Difference problem solving skills, difference problem formulas

The problem of difference times

Meaning:Knowing that the difference between two numbers and the large number is several times the decimal number (or the decimal is a fraction of the large number), and the two numbers are required to be what they are, this kind of application problem is called the difference multiple problem.

Quantitative relationsThe difference between two numbers (several times 1) is a smaller number.

Smaller numbers several times larger numbers.

Ideas and methods for solving problemsSimple questions use formulas directly, and complex problems use formulas when they are adapted.

Example 1 There are 3 times as many peach trees in the orchard as there are apricot trees, and there are 124 more peach trees than apricot trees. How many apricot trees and how many peach trees are there?

Solution (1) How many apricot trees are there? 124 (3 1) 62 (trees).

2) How many peach trees are there? 62 3 186 (trees).

A: There are 62 apricot trees and 186 peach trees in the orchard.

Example 2 If the father is 27 years older than the son, and this year, the father is 4 times the age of the son.

Solution (1) Son age 27 (4 1) 9 (years old).

2) Dad: Age 9, 4, 36 (years).

A: The father and son are 36 and 9 years old this year.

Example 3 After the reform of the operation and management measures of the shopping mall, the profit of this month is more than 120,000 yuan more than twice the profit of the previous month, and the profit of this month is 300,000 yuan more than the profit of the previous month.

Solution If the profit of the previous month is taken as 1 times, then (30 12) yuan is equivalent to (2 1) times of the profit of the previous month, therefore.

Last month's profit (30 12) (2 1) 18 (10,000 yuan).

Profit for the month 18 30 48 (10,000 yuan).

Answer: Last month's profit was 180,000 yuan, and this month's profit is 480,000 yuan.

Example 4 There are 94 tons of wheat and 138 tons of corn in the grain depot, if 9 tons of wheat and corn are shipped out every day, how many days later there will be 3 times as much corn left as wheat?

Solution Since the amount of wheat and corn shipped each day is equal, the remaining quantity difference is equal to the original quantity difference (138 94). If the wheat left after a few days is considered to be 1 times, then the corn that is left after a few days is 3 times the amount, then, (138 94) is equivalent to (3 1) times, therefore.

The amount of wheat left (138 94) (3 1) 22 (tons).

The amount of wheat shipped out was 94 22 72 (tons).

Number of days to transport grain 72 9 8 (days).

A: After 8 days, there are 3 times as much corn left as wheat.

The formula for the difference multiple problem: difference (multiple 1) = decimal number, decimal multiple = large number. The difference multiple problem is to know the difference between two numbers and the multiple relationship between two numbers, and find the two numbers. An integer can be divisible by another integer, then that integer is a multiple of another integer.

The quotient obtained by dividing one number by another. For example, a b = c, that is, a is a multiple of b. For example:

a b = c, then a is c times that of b. There are infinite multiples of a number, which means that the set of multiples of a number is an infinite set. Note:

You can't call a number a multiple alone, you can only say who is the multiple.

Difference multiplier formula: the number with a smaller number = the difference between the two numbers (multiple-1).

Large number = decimal number + difference or: large number = decimal multiple.

The difference multiple problem refers to the fact that the relationship between the multiples of two numbers (usually two numbers) is known, and their difference is known, and the two numbers are found separately.

Solution: 1) Draw a line diagram according to the meaning of the question.

2) Find out the difference and multiple relationship between two numbers. In some questions, the relationship between difference and multiple is not directly given, so it is necessary to find the difference and multiple first; In some questions, the two numbers themselves do not satisfy the multiple relationship, and they need to be increased or decreased before the multiple relationship is satisfied.

3) Use formulas to solve.

and difference times formula.

1. The formula for the sum difference problem.

Sum difference) 2 large numbers.

and difference) 2 decimals.

2. And times the problem.

and (multiples of 1) decimals.

Decimals, multiples, and large numbers.

or with decimal large numbers).

1. The first step is to carefully understand the meaning of the topic, and judge whether it is a sum multiple problem or a difference multiple problem. The general chaotic method of judging the "harmony problem" is to grasp the following key words: "harmony", "total", "who is who", and so on.

To judge the difference problem, you can grasp these few keywords to judge the "ratio." Many. Compare.

Few. How much is the difference", "who is several times who", etc.

2. The second step is to determine the "1 multiple", or "1 multiple", and then draw the line segment diagram according to the multiple relationship. A common way to determine "1 times" is to find keywords, and in general, the amount after "yes", "than", "occupy", and "equal" is "1 times". If two or more of these words appear in a question, then we usually refer to the smaller quantity as "1 fold".

The reason for this is simple, people usually like to do addition rather than subtraction, preferring to do multiplication rather than division. In addition, when drawing a line segment diagram, it is generally necessary to draw "1 times" first, and then draw other amounts. Try to represent the known conditions on the top of the ** segment diagram, which is more intuitive and easy to analyze and understand.

3. The third step is to find the multiple relationship corresponding to "and" or "difference" through analysis. Only by finding a one-to-one correspondence can the correct answer be solved. Generally, "and" corresponds to "multiple+1"; "Difference" corresponds to "multiple-1".

This is important. Of course, specific problems need to be analyzed on a case-by-case basis.

Difference multiple problem: divide the difference by the multiple difference to equal the smaller number (1 fold) Smaller number + difference = larger number (multiple multiples).

Formula: Difference (Multiples of 1) = Decimal; Decimals, multiples, and large numbers.

Examples. The length difference between the two wires is 30 meters, and the long one is 4 times longer than the short one. How many meters are each of these two wires long?

Analysis and Answer: The "difference rematch" = 30 and the multiple = 4 of this question are obtained from the difference multiple formula.

Short wire length: 30 (4 1) = 10 (m), long wire length: 10 + 30 = 40 (m) or 10 4 = 40 (m).

A: The short wire is 10 meters long and the long wire is 40 meters long.

The techniques for solving the sum times problem are as follows:

Knowing the multiplier relationship between the sum of two known numbers and the two numbers, find out what are the two numbers. Problems like this are called the "sum times problem".

For example, a fruit store brings a total of 180 kg of two fruits, of which a watermelon weighs twice as much as an apple. Q: How many kilograms of watermelon does the fruit store ship?

To solve this type of problem, you must first find the sum of two numbers, and the sum of the corresponding multiples, so as to find a multiple, and then find a multiple. The quantity relationship can be expressed as:

The sum of two numbers Multiples of sum = one multiple.

To answer the above question, we first find the sum of the two numbers, which is the sum of the weight of the two fruits 180kg. Looking for the multiple relationship, we can derive from the sentence "the weight of the watermelon is twice that of the apple": assuming that the weight of the apple is one part (times), then the weight of the watermelon is two parts (times), and the sum of the multiples of the watermelon and the apple is 1+2=3.

Substituting the relationship formula yields:

The weight of the apple: 180 (1+2)=60 (kg); So as to find the weight of the watermelon: 180-60=120 (kg); A: The fruit store shipped 120 kilograms of watermelon.

Looking back at this problem, the key to solving the problem is to grasp the known condition that "the weight of a watermelon is twice that of an apple", and find the relationship between the multiples of the two quantities, and the problem can be solved.