Reading should start from a high position, and whoever reads it will read it.
If there is a zero at the end of each stage, you don't have to read it out.
If the other numbers are zero in a row, just read one.
Read "ten thousand" at the end of ten thousand, and read "hundred million" at the end of one hundred million.
Multi-digit song writing
Write a few numbers from it, as many as you want.
Whoever doesn't have a unit, remember to use 0 to occupy the place.
Multidigit size comparison
The number of digits is different from the size, and the number of digits is large;
If you look at the high digits with the same number of digits, the high digits are large.
Comparison of decimal sizes
The decimal size depends on the high position, and the number of hours is large when the integer is large.
If the integers are the same, there will be more decimal places and more hours.
When you look at the percentile with the same decile, the larger the percentile, the longer the time.
Comparison of fractional sizes
Several fractions compare size, numerator and denominator.
The denominator is the same. If you look at molecules, the bigger the molecules, the greater the score.
If the numerator is the same, look at the denominator, and the score with a large denominator is small.
Usage of greater than sign and less than sign
Greater than sign and less than sign.
Smile at the big numbers.
(the opening is big and the tip is small; This number can't be wrong. )
Multi-digit rewriting
Remove the "0" after ten thousand digits and add ten thousand characters to complete the change.
Remove the "0" after one billion digits and add one billion words to correct it.
Integer addition rule
Integer addition is regular, and the same digits should be aligned.
And less than ten fell in the original position, and more than ten entered one.
Go down for more than ten times, and add whichever one is dropped.
Add up the carry, and the result is not less than half a cent.
Integer subtraction rule
Integer subtraction is regular, and the same numbers should be aligned.
Reduce the time and difference greatly, and borrow less.
Minus ten and add it, and the result of addition and subtraction falls in the original position.
Be careful when borrowing continuously, and remember what is left when borrowing.
Multi-digit multiplication rule
Integer multiplication starts from the low bit and several numbers are multiplied several times.
Multiply the number of units by several 1, and the last digit of the product is the number of units.
Ten digits are multiplied by dozens, and the last digit of the product is ten digits.
Hundreds times hundreds, and the last digit of the product is hundreds.
Calculate the correct position and add several products together.
Multiplication rule with zero at the end of factor
If there is a 0 at the end of the factor, write it after it without multiplying it first.
Multiply the product to make up 0 and write a few zeros.
Multi-digit division rule
Integer division starts from the high order. Divide by a few and see how many there are.
This is not enough to see the next one, except which one is for business.
The remainder is less than the divisor, which is not enough for quotient one zero.
Meaning of division
Go "divide" and circle. The word "divide" is preceded by divisor.
Don't forget the dividend after the word "points".
Basic arithmetic
The mixed operations are in sequence, starting from the left side of the peer calculation.
Add, subtract, multiply and divide mixed problems, calculate multiplication first, and then remember division.
If there are brackets, count the questions in brackets first.
rounding-off method
The rounding method is good, and the approximate figure can be found out by law;
Take which one to look at the next one, and then compare it with five words;
It is 5 big 5 forward 1, and all less than 5 are discarded;
The equal sign is replaced by an equal sign, which makes people understand at a glance.
Decimal addition and subtraction rules
Decimals are added and subtracted regularly, and the same numbers should be aligned.
One for one, ten for ten. ……
Ten to ten, percentile to percentile. ……
In short, the decimal points should be aligned.
The calculation result is decimal, and the zero at the end should be crossed out.
Decimal multiplication rule
Starting from the low order of decimal multiplication, calculate the product by integer first.
Look at the decimal places in the factor.
Just count a few points from the right side of the product, and finally there are zeros to cross out.
Decimal division rule
Decimal division starts from the high position, and look for the law of divisor.
Divider is a direct division of an integer, except which manufacturer.
Not enough quotient 10, the quotient and dividend points are aligned.
The divisor is a decimal to an integer, and the divisor decimal point is shifted in the same place.
