* Multiplication exercises within the table (second grade, first volume);
* Division exercises within the table (second grade, second volume);
* Multi-digit multiplied by one-digit exercises (third grade, first volume);
* Division exercises with a one-digit divisor (third grade, second volume);
* Two-digit multiplied by two-digit exercises (third grade, second volume);
* Three-digit multiplied by two-digit exercises (fourth grade, first volume);
* Division exercises with a two-digit divisor (fourth grade, second volume);
* Decimal multiplication exercises (fifth grade, first volume);
* Decimal division exercises (fifth grade, first volume);
Key Points
1. Concepts of multiplication and division:
1 ) Multiplication is a simple operation of adding the same addends to get the sum. The result of multiplication is called product; for example: 6 × 3 means 6 plus 3 times, that is, 6 + 6 + 6 = 18;
2 ) Division is the inverse operation of multiplication. Given the product of two factors and one of the non-zero factors, the operation of finding the other factor is called division;
Division of two numbers is also called the ratio of two numbers. If ab = c (b ≠ 0), the operation of using the product c and the factor b to find the other factor a is division, written as c ÷ b, read as c divided by b (or b divided by c); among them, c is called the dividend, b is called the divisor, and the result of the operation a is called the quotient;
2. Multiplication and division symbols:
1 ) The symbol for multiplication is " × ";
2 ) The symbol for division is " ÷ ";
3. Understanding multipliers and multiplicands:
1 ) The multiplier is the number that is multiplied by the multiplicand in the multiplication operation;
2 ) The multiplicand is the number to be multiplied by the multiplicand;
The multiplicand is before the multiplication sign, and the multiplier is after the multiplication sign; for example: 5 × 6 = 30, where the multiplicand is 5 and the multiplier is 6;
When the multiplicand comes first, use "multiplied by", and when the multiplier comes first, use "multiplied", for example: "a × b" is read as a multiplied by b, or b multiplied a; among them, "a multiplied by b" and "b multiplied a" both mean the addition of b a;
4. Understand the divisor and dividend:
1 ) The dividend is the number that is divided by another number in the division operation;
2 ) The number after the division sign is called the divisor;
For example: 6 ÷ 2 = 3; 6 is the dividend; 2 is the divisor;
First, take each digit of one factor and multiply it by each digit of the other factor. Align the result of each multiplication with the corresponding place value of the digit being used as the multiplier. Then, add up all the products obtained from each step.
7. Commutative and associative laws of multiplication:
1 ) Commutative law of multiplication; exchanging the position of factors will not affect the result; for example: 5 × 3 = 3 × 5 = 15;
2 ) Associative law of multiplication; when multiplying multiple numbers, you can multiply any two numbers first, and then multiply another number, for example: (2 × 3) × 4 = (2 × 4) × 3 = 24
8. Decimal multiplication rules:
First, calculate the product following the rules of integer multiplication. Then, count the total number of decimal places in the factors. Starting from the right of the product, count that number of places and place the decimal point. If there aren’t enough digits, add zeros as needed.
9. Division rules:
1) If the divisor is 1, the result of any number divided by 1 is itself;
2) If the dividend is smaller than the divisor, the quotient is 0 and the remainder is the dividend itself;
3) When the dividend is divisible by the divisor, the quotient is the result of dividing the two numbers, and the remainder is 0;
4) When the dividend is not divisible by the divisor, the quotient is the largest integer part that can be divided, The remainder is the result of subtracting the quotient from the dividend and multiplying the divisor;
5 ) If the quotient is 0, the remainder is the dividend;
6 ) If the divisor is 0, the division is meaningless;
10. Integer division calculation rules:
When doing long division, start the division operation from the highest digit of the dividend (that is, the leftmost digit). If the divisor has several digits, take the first digits from the dividend for comparison. If the first digits are not large enough to be divided by the dividend, you need to take one more digit from the dividend to ensure that it can be divided. The quotient is written above the digit of the dividend that is divided. If there is not enough quotient 1 in a digit, fill it with 0 to make up the place. The remainder of each division must be less than the divisor;
