Percentage to Fraction Conversions and Calculations

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the fractional representation of 108.33%?

  • $10833/100$
  • $325/300$ (correct)
  • $10833/10000$
  • $325/3$

Convert $33\frac{1}{3}%$ into a fraction.

  • $1/6$
  • $1/2$
  • $1/3$ (correct)
  • $1/4$

Determine the value of 7.3% of 47.6 + 4.76% of 27.

  • 4.73 (correct)
  • 4.76
  • 7.3
  • 47.6

Calculate the value of 15% of 20% of 33 1/3% of 7200.

<p>720 (C)</p> Signup and view all the answers

What is 18% of 15% of 25% of 3800?

<p>28.5 (D)</p> Signup and view all the answers

Solve for x: 30% of 400 + x% of 70 = 25% of 536.

<p>30 (D)</p> Signup and view all the answers

Solve for x: $\frac{2}{5}$ of $\frac{1}{2}$ of x = 25% of 360. Find the ratio of x to 200.

<p>9:10 (D)</p> Signup and view all the answers

A positive number, when multiplied by 30% of itself, results in a number 170% larger than itself. What is the number?

<p>$\frac{10\sqrt{3}}{3}$ (C)</p> Signup and view all the answers

3 inches is what percentage of 4 feet?

<p>6.25% (C)</p> Signup and view all the answers

The ratio between 52% of x and 30% of y is 12:5. If x is 50 more than y, find x.

<p>360 (B)</p> Signup and view all the answers

Flashcards

Percentage to Fraction

To convert a percentage to a fraction, divide the percentage by 100 and simplify.

Percentage of a Number

To find a percentage of a number, convert the percentage to a decimal and then multiply by the number.

x% of y + y% of x

When calculating 'x% of y + y% of x', the result is always 2 * (x% of y) or 2 * (y% of x), due to the commutative property of multiplication.

Consecutive Percentages

Consecutive percentages can be converted to fractions directly and multiplied together with the base number. For example, 10% of 20% of a number.

Signup and view all the flashcards

Percentage as Fraction

A percentage can be expressed as a fraction by dividing it by 100. For example, x% = x/100.

Signup and view all the flashcards

Increase by Percentage

To increase a number by a percentage, think of it as adding that percentage of the original number to itself. For example, to increase a number by 25%, multiply by 1.25

Signup and view all the flashcards

Ratio with Percentages

When given a ratio involving percentages, convert the percentages to simplified fractions and solve for the unknown variables.

Signup and view all the flashcards

Percentage of Different Units

Convert all measurements to the same units before calculating percentages. For example, convert feet to inches before comparing inches to feet.

Signup and view all the flashcards

Study Notes

  • This is a math test covering percentage to fraction conversions and percentage calculations.

Converting Percentages to Fractions

  • To convert 108.33% into a fraction, the correct answer isn't provided in the options. To convert a percentage to a fraction, divide the percentage by 100 and simplify. Thus, 108.33% is approximately 108 1/3 %, which equals 325/3 %. Dividing by 100 yields 325/(3*100) = 13/12.
  • To convert % into a fraction, the correct answer isn't provided in the options. To convert a percentage to a fraction, divide the percentage by 100 and simplify to its lowest terms to get the fraction.

Percentage Calculations

  • To find 7.3% of 47.6 + 4.76% of 27, calculate each part separately and then add them: (0.073 * 47.6) + (0.0476 * 27) ≈ 3.4708 + 1.2852 ≈ 4.756. Thus the answer is approximately 4.76.
  • To calculate % of % of 33 % of 7200, convert the mixed fraction percentages to improper fractions. Then multiply all the percentages with 7200 = (1/3 * 4/9 * 1/3) * 7200 = 11.68.
  • To find the value of 18% of 15% of 25% of 3800, multiply the percentages together: 0.18 * 0.15 * 0.25 * 3800 = 25.65.

Finding Unknown Values with Percentages

  • To find x, given 30% of 400 + x% of 70 = 25% of 536. That is: 0.30 * 400 + (x/100) * 70 = 0.25 * 536 simplifies to 120 + 0.7x = 134. Solving for x provides x = (134 - 120) / 0.7 = 14 / 0.7 = 20. Thus, x = 20.

Ratio Problems Involving Percentages

  • The value of of That is x/100 * 25/7 = 20/21, after rearranging, the solution is
  • A positive number multiplied by 30% of itself results in a number 170% more than it. x * (0.3x) = 2.7x can be rewritten as 0.3x^2 = 2.7x. Dividing and simplifying leads to x = 9

Percentage Word Problems

  • Converting 3 inches to feet (3 inches = 3/12 feet = 0.25 feet) and calculating the percentage: (0.25 feet / 4 feet) * 100% = 6.25%.
  • Given 52% of x and 30% of y is 12:5, and x is 50 more than y, establish the equations: 0.52x / 0.30y = 12/5 and x = y + 50. Solving for x and y gives x = 360.

Nested Percentage Calculations

  • To find 0.08% of 0.008% of 8, perform the calculations sequentially: (0.0008 * (0.00008 * 8)) = 0.000000512

Percentage Increase

  • To increase a number by 25%, multiply it by 1 + 25/100 = 1.25, which is equivalent to multiplying by .

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser