred for hundredths, etc.).

Example 5: cast the decimal fraction 3.457 to its normal form:

since the fraction contains "thousandths" (457 thousandths), the denominator of the obtained fraction will be equal to 1000:

3.457 = 3457/1000

Example 6: divide the decimal fraction 1.5 into mixed 1 1/2:

1.5: 1 1/2 = 15/10: 3/2 = 15/10 * 2/3 = (15 * 2) / (10 * 3) = 30/30 = 1.

4

When dividing two decimal fractions, both fractions are preliminarily multiplied by 10 to such an extent that the divisor becomes an integer. After that, the decimal fraction is "completely" divided.

Example 7: 2.48 / 12.4 = 24.8 / 124 = 0.2.

If necessary (based on the conditions of the problem), it is possible to choose a multiplier value such that both the divisor and the dividend become integers. Then the problem of dividing decimal fractions is reduced to the division of integers.

Example 8: 2.48 / 12.4 = 248/1240 = 0.2