If the number on the right is not enough, it should be filled with zeros.
Fraction addition and subtraction rule
Adding and subtracting fractions is very simple, and unifying units is the key.
Use the denominator to add and subtract fractions, only add and subtract numerators, and the denominator size remains the same.
Fractions with different denominators are added and subtracted, and the fractions are divided first and then calculated.
Fractional multiplication rule
Fractional multiplication is simpler and numerator and denominator are calculated separately.
Multiplication of numerator is numerator and multiplication of denominator is denominator.
The numerator and denominator are not prime numbers, so the numerator and denominator should be calculated first.
Fractional division rule
Fractional division is the simplest, and it is calculated by conversion multiplication.
When the divisor becomes a multiplier, the reciprocal of the divisor will appear.
Prime number and composite number
The key to distinguish prime numbers from composite numbers is to look at divisors.
1 has only one divisor, which is neither prime nor composite;
If there are only two divisors, it must be a prime number;
Three divisors or more, it must be a composite number.
Decomposition of quality factors
The decomposition of prime factors is realized by short division.
Divisor is a prime number, and quotient is also a prime number.
The expression form is simple: composite number = prime number × prime number. ...
Prime numbers within 100
Two three five seven one,
Thirteen, nineteen and seventeen,
Two, three, two, three, eleven,
Three, seven, four, three, four, one,
Four, seven, five, three, five, nine,
Six one six seven, hand in hand,
Seven, one, seven, three, seven, nine,
Eight, three, eight, nine,
Look left and right, there is no alignment,
It turned out to be 97 short.
Hour hand and minute hand
Jason Chung's face is round, and the hour hand runs in circles.
The minute hand is long, the hour hand is short, one is fast and the other is slow.
The minute hand ran a full circle, and the hour hand only ran a short one.
Understanding of time and minutes
The hour hand passed the number,
This means that when,
How many points are left,
Please look at the minute hand carefully.
Year, month and day
135780 wax (65438+February),
Thirty-one days is never bad;
April 30th (165438+1October);
February 28th in a normal year,
Add one in February of leap year.
One, three, five, seven, eight, ten, wax, 3 1 day is always big.
April, June, September, November, 30 days is never bad.
February, the most special, February and February changes.
Twenty-nine leap years and twenty-eight average years.
Except the year number is even, the whole century number is marked with double zeros.
There are two ways to be punctual, twenty-four and ordinary.
The time unit is lined up, and the largest unit is the century.
1 century, 100 year; How many days is 1 year? 365 in a normal year and 366 in a leap year.
1 hour 60 minutes 1 minute equals 60 seconds.
Remember the year, month, day, hour, minute and second, and the progressive rate.
Position and direction
Get up in the morning and face the sun. The front is east, the back is west, the left is north, and the right is south.
The orientation of the map is stipulated, so remember it well.
Measuring angle
Center to vertex, line 0 to one side,
When reading the scale, you should divide it inside and outside.
Difference between length, area, volume and volume
One line is long and has a large area;
Volume takes up space and volume counts.
Letter representation number
Letters represent numbers, and the key is to remember,
When omitting the multiplication sign, you should write numbers first, then letters.
The same factor changes the cardinal number, and the number of factors changes the exponent.
The multiplication sign can be abbreviated as a dot, and the addition and subtraction multiplication sign cannot be lost.
Solving application problems with column equations
Column equation to solve application problems, grasp the key points to analyze.
Turn known conditions into numbers and unknown conditions into letters,
Find the relevant algebraic expressions and connect them to read.
Solve application problems
Look at the topic several times to find the key points;
Look at what you want first, and then find conditions;
Reasonable calculation formula, careful calculation;
Ask for more answers to a question, and the unit will not forget it;
Check the results and finally write the answer.
Skillful Learning of Primary School Mathematics (2)
How to read and write multiple numbers?
