Dividing mixed fractions. Dividing mixed numbers: rule, examples

In this article we will figure out how division mixed numbers . First, let's outline the rule for dividing mixed numbers and consider solutions to examples. Next we will focus on dividing a mixed number by a natural number and division natural number to a mixed number. In conclusion, let's look at how to divide a mixed number by a common fraction.

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Dividing a mixed number by a mixed number

Division of mixed numbers can be reduced to dividing ordinary fractions. To do this, it is enough to convert mixed numbers into improper fractions.

Let's write it down rule for dividing mixed numbers: to divide a mixed number by a mixed number, you need to:

divide the corresponding ordinary fractions.

It remains to look at an example of dividing mixed numbers.

Example.

What is the result of dividing a mixed number by a mixed number?

Solution.

To reduce the division of mixed numbers to the division of ordinary fractions, we convert mixed numbers into improper fractions, we get And .

Thus, . Now let's use the rule for dividing ordinary fractions: . At this stage, you can reduce the fraction: . This completes the division of mixed numbers.

Answer:

Dividing a mixed number by a natural number

Dividing a mixed number by a natural number leads to the division of an ordinary fraction by a natural number. To do this, it is enough to convert the mixed number being divided into an improper fraction.

Example.

Divide the mixed number by the natural number 75.

Solution.

First we move from a mixed number to an improper fraction: , Then . It remains to divide the ordinary fraction by a natural number: . After reduction we get the fraction 1/20, which is the quotient of dividing a mixed number by the natural number 75.

Answer:

Dividing a natural number by a mixed number

Dividing a natural number by a mixed number after replacing a mixed number with an improper fraction, it reduces to dividing a natural number by a common fraction. For clarity, let's look at the solution to the example.

Example.

Divide the natural number 40 by a mixed number.

Solution.

First, let's represent the mixed number as an improper fraction: .

Now we can move on to division, we get . The resulting fraction is irreducible (see reducible and irreducible fractions), but improper, so you need to separate the whole part from it, we have . This completes the division of a natural number by a mixed number.

To the question: how to divide two mixed numbers? given by the author Yita Nefedorova The best answer is You need to represent each of them as an improper fraction. It's done like this. If the number is given in the form a + (b/c), then here a - whole part, b/c is the fractional part, and b is the numerator, c is the denominator, then a + (b/c) = ac/c + b/c = (ac + b) / c, i.e. the whole part is needed multiply by the denominator of the fractional part and add to the resulting number - the denominator of the fractional part. This is the numerator of the resulting improper fraction. And its denominator is the denominator of the fractional part of the original number. The result of dividing two resulting improper fractions is a fraction whose numerator is the product of the numerator of the first fraction by the denominator of the second, and the denominator is the product of the denominator of the first fraction by the numerator of the second. The resulting fraction, if it is incorrect, can, if desired, be converted into a mixed number by dividing its numerator by the denominator. The integer part of the quotient is the integer part of the mixed number, the remainder of the division is the numerator of the fractional part, the denominator of an improper fraction is the denominator of the fractional part.

Reply from I-beam[newbie]
The division of mixed numbers can be reduced to the division of ordinary fractions. To do this, it is enough to convert mixed numbers into improper fractions.
Let's write down the rule for dividing mixed numbers: to divide a mixed number by a mixed number, you need to:
convert mixed numbers to improper fractions;
divide the corresponding ordinary fractions.
It remains to look at an example of dividing mixed numbers.
Example.
What is the result of dividing a mixed number by a mixed number?
Solution.
To reduce the division of mixed numbers to the division of ordinary fractions, we convert the mixed numbers into improper fractions, we get and.
Thus, . Now let's use the rule for dividing ordinary fractions: . At this stage, you can reduce the fraction: . This completes the division of mixed numbers.
Answer:
.
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Dividing a mixed number by a natural number
Dividing a mixed number by a natural number results in dividing a common fraction by a natural number. To do this, it is enough to convert the mixed number being divided into an improper fraction.
Example.
Divide the mixed number by the natural number 75.
Solution.
First we move from a mixed number to an improper fraction: , then. It remains to divide the ordinary fraction by a natural number: . After reduction we get the fraction 1/20, which is the quotient of dividing the mixed number by the natural number 75.
Answer:
.
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Dividing a natural number by a mixed number
Dividing a natural number by a mixed number, after replacing the mixed number with an improper fraction, is reduced to dividing the natural number by an ordinary fraction. For clarity, let's look at the solution to the example.
Example.
Divide the natural number 40 by a mixed number.
Solution.
First, let's represent the mixed number as an improper fraction: .
Now we can move on to division, we get. The resulting fraction is irreducible (see reducible and irreducible fractions), but improper, so you need to separate the whole part from it, we have. This completes the division of a natural number by a mixed number.
Answer:
.
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Dividing a mixed number by a fraction
It is clear that dividing a mixed number by an ordinary fraction can easily be reduced to dividing ordinary fractions. To do this, you just need to convert the mixed number into an improper fraction.
Let's figure this out when solving the example.
Example.
Divide the mixed number by the fraction 28/15.
Solution.
Let's replace the mixed number with an improper fraction: . Now let's do the division: . Here we need to perform a reduction, we get.
Answer.

