1
First, knowledge points
1
An object or a whole composed of several objects can use natural numbers.
1
To show that we usually
Make a phone call
Unit "
1
"
2
Divide the unit "1" into several parts on average, and the number representing such a part or parts is called
mark
. take for example
3/7
It means to divide the unit equally "1".
seven
Copy that. Take one of them.
three
Share it.
three
.
5/8
According to the meaning of the score, the instrument indicates:
keep
1
Average rice share
eight
Copy that. Take one of them.
five
share
. By score
The relationship with the department shows that:
keep
five
Average rice share
eight
Copy that. Take one of them.
1
share
four
Divide the unit "1" into several parts on average, and the number representing one part is called.
Fractional unit
five
.
The relationship between fraction and division
Yes: the numerator of a fraction is equivalent to the dividend in division, and the fractional lines of the fraction are in phase.
When a division symbol is used for division,
The denominator of a fraction is equivalent to the divisor in division.
The fractional value of a fraction is equivalent to division.
In business.
six
Divide a whole into several parts, calculate how much each part is, and then divide it. Total copies/copies = copies.
seven
Find the score of another quantity from one quantity and divide it.
One quantity ÷ another quantity = fraction (multiple).
eight
The fraction of numerator less than denominator is called
proper fraction
. True score is less than
1
nine
A fraction whose numerator is greater than the denominator or whose numerator and denominator are equal is called.
improper fraction
. Error score greater than
1
Or equal to
1
10
.
mixed number
Includes an integer part and a decimal part, and the decimal part should be a true fraction.
Score greater than
1
1 1
.
The method of transforming pseudo-fraction into fraction
Is to divide the numerator by the denominator,
The quotient is an integer part,
The remainder are molecules,
The denominator remains the same.
The method of turning a score into a false score
The numerator is the product of the integer part multiplied by the denominator and the original molecule.
denominator
there will be no changes.
12
Integer can be regarded as denominator is
1
False scores. take for example
five
Can be seen as
5/ 1
13
Numerator and denominator of fraction
meanwhile
Multiplication or division
identical
quantity
(
Except)
, the size of the score remains unchanged. this
It should be called ...
Basic properties of fractions.
14
.
The common factor of several numbers is called theirs.
common factor
The greatest common divisor among them is called theirs.
grand duke
Factor/coefficient
. The minimum common factor must be
1
15
.
Several numbers share a multiple called them.
common multiple
The least common multiple is called theirs.
Lowest male
multiple
. There is no greatest common multiple.
16
To find the greatest common factor or the least common multiple, we can decompose the prime factor by enumeration or short division.
General review of the significance and basic nature of mathematics scores in the second volume of the fifth grade
2
17
.
The common factor is just
1
These two numbers are called
Mutual prime number
The numerator and denominator have only common factors.
1
Scores,
It should be called ...
The simplest score.
(Fractions in which both numerator and denominator are prime numbers are called
Reduce to the lowest score
. )
The simplest score is not necessarily true.
Scores.
The common factor of two numbers is the factor of the greatest common factor of these two numbers;
The common multiple of two numbers is the multiple of the least common multiple of these two numbers.
practise
1.
Write two numbers as required so that their greatest common divisor is
1
( 1)
Both numbers are prime numbers.
: ____
and
____
(2)
Both numbers are composite numbers.
: ____
and
____
(3)
A prime number and a composite number
: ____
and
____
2.
Find the least common multiple of the following numbers in each group.
2
and
8 3
and
8 6
and
15 6
and
nine
four
and
5 1
and
7 4
and
10 8
and
10
18
The result of division calculation can be expressed in fractions, which is more convenient. If the calculation results can be simplified,
Simplify it to the simplest fraction.
19
.
If two numbers are multiples,
Then their greatest common divisor is a small number,
The least common multiple is
A bigger number.
If two numbers are coprime relations, then their greatest common factor is
1
The least common multiple is their product.
20
Number A× number b = their greatest common factor × their least common multiple.
2 1
Several special cases in which two numbers are prime numbers are: ①
1
And any number is a prime number; ②
Two stages
Adjacent natural numbers must be prime numbers;
③ Two adjacent odd numbers must be prime numbers;
④ Two different prime numbers.
Must be a prime number; ⑤ The sum of a prime number and its multiples must be a prime number.
22
Turning a fraction into an equal fraction with smaller numerator and denominator is called
Reduce (part of)
Reduction method
Is that the numerator and denominator are divided by their common factor at the same time.
It is called "dividing the scores of different denominators by the scores of the same denominator equals the original score"
Turn fractions into common denominators
When sharing points,
Take the least common multiple of two denominators as the common denominator,
Don't forget that the numerator and denominator are multiplied at the same time.
The number of.
General review of the significance and basic nature of mathematics scores in the second volume of the fifth grade
three
Using both reduction and general division.
Basic properties of fractions.
Fraction simplification includes two steps.
One is about integration; The second is to turn false scores into integers or fractions.
23
.
General method of converting fractions into decimals
Is the numerator divided by the denominator;
Press "four" as needed when you can't use it up.
"Five decimal places" method)
Special method: ① denominator is
10
100
1000
,? Time and integrity
Then write it as a decimal.
② The denominator is
10
100
1000
When the factor,
The matrix of modifiable components is
10
100
1000
Fractions, and then written as decimals.
The method of converting decimals into numbers.
Is to write the decimal directly as the denominator is
10
100
1000
, scores,
Simplify again.
24
.
If the denominator of the simplest fraction is divided by
2
and
five
In addition,
Does not contain other prime factors,
This score
It can be reduced to a finite decimal.
25
The greatest common factor of two numbers is equal to the product of the prime factor shared by two numbers;
The least common multiple of two numbers is equal to the prime factor shared by two numbers × their unique prime factor.
26
.
Compare the size of the score.
Look at whether the numerator or denominator are the same first,
①
Two fractions with the same denominator, point
Sub-big scores are bigger.
Having two parts of the same molecule,
Scores with larger denominator are smaller.
② numerator and denominator
If the scores are all different, you can score or score first, and then compare the scores.