From high to low,
The specific pronunciation is the same level,
Read 10 thousand at the end of 10 thousand,
At the end of the billion scale,
There is a 0 in the middle, read one,
There is a 0 at the end, not to mention.
Writing and reading are the same,
Also from high to low,
Who doesn't have a unit,
Pay attention to writing 0. Don't forget.
Rewriting of names
Pay attention to the rewriting of names.
Units of measurement should remember:
High-level units become low-level,
The multiplication rate is ok;
If you come across a compound number,
Don't be careless when rewriting adds up.
Low-level units become advanced,
Divided by the forward speed;
If the division has a remainder,
The rest are still low-level.
rounding-off method
The rounding method is good,
Approximation can be found by law;
Keep who looks at the next position,
Then compare it with five words;
It's the top five strikers 1,
Give up all less than 5;
Replace the equal sign with an approximate equal sign,
Let people understand at a glance.
Carry addition
Don't forget to bring the addition:
The same numbers should be aligned,
Starting from the unit,
Don't worry if it exceeds 10.
Go to ten digits and enter 1.
Abdication subtraction
Subtraction of abdication should be kept in mind:
The same numbers should be aligned,
Let's talk about the unit first.
If the number of digits is not enough, 1 will be returned.
After 1, above 10, add a little more,
Just keep reducing it.
Integer multiplication
Integer multiplication should remember:
Multiply the multiplicand by the multiplier,
From low to high,
Who should I take? Don't be careless,
The last digit of the multiplication number,
Aim at that. Don't be careless,
Add it up several times,
The calculation results show that.
Multiplication of factors with 0 in the middle.
If there is 0 between multipliers,
The calculation process can be simple,
You don't have to take a bus after 0.
Digital calibration is the key.
Multiply by 0 at the end of the factor
Forget the zero at the end,
Count the other numbers,
Remember to work out the result:
Add a total of 0 at the end.
Integer division
Let's first look at how many divisors there are.
Try to divide by the first few digits of the dividend.
If it is less than the divisor,
Try to meet one more person,
Except which one is separated,
The business is written in that one;
Remember after each division:
The remainder is less than the divisor.
Divider, division with zero at the end of divisor
First, eliminate the number of zeros,
Divider 0 is the same as elimination,
Calculate after eliminating 0,
The calculation rule remain unchanged,
If the result has a remainder,
The eliminated zeros need to be supplemented.
Four algorithms
Four operations are not difficult,
Calculate multiplication and division first, then add and subtract;
If there are parentheses in the question,
First calculate in parentheses,
Parentheses are completed in turn,
Ensure that the operation will not be chaotic;
So is the fractional part,
The algorithm is the same.
Decimal addition and subtraction
Decimal addition and subtraction are simple,
Be sure to align the decimal point,
The calculation rule is the same as integer,
Don't be biased when calculating;
Below the decimal point alignment point.
Decimal multiplication
Decimal multiplication is easy to calculate,
You don't have to align the decimal point,
A few digits in the decimal part,
As a result, looking back,
Count enough people before counting.
Decimal multiplication is not difficult,
The key point is a good decimal point;
Sum of factor decimal places,
Decimal digits in equivalent products;
If the intermediate product is not enough,
Make it up with 0, click it.
If the factor is not 0,
There is a mystery in this;
One factor is less than 1,
Another factor is greater than the product;
A factor greater than 1,
Another factor is smaller than the product.
Decimal division
Don't be careless in decimal division.
Look at the divisor before calculating,
If integers are not troublesome,
If it is a decimal, please remember:
Move the decimal point to the right,
To turn decimals into integers,
The divisor has moved several positions to the right,
Dividend transfer, don't be vague,
Count enough digits, click on it,
The number of digits is not enough to fill 0;
The calculation rule is the same as integer,
Except for the balance at the end of the dividend,
Add 0 to the remainder to continue the division.
Remember the calculation results:
The decimal point of quotient and dividend,
It must be aligned and cannot be neglected.