In this article we will look at the rule by which mixed numbers are divided. How to divide mixed numbers? How to divide a whole number by a mixed fraction? How to divide a whole number by a mixed fraction and how to divide a mixed fraction by a whole number? You will know the answers to these questions after reading the material.

Dividing a mixed number by a mixed number

The division of a mixed number by a mixed number is most conveniently reduced to the division of ordinary fractions. What does the rule for dividing mixed numbers look like? Let's formulate it.

Rule for dividing mixed numbers

To divide a mixed number by a mixed number:

Convert the dividend and divisor of mixed numbers into ordinary fractions.
Perform division of ordinary fractions.

Let's move on to an example and analyze the process of solving it.

Example 1: Dividing a mixed number by a mixed number

Divide 1 1 35 by 3 6 7.

After converting mixed numbers to improper fractions, we get:

1 1 35 = 1 35 + 1 35 = 36 35

3 6 7 = 3 7 + 6 7 = 27 7

Now we divide ordinary fractions and reduce the result:

36 35 ÷ 27 7 = 36 35 7 27 = 4 1 5 3 = 4 15.

This completes the division of mixed numbers.

1 1 35 ÷ 3 6 7 = 4 15.

Dividing a mixed number by a natural number

In this case, only the divisible mixed number needs to be converted into a common fraction. After all, any natural number can be represented as an improper ordinary fraction with a denominator of 1.

Example 2: Dividing a mixed number by a natural number

Divide the mixed number 3 3 4 by the natural number 75.

We move from a mixed number to an ordinary improper fraction:

3 3 4 = 3 4 + 3 4 = 15 4

We divide and reduce:

3 3 4 ÷ 75 = 15 4 ÷ 75 = 15 4 75 = 1 20

This completes the division of a mixed number by a natural number.

3 3 4 ÷ 75 = 1 20.

Dividing a natural number by a mixed number

As in the previous paragraph, such division comes down to converting a mixed number into an ordinary fraction.

The only difference is that earlier we converted the dividend into an ordinary fraction, but now we will convert the divisor.

Example 3. Dividing a natural number by a mixed number

Divide the natural number 40 by the mixed number 8 3 10.

Let's convert the dividend into the form of an ordinary fraction:

8 3 10 = 8 10 + 3 10 = 83 10

Now we do the division:

40 ÷ 8 3 10 = 40 ÷ 83 10 = 40 10 83 = 400 83.

This improper fraction is irreducible. For convenience, you can convert it back to a mixed number

400 83 = 4 68 83 .

This is the result of division.

Dividing a mixed number by a fraction

Like all previous cases, dividing a mixed number by an ordinary fraction also comes down to dividing ordinary fractions. In any unclear situation, convert a mixed number to a common fraction!

Example 4. Dividing a natural number by a mixed number

Divide the mixed number 2 8 45 by the fraction 28 15.

We also convert the dividend into the form of an ordinary fraction:

2 8 45 = 2 45 + 8 45 = 98 45.

We divide, reduce and get the answer:

98 45 ÷ 28 15 = 98 45 15 28 = 98 3 28 = 98 84 = 7 6 = 1 1 6

2 8 45 ÷ 28 15 = 1 1 6.

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Then we follow the rule: we multiply the first fraction by the fraction inverse to the second (that is, by an inverted fraction in which the numerator and denominator change places). When multiplying fractions, we multiply the numerator by the numerator, and the denominator by the denominator.

Let's look at examples of dividing mixed numbers.

We begin dividing mixed numbers by converting them into improper fractions. Then we divide the resulting fractions. To do this, multiply the first fraction by the inverted second. 20 and 25 by 5, 3 and 9 by 3. We got the wrong fraction, so we need to.

Convert mixed numbers to improper fractions. Next, according to the rule for dividing fractions, we leave the first number and multiply it by the reciprocal of the second. We reduce 15 and 25 by 5, 8 and 16 by 2. From the resulting improper fraction we select the whole part.

Replace mixed numbers with improper fractions and divide them. To do this, we rewrite the first fraction unchanged and multiply it by the inverted second. We reduce 18 and 36 by 18, 35 and 7 by 7. The result is an improper fraction. We select a whole part from it.