?% of 0.4 = - 1.22: Given two numbers, 0.4 and - 1.22, calculate what is the missing percent value, calculated of 0.4, that equals the other number, - 1.22

What missing percentage p% calculated of 0.4 = - 1.22?

Detailed calculations and verification of the result

A brief introduction. Percent, p%

'Percent (%)' means 'out of one hundred':

p% = p 'out of one hundred',

p% is read p 'percent',

p% = ^{p}/_{100} = p ÷ 100.

100% = ^{100}/_{100} = 100 ÷ 100 = 1.

Multiply a number by the fraction ^{100}/_{100}, ... and its value doesn't change.

What does it mean: What missing percent value p calculated of 0.4 is equal to the number - 1.22?

p% of 0.4 = - 1.22

... is equivalent to multiplying them:

p% × 0.4 = - 1.22

Percentage calculation

What missing percentage of the number 0.4 is equal to the number - 1.22?

Let p be the missing percent value that we have to calculate.

p% × 0.4 = - 1.22 =>

p% =

- 1.22 ÷ 0.4 =

- 1.22 ÷ 0.4 × ^{100}/_{100} =

^{(- 1.22 ÷ 0.4 × 100)}/_{100} =

^{(- 1.22 × 100 ÷ 0.4)}/_{100} =

^{(- 122 ÷ 0.4)}/_{100} =

^{- 305}/_{100} =

- 305%

- 305% of 0.4 = - 1.22

The proof of the calculations

Calculate the second number:

We calculate the percentage of the first number below.

Will we get the second number, - 1.22?

We will prove below that the calculations are correct:

- 305% × 0.4 =

(- 305 ÷ 100) × 0.4 =

- 305 × 0.4 ÷ 100 =

- 122 ÷ 100 =

- 1.22

The answer:

What missing percentage p% calculated of 0.4 = - 1.22?

- 305% of 0.4 = - 1.22

The symbols used: % percent, ÷ division, × multiplication, = the equal sign, / the fraction bar, ≈ approximately the same. Writing numbers: comma ',' - as a thousands separator, point '.' as a decimal mark.

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Three examples of problems that can be solved using the information in this section:

Problem 1:

The amount of 100,000 dollars of the annual profit of a company was invested in buying some new equipment. The annual profit of the company was 400,000 dollars. What is the percentage of the annual profit that was invested in buying the new equipment?

7 students in the terminal year have enrolled into the swimming class. There are 35 students in the terminal year. What percentage of students have enrolled into the swimming class?

Solution: x% of the 35 students means 7 students => x% × 35 students = 7 students => x% = 7 ÷ 35 = 1 ÷ 5 = 0.2 = 20%;

Problem 3:

In the last elections, 17,920 of the community members voted for the B Party. The community has a total of 56,000 people. What percentage of the community members voted for the B Party?

Solution: x% of the total number of 56,000 of community members means 17,920 people => x% × 56,000 people = 17,920 people => x% = 17,920 ÷ 56,000 = 0.32 = 32%.