On-off, on-off and on-off by nature

In actual production and life, people often can't get integer results when measuring and calculating. At this time, a new number fraction is generated to represent it.

Section 1 Mutual Understanding of Score Mastery

First, the meaning of the score

1, the unit "1" is divided into several parts on average, indicating the number of such one or several parts, which is called

score Divide a line segment into four parts, each part belongs to it, and three parts are it.

about

(1) average score as denominator.

(2) take the number of molecules.

③ An object, a counting unit, multiple objects, the population of a collective and the gross national product can all be regarded as the unit "1"; ④ The unit "1" is divided into several parts on average, and the number representing one part is called decimal unit.

For example, the decimal unit of is and the decimal unit of 2 is.

2, the relationship between fraction and division

(1) dividend = dividend

Parting line a

(2) If a represents the dividend and b represents the divisor, then a÷b= b(b≠ 0).

Because the divisor cannot be 0, the denominator cannot be 0.

3. What is a true score? What is a false score?

(1) molecular score The score of the alma mater is called the true score.

Such as: ...10,1,12, 13, 14, 15, 15,/kloc. kloc-0/9、 19、 19、 19、 19、 19、 18、 19、 19、 19、 19、 19、 19、 1 9、 19、 19、 19、 19、 19、 19、 19、 19、 19、 19、 19、 19、 19、 / kloc-0/9、 19、 19、 19、 19、 19、 19、 19、 19、 19、 19、 19、 19、 1 9、 19、 19、 19、 19、 19、 1

② Fractions with numerator greater than denominator or numerator equal to denominator are called false fractions.

For example:,,, ... are all false scores, and the false score is greater than or equal to1;

4. What is a score?

Some false fractions can be written as integers and true fractions, which are usually called fractions;

For example, 3, 5, 7 ... are all called by fractions.

Second, the relationship among integer, false fraction and band fraction.

1, integer becomes false fraction.

Turning an integer into a false fraction means using the specified denominator as the denominator and using the product of the denominator and the integer as the numerator;

For example, the error score of a binary component with the letter 4 is: 2=

2. Turn the false fraction into an integer.

In some false fractions, the numerator is just a multiple of the denominator, that is, the numerator is divided by the denominator to get an integer.

For example:

3. Turn fake scores into scores.

Turning a false fraction into a fraction is to divide the numerator by the denominator, the quotient is the integer part with the fraction, the remainder is the numerator of the fraction, and the denominator remains unchanged;

For example, =2, =2

4. Turn the band soundtrack into a fake soundtrack.

Turn a fraction into a false fraction, use the original denominator as the denominator, and use the product of denominator and integer plus the original numerator as the numerator, and the denominator remains unchanged;

Like 8.

The second section points and points by nature

First, the basic nature of music score

1, what are the basic properties of the fraction/

The numerator or denominator of a fraction is multiplied or divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged; For example:

2. Apply the basic properties of the score and fill in the appropriate figures in the brackets below.

(1) Because 45÷ 15=3, that is, the denominator is enlarged three times, so the numerator 9 should also be enlarged three times, that is, 9× 3 = 27;

(2) Because 18÷9=2, that is, the molecular amplification is 2 times, so the denominator should also be 2 times, that is,15× 2 = 30;

Second, the approximate score

1, what is the approximate score?

Changing a fraction into a fraction equal to it but with smaller numerator and denominator is called divisor.

2. What is the simplest score?

Both numerator and denominator are prime numbers, which is called the simplest fraction.

For example, .............................................................................................................................................................................

3. how to divide it?

① Generally use the common divisor of the numerator and denominator (except 1) to remove the numerator and denominator of the fraction;

② It is easier to find the greatest common divisor of numerator and denominator first, and then remove numerator and denominator by common divisor;

③ Generally divide by the simplest fraction (that is, both numerator and denominator are prime numbers);

such as

Third, the general score |

1, what is the general score?

Dividing the scores of different denominators by the scores of the same denominator equals the original score, which is called the total score.

2, the general method of sharing

① First, find out the least common multiple of the original denominator as the common denominator;

② What is the quotient obtained by dividing the common denominator by the original denominator?

③ The quotient obtained by multiplying the numerator and denominator of the original score.

divide and rule

Find the least common multiple of 8 and 12.

