When solving a problem, first find out how much a copy is (that is, the single quantity), and then find out the required quantity based on the single quantity. This kind of application problem is called standardization problem.

magnitude relation

Total amount/number of copies = 1 number of copies

1 number of copies × number of occupied copies = number of requested copies.

In addition, total amount ÷ (total amount ÷ number of copies) = required number of copies.

Ideas and methods to solve problems

Find a single quantity first, and then find the required quantity according to the single quantity.

Example 1

It costs 0.6 yuan money to buy five pencils, and how much does it cost to buy the same 16 pencil?

Solution:

(1) How much is it to buy 1 pencils? 0.6 ÷ 5 = 0. 12 (yuan)

(2) How much does it cost to buy a 16 pencil? 0.12×16 =1.92 (yuan)

The comprehensive formula is 0.6 ÷ 5×16 = 0.12×16 =1.92 (yuan).

A: 1.92 yuan is required.

Example 2

Three tractors cultivated 90 hectares of land in three days. According to this calculation, how many hectares have been cultivated by five tractors in six days?

Solution:

How many hectares of arable land is (1) 1 tractor 1 day? 90 ÷ 3 ÷ 3 = 10 (hectare)

(2) How many hectares of farmland are cultivated by five tractors in six days? 10× 5× 6 = 300 (hectare)

It is listed as a comprehensive formula 90 ÷ 3 ÷ 3× 5× 6 = 10× 30 = 300 (hectare).

Five tractors cultivated 300 hectares of land in six days.

Example 3

Five cars can be transported in four times 100 tons of steel. If the same 7 vehicles are used to transport 105 tons of steel, how many times do you need to transport it?

Solution:

(1) 1 How many tons of steel can cars transport 1 time? 100 ÷ 5 ÷ 4 = 5 (ton)

(2) How many tons of steel can be transported by seven cars 1 time? 5× 7 = 35 (ton)

(3) How many times do seven cars 105 tons of steel need to be transported? 105 ÷ 35 = 3 (times)

Column into a comprehensive formula105 ÷ (100 ÷ 5 ÷ 4× 7) = 3 (times).

A: It needs to be shipped three times.