Fractional addition and subtraction
The denominator is the same, the simplest,
Only add and subtract molecules;
It is not difficult to have different denominators.
Calculation after sharing;
Remember that the denominator remains the same,
The result should be simplified.
Fractional multiplication and division
Remember fractional multiplication clearly,
Multiplication of numerator and denominator;
To simplify the calculation,
Cut if you can.
Fractional division is not difficult to calculate,
Divider inversion, disguised multiplication;
For that wrong score,
The calculation rules are still the same.
Comparison of fractional sizes
The denominator is the same. Look at the molecules,
The bigger the molecule, the bigger the volume.
The molecules are the same. Look at the denominator,
The denominator is small but large.
False fraction with fraction or integer
A false score with scores,
Divide the numerator and denominator,
Quotient is integer remainder,
Remember that the denominator is the same.
If two numbers are divisible,
Quotient is an integer.
Fraction error score
Scores, wrong scores,
The original denominator is still the denominator,
The product of denominator integers,
Add a position to the original molecule,
To be a molecule, remember.
Conversion between percentage and decimal
Decimals are converted into percentages,
The decimal point moves to the right. Remember,
Move two places and do:
Add hundreds of semicolons at the end.
Percentages should be decimal,
The decimal point moves to the left. Remember,
Move two places and do:
The percent sign must be removed.
Reciprocity of percentage and fraction
The score should be a percentage,
First, decimal fraction;
Don't worry when you can't finish it,
You can keep three decimal places.
Decimals to remember:
Decimal percentage
Percentages should be divided into fractions,
Rewrite it to the component number,
Provide points that can be reduced,
This is done in the simplest way.
Judgement of general application problems of fractional (percentage) multiplication and division method
Judge the problem of score application,
The key is to determine the unit "1".
As long as we find the standard quantity,
Compare the quantity and then compare.
Find the fraction of a number by multiplication,
Knowing what the score of a number is,
Find a number division problem.
Fractional multiplication and division can distinguish,
The percentage is the same principle.
Distinguish between big months and small months
135780 wax *,
Thirty-one days is never bad;
April, June, September and November,
There is no doubt that within thirty days;
February 28th in a normal year,
Add another day of leap year.
La: This refers to1February.
Lines, segments and rays
These two endpoints are called line segments,
An endpoint is called a ray,
No endpoint is called a straight line,
The length of a straight line is infinite.
Classification of angles
An angle of 900 is called a right angle,
Less than a right angle is called an acute angle,
1800 call a boxer,
Greater than right angle and less than right angle,
Such an angle is called an obtuse angle,
3600 is called fillet.
Classification of triangles
Right triangle, right angle,
Three acute angle of a triangle,
Obtuse triangle-obtuse angle,
An equilateral triangle has three equilateral sides.
An isosceles triangle is isosceles.
Angle measurement
Keywords protractor, angle setting edge,
Find the center, the vertex,
0 degree line, to one side,
Want to know what the angle is,
Look at the other side of the corner,
A distinction should be made between internal and external scales.
Calculation of geometric figure ①
Zhou? long
The square is the best to remember,
Its side length is multiplied by 4;
Play a rectangle,
The sum of length and width multiplied by 2;
The circumference of the circle is a bit strange,
Measure the diameter times π.
Face? gather
Area calculation is easy,
Finding out the truth is the premise:
Based on this rectangle,
Multiplying the length and width is the area;
A square with equal adjacent sides,
Can be multiplied by the side length;
Like a parallelogram,
Wide is high, long is bottom;
The trapezoid has an average top and bottom,
The principle of multiplication with height is the same;
The upper bottom is a 0 triangle,
And trapezoid are the same;
Divide a circle in half,
Spread out and look carefully,
Radius squared times cycle rate,
A sector is a part of a circle,
The central angle times the area,
Divided by the circumference 360,
The calculated area is beyond doubt.
