You will need

- a textbook on mathematics for 5 and 6 classes

Instruction

1

It is customary to divide common and decimal

**fractions**, familiarity with which begins in high school. Currently there is no area of knowledge where you would not apply this concept. Even in history we're talking the first quarter of the 17th century, and all at once understand what we mean 1600-1625. Also often have to deal with basic operations on fractions and convert from one form to another.2

Reduction of fractions to a common denominator is perhaps the most important operation on ordinary fractions. This is the basis for all calculations. So, let's say there are two

**fractions**a/b and c/d. Then, in order to bring them to a common denominator, you need to find the least common multiple (M) numbers b and d, and then multiply the numerator of the first**fraction**to (M/b) and the numerator of the second to (M/d).3

Compare fractions, is another important task. In order to do this, give a set of simple

**fractions**to a common denominator and then compare numerators whose numerator is greater than the fraction and more.4

In order to perform the addition or subtraction of ordinary fractions, you need to bring them to a common denominator, and then produce the desired mathematical operation with the numerators of these fractions. The denominator remains unchanged. Let's say you need from a/b subtract c/d. This requires to find the least common multiple of M numbers b and d, and after you subtract one numerator from the other, without changing the denominator: (a*(M/b)-(c*(M/d))/M

5

Simply multiply one fraction by another, simply multiply their numerators and denominators:

(a/b)*(c/d)=(a*c)/(b*d)to divide one fraction by another, you need a fraction of the dividend multiplied by a fraction the inverse of the divisor. (a/b)/(c/d)=(a*d)/(b*c)

To cost to remind that in order to get the reverse shot, you need the numerator and denominator are reversed.

(a/b)*(c/d)=(a*c)/(b*d)to divide one fraction by another, you need a fraction of the dividend multiplied by a fraction the inverse of the divisor. (a/b)/(c/d)=(a*d)/(b*c)

To cost to remind that in order to get the reverse shot, you need the numerator and denominator are reversed.

6

Order from the ordinary

**of the fraction**go to a decimal, you need to divide the numerator by the denominator. The result can be both finite and infinite.If the decimal**fractions**you need to go to an ordinary, lay your number for a whole hour and the fractional presenting the past in the form of a natural number divided by ten to the appropriate degree.Useful advice

Do not forget to reduce the fraction.

# Advice 2 : How to divide a fraction by a fraction

Sometimes when performing calculations you must divide the fraction to the fraction. Fractions can have different views. And this can cause all sorts of difficulty. But dealing with them can be a snap.

Instruction

1

In order to divide common fraction to common fraction, multiply the first fraction by the inverted second fraction. This "inverted" ordinary fraction, where the numerator and denominator are reversed is called reverse.

When dividing fractions it is necessary to pay attention to the fact that the second fraction is not equal to zero. Sometimes, if the fraction is quite bulky, it is extremely difficult to make. In addition, the second fraction can contain some variables (unknown) value, which for certain values of the draw roll to zero. You also need to pay attention to those cases where the denominator of the second fraction vanishes. When the action variables for all these cases, you must specify in the final answer.

For example: see Fig. 1

2

To divide a mixed fraction by a mixed, a mixed fraction to an ordinary or common in mixed, get mixed fractions to an ordinary mind. Then to make the division as specified in step 1.

To transfer mixed fraction to an ordinary need the integer part of mixed fraction multiplied by its denominator and add the resulting product to the numerator.

Example: see Fig. 2

3

When dividing decimal fractions to ordinary (mixed) or division of ordinary (mixed) fraction to a decimal, all fractions are reduced to the ordinary mind. After this division is done according to step 1. To translate decimals to fractions, the "throw" of the decimal point and recorded in the numerator and in the denominator write one and as many zeros as digits stood to the right of the decimal point.

Example: see Fig. 3

4

To divide two decimals need in divisible and the divider to move the decimal point that many digits to the right of the second fraction to make a whole number and divide the resulting number.

For example: 24,68/123,4=246,8/1234=0,2.

If the divisible to transfer the decimal point in the "missing" digits, missing digits are replaced with zeros.

Example: 24,68/1,234=24680/1234=20

For example: 24,68/123,4=246,8/1234=0,2.

If the divisible to transfer the decimal point in the "missing" digits, missing digits are replaced with zeros.

Example: 24,68/1,234=24680/1234=20

Note

The divisor and denominator of a fraction can't be 0.

# Advice 3 : How to do fraction

Common fraction - number whimsical. Sometimes you have to suffer to find the solution of the problem with the

**shot**and present it in the proper form. Learning to solve**examples**with**fraction**, you will easily cope with this unpleasant thing.Instruction

1

Consider addition and subtraction of fractions. For example, 5/2+10/5. Bring both fractions to a common denominator. To do this, find the number that can be divided without remainder by the denominator of the first and second fractions. In our case this number is 10. Convert the above fraction, obtained 25/10+20/10.

Now add together the numerators, and leave the denominator unchanged. It turns out 45/10.