2| 8 12

2| 4 6

2 3 2×2×2×3=24

2 24 ÷ 8 = 3,24 ÷ 12 = 2

The quotient obtained by multiplying the numerator and denominator of the original fraction.

In the third section, compare scores.

1. How to compare scores with the same denominator?

Fractions with the same denominator have large numerator and small numerator.

For example, compare the sizes of and.

Second, how to compare the scores of the same molecule?

For fractions with the same numerator, the smaller denominator is larger, and the larger denominator is smaller.

The size of the sum

or

Third, compare the scores.

1, the band with large integer part has large score, and the band with small integer part has small score;

Such as >

2. For integer parts with the same score, the score is large and the score is small.

Fourth, scores with different denominators and different numerators should be divided first and then compared.

1, compare the size of sum.

because

therefore

2. Compare the size of sum.

Because of this. ...

From the above two questions, the following laws are drawn:

① Divide the scores of different denominators first;

Secondly, according to the scores with the same denominator, the scores with large molecules are large and the scores with small molecules are small.

(3) Finally, change to the known number of copies.

Percentage in the fourth quarter

First, the meaning of percentage.

1, why use percentage?

In production, work and study, in order to facilitate investigation, statistics, analysis and comparison, percentages are often used to explain the situation, which is conducive to guiding practical activities.

2. What is percentage?

A number indicating that one number is a percentage of another number is called a percentage. Percentage is also called percentage.

Or percentage.

Second, the percentage of reading and writing.

1, read the following percentage.

1﹪ 25﹪ 13 1.7﹪ 2 15﹪

1 = read 1% 25 = read 25%.

13 1.7% read131.7% 2 15% read 215%.

Remember the pronunciation of percentage.

① Read the percent sign first, that is, "percentage"

(2) according to the integer or decimal reading method, read the molecular part;

2. Write down the following percentages.

Five percent, 30 percent, 500 percent and 0.9 percent.

Writing is 25.7%, writing is 5%, and writing is 30.5%.

0.9% writing 0.9%, 25.7% writing 25.7%

Remember how to write percentages.

(1) Write in integers or decimals first, and write out the molecular part of percentage;

② Then add a percent sign;

Third, the relationship between fractions, decimals and percentages.

1. Decimate the following fraction.

≈0.333

Remember the method of fractional decimal.

(1) The numerator is divided by the denominator (when it is used up, it is generally rounded to the fourth place after the decimal point and rounded to three places after the decimal point);

(2) Fractions into decimals generally use the integer part of fractions as the integer part of decimals, and the quotient of numerator divided by denominator as the decimal part;

2. Decimal following components.

0.5 0.35 0.375 1.25

Remember how to divide decimals into numbers:

(1) First, rewrite one decimal as a fraction with the mother letter 10, two decimal as a fraction with the mother letter 100, and three decimal as a number with the mother letter 1000. ...

(2) An offer that can be reduced to the simplest score;

(3) False scores should be converted into component numbers or integers.

3. Rewrite the following scores into percentages.

How to remember the percentage of fractions:

① First, the fraction is converted into decimal;

② Move the decimal point two places to the right (not enough to add 0) and add a percentage sign;

4. Rewrite the following percentages to the number of components.

Remember the percentage scoring method:

(1) First rewrite the number of components with the percentage of 100;

(2) If the numerator is a decimal, it should be rewritten as a numerator, and the denominator is a fraction of an integer;

(3) It can be reduced to the simplest score;

(4) False scores should be converted into component numbers or integers;

5. Rewrite the following decimals into percentages.

0.28=28﹪ 2.05=205﹪

0.045=4.5﹪ 5=500﹪

Remember how to rewrite decimals into percentages.

Move the decimal point two places to the right, and then add a percent sign.

6. Rewrite the following percentages into decimals.

29﹪=0.29 105﹪== 1.05

125﹪== 1.25 0.6﹪=0.006

Remember how to rewrite percentages into decimals.

Rewrite the percentage into decimal, only remove the percent sign, and move the decimal to the left by two places;

....

7. Divide 0.53 and 0.2 13 into components.

A .....

0.5 3 =0.53 ①

....

0.53 × 100==53 .53 ②

........

②-① 0.53 × 100- 0.53=53.53—0.53

..

0.53X( 100 - 1)=53

..

0.53X99=53

.. 53 ... Abdominal muscles

0.53 =-that is, 0.ab =-.

99 99

B.

