"Finding what percentage of a number is" PPT courseware for the application of percentages

Description

"Finding what percentage of a number is" PPT courseware for the application of percentages

teaching objectives

1. Combined with specific examples, experience the process of independently solving slightly complex practical problems of finding what percentage is.

2. It will answer the practical question of finding what percent of a number is a two-step calculation.

3． Experience the wide application of percentages in real life, gain successful experience in solving problems independently, and enhance your confidence in learning mathematics well.

The water park lake area is 2,800 square meters and is planned to be expanded by 35%. What is the area of ​​the enlarged lake in square meters?

Method 1: First find the lake area planned to be expanded.

2800 × 35% = 980 (square meters)

Add the original lake area to find the expanded lake area.

2800 + 980 = 3780 (square meters)

Answer: The expanded lake area is 3780 square meters.

Method Two:

2800×(1+35%)

= 2800×135%

= 2800×1.35

= 3780 (square meters)

Answer: The expanded lake area is 3780 square meters.

In conclusion

1. The problem of finding what percentage is more (or less) than a number is characterized by the fact that the quantity of unit "1" is known.

2. Problem solving method:

(1) The quantity of unit "1" ± the quantity of unit "1" × the percentage of another quantity that is more (or less) than the quantity of unit "1" = another quantity.

(2) The quantity of unit "1" × 1 ± the percentage of another quantity that is more (or less) than the quantity of unit "1" = another quantity.

In a certain area, 630 hectares of farmland were converted to forests last year, exceeding 20% ​​of the planned area to be converted to forests. How many hectares of farmland were planned to be converted into forests last year?

Solution to column equation:

Solution: Suppose it was planned to return x hectares of farmland to forests last year.

Method 1: x+20%x=630

120%x=630

x＝630×100/120

x=525

Answer: Last year, we planned to convert 525 hectares of farmland into forests.

Method 2: (1+20%)x=630

120%x=630

x＝630×100/120

x=525

Answer: Last year, we planned to convert 525 hectares of farmland into forests.

In conclusion

1. Find what percentage is more (or less) than a number. The characteristic of the problem of finding this number is that the quantity of the unit "1" is unknown.

2. Problem solving method:

Let the quantity with the unit "1" be x, and series of equations based on the equivalence relationship in the question. x (quantity in unit "1") × 1 ± the percentage of another quantity that is more (or less) than the quantity in unit "1" = another quantity.

practice

1. Ask questions and answer them.

2. Shuangfeng Farm’s rice planting area was 504 hectares last year, and this year it plans to increase it by 15% compared to last year. How many hectares of rice are planned to be sown this year?

504×(1+15%)

=504×115%

=579.6 (hectare)

Answer: This year we plan to sow 579.6 hectares of rice.

3. Due to the adoption of a new process in a factory, the cost of each product is now 475.2 yuan, 12% lower than before. How much does each product cost?

Solution: Assume that the original cost of each product is x yuan.

(1-12%)x=475.2

88%x=475.2

x＝475.2÷0.88

x=540

Answer: The original cost of each product is 540 yuan.

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Update Time: 2024-06-28

This template belongs to Mathematics courseware Hebei Education Edition Sixth Grade Mathematics Volume 1 industry PPT template

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