How to divide a fraction by a fraction | Education 2022

Dividing a fraction into a fraction is not difficult, you just have to multiply the first fraction by the second “inverted”. However, there are some nuances to consider here.

How do you divide a fraction by a fraction?
How do you divide a fraction by a fraction?


Step 1

You must multiply the first fraction (dividend) by the second inverted fraction (divisor) when dividing regular fractions. Such a fraction, where the numerator and denominator are interchanged, is called the inverse (after the original).

When dividing fractions, it is necessary to check that the second fraction and the denominators of both fractions are not equal to zero (or do not take zero values ​​for specific values ​​of the parameters/variables/unknowns). Sometimes, because of the cumbersome shape of the fracture, it is not very obvious. All values ​​of the variables (parameters) that make the divisor (second fraction) or the denominators of fractions zero must be indicated in the answer.

Example 1: Divide 1/2 by 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/c: x/c = a/c * c/x = (a * c) / (c * x) = a/x, where c? 0.x? 0.

Step 2

You need to bring them into their usual form to separate mixed fractions. Then we proceed as in step 1.

To convert a mixed fraction to a traditional form, multiply the integer part by the denominator and add this product to the numerator.

Example 3: Convert a mixed 2 2/3 to a fraction:

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

Example 4: Divide 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

Step 3

When dividing fractions of different types (mixed, decimal, ordinary), all fractions are reduced to a standard form for the time being, according to item 1. The decimal fraction is converted into an ordinary one: the decimal fraction without a comma is written in the numerator, and the order of the fraction is written in the denominator (ten for tenths, hundred for hundredths, etc.).

Example 5: Convert the decimal fraction 3.457 to its usual form:

since the fraction contains “thousandths” (457 thousandths), the denominator of the resulting fraction is 1000:

3, 457=3457/1000

Example 6: Divide the decimal 1, 5 by 1 1/2 mixed:

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

Step 4

When dividing two decimal fractions, both fractions are pre-multiplied by 10 to the point where the divisor becomes an integer. Then the decimal fraction is divided “completely.”

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

If necessary (depending on the circumstances of the problem), you can choose such a value of the multiplier so that both the divisor and the dividend become integers. So the problem of dividing decimal fractions will reduce to dividing integers.

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

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