....

0.2 13x 10 = 2. 13①

..。 .

0.2 13x 1000 = 2 13. 13②

②-①

........

0.2 13x 1000 _ 0.2 13x 10 = 2 13. 13 _ 2. 13

..

0.2 13x990=2 12

..

0.2 13= 2 12 ..abc — a

990 means: 0.abc= 990.

Exercise 3,

Fill in the blanks

1, the unit "1" is evenly divided into several parts, and the number representing such one or several parts is called ();

2. The molecular score of the alma mater is called (), and the numerator is greater than the denominator or the numerator and denominator are equal.

3. Some false scores can be written as numbers composed of integers and true scores, which are usually called ();

4. Turning an integer into a false fraction is to use the specified denominator to make the product of () and () as the numerator.

5. Turning a false fraction into a fraction is to divide () by (), the quotient is the fraction (), the remainder is the fraction (), and the denominator remains unchanged.

6. Turn the band fraction into a false fraction, use the original denominator as (), and use the product of () and () plus the original () as the numerator, and the denominator remains unchanged.

7. The numerator or denominator of a fraction is multiplied or divided by the same number at the same time (except 0), and the size of the fraction ()

8. Turning a fraction into a fraction equal to it but with a smaller denominator is called ();

9. Both numerator and denominator are (), which is called simplest fraction.

10. It is called () to replace different denominator scores with the same denominator score equal to the original score.

1 1, the general method of general division is to first find the () of the original denominator as the common denominator; Divide the common denominator by the original denominator, and then multiply the numerator and denominator of the original fraction to get the quotient.

12, the general reduction method is to use 2, 3, 5, 7, 1 1, 13, 17, 19, 23, 29 ... to reduce the score respectively, or

13, fractions with the same denominator, fractions with large numerator () and fractions with small numerator ().

14. Fractions with the same numerator have a smaller denominator () and a larger denominator ().

15, the integer part with fraction is large () and the integer part is small ().

16, if the integer parts are the same, score; If the decimal part is large, compare (); If the decimal part is small, compare ();

17, the scores of different denominators and different molecules should be divided first and then compared ();

18, which means that a number is a percentage of another number is called (). Also known as () or ().

19, true fraction, false fraction into decimal, generally divided by ().

20. Fractions are used to enter decimals. Generally, fraction () is used as the integer part of decimals, and quotient of numerator divided by denominator is used as ();

2 1. Decimalization component number. First, the decimal is rewritten as the constituent letters 10, 100, 1000 ... (), and then approximated as () points;

22. Rewrite the score into a percentage, and first change the score into (); Then move the decimal point two places to the right (add 0 if it is not enough) and add ()

23. Rewrite the percentage to the number of components. First rewrite the percentage into a score of ();

What can be reduced should become ()

24. Rewrite the decimal point into a percentage, put the decimal point to the right () two places, and add ();

25. When converting percentages into decimals, only () is removed, and the decimal point is moved by two places ();

Second, judge whether it is right or wrong (mark "√" correctly and "×" wrongly).

The decimal unit of 1 is ()

2. There are 7 ()

3, 5 kg and 1 kg have the same weight ()

4. 1 has 7 or 99 ().

5. A false score is a number whose numerator is greater than the denominator ()

6. The scores are all less than an integer ()

7. The numerator and denominator of the score are multiplied or divided by the same number, and the size of the score remains the same ()

8. The scores greater than and less than are only ()

9. The numerator and denominator of the fraction should be expanded by 5 times, and the fractional value should also be expanded by 5 times ()

10, the greater the denominator of the fraction, the smaller the decimal unit ()

1 1, add 1 to the numerator and denominator, and the size of the fraction remains the same ().

12, the numerator and denominator of a fraction are prime numbers, which must be the simplest fraction ().

13, the denominator of a fraction remains unchanged, the numerator is reduced by 5 times, and its fractional value is reduced by 5 times ()

14, because =, their decimal units are the same ()

15, reverse the numerator and denominator of a false fraction to get a true fraction ()

Three, multiple choice questions (choose the correct answer number, fill in the brackets)

1. Divide the class into 9 groups on average, including 4 groups of girls, accounting for () of the class.

① ② ③ ④

2, 5 cm = () meters

① ② ③ ④

3. In, a is a natural number and a () is a true fraction.

①a=8 ②a8 ④0