It is possible to reduce the resulting fraction, i.e., divide the numerator and the denominator by the same number. It turns out 9/2.

Highlight the whole part. Find the maximum number that can be divided without remainder by the denominator. The number 8. Divide it by the denominator - this will be a part of it. So, the result is 4 1/2.

Perform the same steps in subtracting fractions.

Now add together the numerators, and leave the denominator unchanged. It turns out 45/10.

It is possible to reduce the resulting fraction, i.e., divide the numerator and the denominator by the same number. It turns out 9/2.

Highlight the whole part. Find the maximum number that can be divided without remainder by the denominator. The number 8. Divide it by the denominator - this will be a part of it. So, the result is 4 1/2.

Perform the same steps in subtracting fractions.

2

Consider the multiplication of fractions. Here everything is simple. Multiply together the numerators and denominators. For example, 2/5 is multiplied by 4/2 turns 8/10. Simplify the fraction, it turns 4/5.

3

Consider dividing fractions. In this step, you flip one of the fractions, then multiply numerators and denominators. For example, 2/5 divided by 4/2 - turns 2/5 times 2/4 - it turns out 4/20. Simplify the fraction, it turns out 1/5.

# Advice 4 : How to divide a fraction by another fraction

To divide

**to****a fraction****is easy - just multiply the first****a fraction****on the bottom of the second. However, there are some nuances to consider who still need.****fraction**Instruction

1

When dividing fractions, multiply the first

When dividing fractions it is necessary to check that the second

Example 1: to divide 1/2 by 2/3

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

Example 2: split a/C to x/s

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

**(numerator) by the inverted second****fraction****(the divisor). Such****fraction****where the numerator and denominator are reversed is called reverse (to source).****a fraction**When dividing fractions it is necessary to check that the second

**and the denominators of both fractions are not equal to zero (or did not take zero values at certain values of parameters/variables/unknown). Sometimes, due to cumbersome fractions, it is very obvious. All values of variables (parameters), converting to zero the divisor (the second****fraction****) or denominators of fractions must be specified in the response.****fraction**Example 1: to divide 1/2 by 2/3

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

Example 2: split a/C to x/s

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

2

To divide mixed fractions, you need to bring them to the ordinary mind. Next, act as in claim 1.

To convert a mixed fraction to an ordinary mind it is necessary the whole part times the denominator and then add this product to the numerator.

Example 3: convert the mixed

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

Example 4: to divide

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

To convert a mixed fraction to an ordinary mind it is necessary the whole part times the denominator and then add this product to the numerator.

Example 3: convert the mixed

**2 2/3 in common:****fraction**2 2/3=(2 + 2*3)/3=8/3

Example 4: to divide

**3 4/5 to 3/10:****fraction**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, different types (mixed, decimal, common), all the fractions previously given to the ordinary mind. Further, according to claim 1. A decimal

Example 5: allow the decimal

since fractions are "mils" (thousandths 457), and the denominator will be equal to 1000:

3,457=3457/1000

Example 6: divide a decimal

1,5 : 1 1/2 = 15/10 : 3/2 = 15/10 * 2/3 = (15*2)/(10*3) = 30/30 = 1.

**is translated into common is very simple: the numerator is written decimal****fraction****without the decimal, and the denominator order fractions (tenths to ten, a hundred for hundredths, etc.).****fraction**Example 5: allow the decimal

**3,457 ordinary mind:****fraction**since fractions are "mils" (thousandths 457), and the denominator will be equal to 1000:

3,457=3457/1000

Example 6: divide a decimal

**to a mixed 1,5 1 1/2:****fraction**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 pre-multiplied by 10 to the extent that the divisor was a whole number. After dividing decimals "completely".

Example 7: 2,48/12,4=24,8/124=0,2.

If necessary (based on the conditions of the problem), you can find a multiplier value, to become whole as the divisor and the dividend. Then the task of dividing decimals is reduced to the division of integers.

Example 8: 2,48/12,4=248/1240=0,2

Example 7: 2,48/12,4=24,8/124=0,2.

If necessary (based on the conditions of the problem), you can find a multiplier value, to become whole as the divisor and the dividend. Then the task of dividing decimals is reduced to the division of integers.

Example 8: 2,48/12,4=248/1240=0,2

# Advice 5 : How to calculate fractions

The number composed from a certain number of share units, in arithmetic, is called a fraction. It usually consists of two parts - the numerator and the denominator. Each of them is an integer. Literally the denominator shows how many parts the unit is divided, and the numerator how many of these parts took.

