1. Fill in the operation symbol ("+"-"× "∫) in the appropriate circle, each operation symbol can only be used once, and fill in the appropriate integer in the box to make the equation hold.

Answer: 45× 0+10 =10; 16÷2-5=3

2. Analysis: Seven numbers are needed to form five numbers, three of which are single digits and two are two digits. Obviously, the number and dividend in □ are two digits, and the multiplier and divisor are one digit. Find a number first. 0 and 1 should not be used as multipliers, let alone as divisors, because 2×6= 12(2 occurs twice), 2×5= 10 (irrelevant after the test), 2×4=8 (none of these seven numbers is 8) and 2×3=6.

3. Analysis: According to the characteristics of the topic, first look at the unit, 5+7= 12, fill in the unit of sum, and enter 1 into ten; Look at ten more. The unit of the sum of +4+ 1 is 1. So the tenth digit of the first addend can only be filled with 6, and the digit is 1. Last few hundred, 6+? The digit of the sum of+1 is 2, so the hundredth digit of the second addend can only be filled with 5, and the thousandth digit of the sum is 1, so the thousandth digit of the sum is 8.

7665+547=82 12

4. Answer: I = 1, student =8, love =3, number =2, study =5 or I = 1, student =6, love =9, number =7 and study =5.

Analysis: the breakthrough of this question is learning, and the sum of the four studies is 0, so learning can only be 5 or 2 to10; The number of digits of the sum of number+number+number +2 is 0, so the number is 2 or 7; (1) If the number is 2 and the sum of love+love+love+1 is 0, so love =3 and the sum of us+1 is 0, I can't be equal to 2, so I = 65438. (2) If the number is 7, enter 1% of 3, and the unit of the sum of love+love+love +3 is 0, so love =9, and enter 1/1000 of 3, so I = 1, and we =6.

The change law of the sum:

If one addend increases (or decreases) a number (not 0) and the other addend remains the same, their sum will also increase (or decrease) by the same number.

If one addend increases by one number (not 0) and another addend decreases by the same number, the sum remains the same.

The changing law of differences;

If the minuend is increased (or decreased) by a number (other than 0) and the minuend remains unchanged, the difference is increased (or decreased) by the same number.

If a minuend and a minuend increase (or decrease) a number (not 0) at the same time, the difference remains the same.

If the minuend is unchanged, the minuend is increased (or decreased) by a number (non-zero), and the difference is also decreased (or increased) by the same number.

Law of product change:

1. If one factor is expanded (or reduced) several times while the other factor remains the same, the product is also expanded (or reduced) by the same multiple.

2. One factor expands (or shrinks) several times, and the other factor shrinks (or expands) the same multiple, and their product remains unchanged.

3. When one factor is multiplied by (or divided by) A and another factor is multiplied by (or divided by) B, the product is multiplied by (or divided by) the product of ab.

The changing law of quotient:

1. The divisor is expanded (or reduced) several times, and the quotient is also expanded (or reduced) by the same factor under the condition that the divisor is unchanged.

2. The dividend is unchanged, the divisor is expanded (or reduced) several times, but the quotient is reduced (or expanded) by the same multiple.

3. Divide by A, divide by B, and multiply the quotient by the product of ab.

Divide the dividend by a, multiply the divisor by b, and the quotient will be divided by the product of ab.

draw

Reference answer:

1, two numbers are added. If one addend subtracts 9, what should be done with the other addend in order to increase the sum by 9?

Thinking of solving problems: If one addend is subtracted by 9, assuming the other addend remains unchanged, the sum is subtracted by 9; The title requires 9, so the other addend needs 9+9= 18.

2. Subtract two numbers. If the minuend decreases by 10, the minuend also decreases by 10. Has the difference changed?

Think about solving problems:

Minus 10, assuming that the minuend is unchanged, the difference is10; Assuming that the minuend is unchanged, it is reduced to 10 and10; The difference is first reduced by 10 and then increased by 10, so there is no change.

Subtraction, subtraction and difference add up to 2076, and the difference is half of subtraction. If the minuend remains the same and the difference increases by 42, how much should the minuend become?

Think about solving problems:

The sum of subtraction and difference is the minuend. There were two minuets in 2076, and the minuet was equal to 2076÷2= 1038. Difference is half of subtraction, that is to say, subtraction is twice of difference, difference should be 1038÷(2+ 1)=346, and subtraction is 346×2=692. The minuend is unchanged, the difference increases by 42, and the reduction should be reduced by 42, so the reduction should become 692-42=650.

4. Multiply two numbers, one multiplier is magnified 3 times, and the product is magnified 9 times. How to change the other multiplier?

Think about solving problems:

If one multiplier is enlarged by 3 times, assuming the other multiplier remains unchanged, the product is enlarged by 3 times; To enlarge the product by 9 times, the other multiplier should be enlarged by 9÷3=3 times.

5. Multiply two numbers and the product is 100. If one factor is expanded by 6 times and the other factor is also expanded by 6 times, what is the product?

Think about solving problems:

It is known that the product is 100, and a factor is enlarged by 6 times. Assuming that other factors remain unchanged, the product is enlarged by 6 times, that is,100× 6 = 600; The other factor is also expanded by 6 times, so the product is expanded by 6 times, that is, 600×6=3600. So the product is 3600.

6. When two numbers are divided, the dividend is enlarged by 3 times, and the divisor is enlarged by 15 times. How does the quotient change?

Think about solving problems:

The dividend is expanded by 3 times, assuming that the divisor is unchanged, then the quotient is expanded by 3 times; Because the divisor is enlarged by 15 times, after being enlarged by 3 times, the quotient is reduced by 15 times, that is, the quotient is reduced to the original 3÷ 15= 1/5.

7. When two numbers are divided, the quotient is 5 and the remainder is 15. What is the quotient of dividend and divisor expanding 20 times at the same time? What is the remainder?

Think about solving problems:

Suppose the formula is 95 ÷ 16 = 5... 15, and the dividend expanded 20 times is 95 × 20 =1900; The divisor expanded by 20 times is 16× 20 = 320, 1900 ÷ 320 = 5...300. The divisor and divisor are expanded by 20 times at the same time, the quotient is unchanged, and the remainder is expanded by 20 times, so the quotient is 5 and the remainder is 300.