Draw a circle
Determine the center and radius,
The tip of the compass defines the center of the circle,
Turn your other foot around,
Draw a circle.
Calculation of geometric figure ②
superficial area
Calculate that surface area of an object,
Can calculate the plane as the premise:
A rectangle has six sides,
Total area or surface area of hexagon;
Cylinders and cones,
The edge is not the bottom,
The circumference of that bottom surface is multiply by the height,
I.e. cylindrical side areas;
The cone is fanned out,
The sector is the lateral area;
Find the side and add the bottom,
The result is surface area.
Body? gather
It is not difficult to calculate the volume.
Knowing the truth is the key:
Based on a cuboid,
Multiplying length, width and height;
There are three equal cube,
An edge cube is a volume;
The bottom surface of that cylinder is multiply by the height,
One-third cone;
The volume should be measured from the inside,
The calculation method is the same as the volume.
Cardinality and ordinal number
Cardinal ordinal numbers are not connected,
The numbers are the same but different:
What is the cardinality,
Ask which ordinal number to use.
Quality? count
Prime numbers are born with a strange temper,
The divisors are only 1 and self.
The minimum value is 2 infinity,
Complex number is its antonym.
Skilled memory of prime numbers within 100
Two, three, five, seven, eleven,
Thirteen, nineteen, seventeen,
23, 29, 3 1 and 37,
4 1, 43, 47,
Five, three, five, nine, six and seven,
73, 79, 7 1,
83, 89, 97,
Remember the prime numbers within 100.
A feature that is divisible by 2, 3 and 5.
A number is divisible by 2,
The last digit must be an even number;
A number is divisible by 3,
The sum of each number is a multiple of 3;
A number is divisible by 5,
The last digit must be 0 or 5.
Decomposition of quality factors
Composite factorization prime factor,
Divided by the smallest prime number,
Quotient is a prime number,
The divider to be written is multiplied by the quotient;
Quotient is a composite number,
Continue to divide according to this method,
Until you get the quality quotient,
And then use multiplication to represent it.
Find the greatest common divisor
Need the greatest common divisor,
Divided by the common divisor,
Until the quotient is a prime number,
Division and multiplication;
If you compare two numbers,
Small is a divisor of a large number,
There is no need to use short division,
Decimals are common divisors.
Find the least common multiple
Requires the least common multiple,
Divided by the common prime factor,
Until the quotient is a prime number,
Divider multiplied by quotient;
If two numbers are prime numbers,
The product is a common multiple;
Big is a multiple of decimal,
You don't have to ask for it.
Judging the positive-negative ratio
It's easy to judge the proportion,
Find the relationship between two quantities:
The ratio "sure" is proportional,
The product "must" is inversely proportional.
(Can also be abbreviated as: business is positive, product is negative)
Conversion of common units of measurement
The unit of measurement is easy to convert,
Remember, the speed of progress is the key:
Kilograms, that is, kilograms,
The tonnage rate is1000;
Kilometers and kilometers as a whole,
1km is1000 m;
Millicent should be familiar with it,
The forward speed between them is10;
Area and volume are the simplest,
The forward speed is divided into hundreds and thousands;
1000 ml is one liter,
Cubic decimeter is the same;
24 o'clock is a day,
Remember 60 minutes.
General application problem solving steps
It is not difficult to apply this solution.
Understanding the meaning of the problem is the key:
Considering the known conditions,
Look at the questions you ask;
You can also think backwards,
Comprehensive analysis and judgment;
Drawing can help clear your mind.
No deviation can be deduced from this;
Calculate first, then calculate in order,
List the formulas carefully;
The calculation results should be tested,
Finally, don't forget to write the answer.
The method of solving application problems with column equations
Column equation, remember:
We must find out the unknown first,
Fine analysis of equivalence relation,
Understand the meaning of the question, don't be vague,
Then list the equations,
X stands for unknown,
Be careful when solving equations,
Don't neglect the inspection process.