27 is 45 of what number

Problem: 27 is 45 percent of what number?

Solution:

One way to calculate percentages is to use this general percentage formula:

If you know any two values of the formula, you can calculate the third one. In this example, you know the 'part' (27) and the 'percentage' (45%). So, you can find the 'whole'.

By replacing the given values in the formula, you get:

Cross-multiply:

45 × whole = 27 × 100

Divide by 45 and get the whole:

27 is x percent of what chart

Above, we have a grafical representation using strip diagrams (or percent bars) of 27 is x percent of what, where x ranges from 1 to 100%, for your reference.

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• p% of A = ?
• p% of ? = A
• ?% of A = B
• fractions a/b = ?%
• relative change
• p% = ? number
• (1 + p%) × n
• (1 - p%) × n

45% of what missing number = 27?

Detailed calculations and the verification of the result

A brief introduction. Percent, p%

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

45% = 45 'out of one hundred',

p% is read p 'percent',

p% = p/100 = p ÷ 100

45% = 45/100 = 45 ÷ 100 = 0.45

100% = 100/100 = 100 ÷ 100 = 1

What does it mean: Percentage of 45% of which number is equal to 27?

45% of what number = 27

... is equivalent to multiplying them:

45% × number = 27

Number calculation, finding the missing unknown number

Percentage of 45% of what number = 27?

Let y be the number that we have to calculate.

45% × y = 27 =>

y =

27 ÷ 45% =

27 ÷ (45 ÷ 100) =

(100 × 27) ÷ 45 =

2,700 ÷ 45 =

60

45% of 60 = 27

Proof of the calculations

How do we check the result?

We carry out the reverse operation:

If 45% × 60 = 27 =>

Divide the number 27 by the number 60...

... And see if we get as a result: 45%

A quick note:

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

100/100 = 100 ÷ 100 = 1

n/100 = n%, any number.

Calculate the percentage value: See if we get the percentage of 45%

We will prove below that the calculations are correct.

27 ÷ 60 =

0.45 =

0.45 × 100/100 =

(0.45 × 100)/100 =

45/100 =

45%

The answer:

Percentage of 45% of what number = 27? 45% × ? = 27 45% of 60 = 27

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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• p% of what missing number = the given number N?

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

• Problem 1:

• 25% of the annual profit of a company was invested in buying some new equipment. The total amount invested in buying the new equipment was 100,000 dollars. What was the annual profit of the company?
• Rewrite: 25% of the Profit means 100,000 dollars => 25% × Profit = 100,000 dollars => Profit = 100,000 ÷ 25% dollars = 100,000 ÷ 25/100 dollars = 100,000 × 100/25 dollars = 100,000 × 4 dollars = 400,000 dollars;

• Problem 2:

• A number of 20% of the students in the terminal year have enrolled into the swimming class. In total, 7 students have enrolled. How many students are in the terminal year?
• Rewrite: 20% of the students means 7 students => 20% × Total number of students = 7 => The total number of students = 7 ÷ 20% = 7 ÷ 20/100 = 7 × 100/20 = 7 × 5 = 35;

• Problem 3:

• In the last elections 49% of community memebrs voted for the A Party, 32% for the B Party, and the rest for the C Party. 17,920 people voted for the B Party. How many members are in the community, all in all?
• Rewrite: 32% of the total community members means 17,920 people => 32% × The total number of community members = 17,920 => The total number of community members = 17,920 ÷ 32% people = 17,920 ÷ 32/100 people = 17,920 × 100/32 people = 17,920/32 × 100 = 560 × 100 people = 56,000 people.

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