Hypothesis is a common problem in the first volume of sixth grade mathematics. It is generally used to solve some complex problems, and it is solved by hypothetical methods. The steps to solve the problem with the hypothesis method are as follows:

Put forward a hypothesis and determine the hypothetical situation. Reasoning according to the hypothetical situation and seeking conclusions.

Check whether the conclusion is correct. Determine the answer.

For example, a store has * * 136 color TV sets and black-and-white TV sets, and sells 2/5 color TV sets and 3/7 black-and-white TV sets, and * * * sells 57 sets. Q: How many color TV sets and black-and-white TV sets were there? This problem can be solved by hypothesis.

Hypothesis is a common method to solve problems, which can be used to solve various complex problems. In mathematics, the hypothesis method usually puts forward a hypothesis first, and then makes reasoning and calculation according to this hypothesis, so as to draw a conclusion.

Here are the steps to solve the hypothetical problem:

Put forward a hypothesis:

When solving mathematical problems, we must first make clear the known conditions and unknown conditions in the problems. Then according to the requirements of the problem, put forward reasonable assumptions. This assumption can be in any form, such as setting the unknown to x or y, or assuming that a relationship is established.

Reasoning according to assumptions:

According to the proposed hypothesis, through logical reasoning or mathematical calculation, the conclusions related to this hypothesis are deduced. This reasoning process needs to use known conditions and mathematical rules, such as theorems and formulas.

Inspection conclusion:

After the conclusion is reached, it is necessary to compare the conclusion with the known conditions to verify whether the conclusion is correct. If the conclusion is consistent with the known conditions, then the assumption may be correct. Otherwise, we need to put forward the hypothesis again and make reasoning.

Determine the answer:

After testing, if the conclusion is correct, then the final answer can be obtained according to the conclusion. If the conclusion is incorrect, it is necessary to rethink the hypothesis, put forward a new hypothesis, and conduct reasoning and testing again.

Here is a concrete example:

Title: A store has * * 136 color TV sets and black-and-white TV sets, and sold 2/5 color TV sets and 3/7 black-and-white TV sets, and * * * sold 57 sets. Q: How many color TV sets and black-and-white TV sets were there?

Steps to solve problems by hypothesis method:

Put forward a hypothesis: suppose that the original color TV set has X sets, and the black and white TV set has Y sets.

According to hypothetical reasoning: according to the subject conditions, we can list two equations: x+y = 136 (total number of units) and 2/5x+3/7y = 57 (number of units sold).

Test conclusion: x=9 1 and y=45 are obtained by solving the equations. This means that there were 9 1 color TV sets and 45 black and white TV sets in the store.

Determine the answer:

So, there are 9 1 color TV sets and 45 black and white TV sets in the store.