You will need

- a textbook on mathematics for 5 and 6 classes

Instruction

1

It is customary to divide common and decimal

**fractions**, familiarity with which begins in high school. Currently there is no area of knowledge where you would not apply this concept. Even in history we're talking the first quarter of the 17th century, and all at once understand what we mean 1600-1625. Also often have to deal with basic operations on fractions and convert from one form to another.2

Reduction of fractions to a common denominator is perhaps the most important operation on ordinary fractions. This is the basis for all calculations. So, let's say there are two

**fractions**a/b and c/d. Then, in order to bring them to a common denominator, you need to find the least common multiple (M) numbers b and d, and then multiply the numerator of the first**fraction**to (M/b) and the numerator of the second to (M/d).3

Compare fractions, is another important task. In order to do this, give a set of simple

**fractions**to a common denominator and then compare numerators whose numerator is greater than the fraction and more.4

In order to perform the addition or subtraction of ordinary fractions, you need to bring them to a common denominator, and then produce the desired mathematical operation with the numerators of these fractions. The denominator remains unchanged. Let's say you need from a/b subtract c/d. This requires to find the least common multiple of M numbers b and d, and after you subtract one numerator from the other, without changing the denominator: (a*(M/b)-(c*(M/d))/M

5

Simply multiply one fraction by another, simply multiply their numerators and denominators:

(a/b)*(c/d)=(a*c)/(b*d)to divide one fraction by another, you need a fraction of the dividend multiplied by a fraction the inverse of the divisor. (a/b)/(c/d)=(a*d)/(b*c)

To cost to remind that in order to get the reverse shot, you need the numerator and denominator are reversed.

(a/b)*(c/d)=(a*c)/(b*d)to divide one fraction by another, you need a fraction of the dividend multiplied by a fraction the inverse of the divisor. (a/b)/(c/d)=(a*d)/(b*c)

To cost to remind that in order to get the reverse shot, you need the numerator and denominator are reversed.

6

Order from the ordinary

**of the fraction**go to a decimal, you need to divide the numerator by the denominator. The result can be both finite and infinite.If the decimal**fractions**you need to go to an ordinary, lay your number for a whole hour and the fractional presenting the past in the form of a natural number divided by ten to the appropriate degree.Useful advice

Do not forget to reduce the fraction.

# Advice 6 : How to turn fraction

Under the phrase "flip

**the fraction**" one can understand various mathematical transformations. Anyway, the result of these changes the numerator in a certain way must change places with the denominator. Depending on the kind of conversion the number can change and remain the same.You will need

- Knowledge of the rules of converting fractions

Instruction

1

The most trivial transformation is a simple flipping of a fraction or a permutation of the numerator and denominator swapped. The result is a number, reverse the source and the product of these two numbers will give the unit. Example: (2/5)*(5/2) = 1.

2

As you can see from the previous example, if you divide a unit into any number we get the number back to him. But divide the number of units a number is a number x to the power of -1. Therefore, (x/y) = (y/x)^(-1). Example: (2/3) = (3/2)^(-1).

3

Sometimes, the calculations can get cumbersome, "multistoried" fraction. To simplify a fraction they also need to turn. Turn these fractions according to the following rules: x/(y/c) = (x*c)/y (x/y)/c = x/(y*c), (x/y)/(b/c) = (x*c)/(y*b).

4

It is useful to change the type of shot and in the case where in the denominator there is an irrational number. To do this, the numerator and denominator of this fraction must be multiplied by is an irrational number. Then an irrational number will be in the numerator of the fraction. Example: 1/sqrt(2) = sqrt(2)/(sqrt(2)*sqrt(2)) = sqrt(2)/2.Source: Maths: a Big book reference for students and University entrants", D. I. Averyanov, P. I. Altynov, I. I. Bavrin., 1998

Note

It is important to remember that the number in the denominator must be nonzero, otherwise all permutations are losing their correctness.

# Advice 7 : How to divide number by fraction

**A fraction**is a noninteger, or augmented

**the number**, such as 1/2 (=0.5) or 7,5/5 (=1.5 m). Sometimes a fraction can be any integer

**number**m, for example, 20/5 (=4), but its entry does not have the mathematical meaning, which is entered in the roll.

Instruction

1

First recall that the simple or ordinary fraction can be written as X / Y where X is the numerator and Y the denominator. For example, 1/4, or 0.25 in digital recording. For convenience of further calculations, it is recommended to write the fraction vertically: a numerator, a horizontal bar dividing under him, and the denominator in the runway.To divide a number by a fraction, you need to present

**the number**as a fraction. Since**the number**is the number of integer parts, then it goes in the denominator and in the numerator of the prescribed what is the number of divided parts to obtain the very same himself – that is, one. 8 should be written as 8/1, and 263 – how 263/1, and so on.2

After that you need to divide

**number**to fraction. Suppose you have**the number**127 and the fraction 4/15. Then the operation 127 : 4/15 should be written as follows:127/1 : 4/15;3

It turns out the three-story fraction at which the average division (division of fractions) should be replaced by multiplication, and the numerator and denominator flip:127/1 * 15/4;

4

Writing this action in the usual fraction with a horizontal division, you will receive:(127*15)/4;the Result of 467 1/4.

5

Counting on the calculator every roll, you will receive the following:127 : 1 = 127

4 : 15 = 0,2666...

127 : 0,2666... = 476, 476 2500001 or 1/4.The results coincide.

4 : 15 = 0,2666...

127 : 0,2666... = 476, 476 2500001 or 1/4.The results coincide.