Work out a Fraction of an Amount
Finding a fraction of an amount is a useful skill you need for everyday, real-world math problems. For example, to find a discount price, or to determine a portion of something that you have (or a what portion you are missing), you need to know how to find the fraction of an amount. In these types of problems you will need to know how to multiply a fraction by a whole number, or how to create a fraction based on the information you are given. You might find that the most difficult part of these types of problems is determining what the problem is asking.
Contents
Steps
Calculating an Amount
- Set up the problem. When a problem asks you what a fraction of a whole number is, the problem is one of multiplication, and you need to multiply the fraction and the whole number. Look for the keyword of. When you see of in a word problem, you need to multiply.
- For example, if the problem asks, “What is <math>\frac{5}{6}</math> of <math>294</math>," you need to set up <math>\frac{5}{6} \times 294</math>.
- Turn the whole number into a fraction. To do this, give it a denominator of 1. Remember, the denominator is the number underneath the fraction bar.
- For example, you would change <math>294</math> to <math>\frac{294}{1}</math>. So the new problem becomes <math>\frac{5}{6} \times \frac{294}{1}</math>.
- Multiply the numerators. Remember that the numerators are the numbers above the fraction bars.
- For example, <math>5 \times 294 = 1,470</math>.
- Multiply the denominators. Place this number under the product of the numerators.
- For example, <math>6 \times 1 = 6</math>, so <math>\frac{5}{6} \times \frac{294}{1} = \frac{1,470}{6}</math>.
- Simplify the fraction. To do this, divide the numerator by the denominator. This will give you your final answer as a whole number or in decimal form. If the result is not a whole number and you need the answer written in the form of a fraction, you should reduce the fraction by dividing the numerator and denominator by their greatest common factor. For complete instructions on how to reduce a fraction, read Reduce Fractions.
- For example, <math>1,470 \div 6 = 245</math>, so <math>\frac{5}{6}</math> of <math>294 = 245</math>.
Calculating a Fraction
- Understand what the problem is asking. When a problem asks you what fraction one whole number is of another whole number, you need to create a fraction and reduce it. Look for the key phrases “fraction of” or “out of.”
- For example, if the problem asks, “What fraction of <math>294</math> is <math>245</math>,” you need to create a fraction from the two given whole numbers.
- Determine the numerator and denominator. The numerator is the fraction of the whole. Often this will be the smaller number, but not always, so read the problem carefully. The denominator is the “complete” number. Look for the key phrase “fraction of <math>x</math>.” The <math>x</math> variable will be the denominator.
- For example, if the problem asks, “What fraction of <math>294</math> is <math>245</math>,” you know that <math>245</math> is the numerator, because this is the number that is a part, or fraction, of <math>294</math>. So the fraction is <math>\frac{245}{294}</math>.
- Simplify the fraction. To do this, find the greatest factor that is common to the numerator and the denominator, then divide each by that factor. For complete instructions on how to reduce fractions, read Reduce Fractions.
- For example, the greatest common factor of <math>245</math> and <math>294</math> is <math>49</math>:
<math>245 \div 49 = 5</math>, so the reduced numerator is <math>5</math>.
<math>294 \div 49 = 6</math>, so the reduced denominator is <math>6</math>.
So, <math>245</math> is <math>\frac{5}{6}</math> of <math>294</math>.
- For example, the greatest common factor of <math>245</math> and <math>294</math> is <math>49</math>:
Changing an Amount By a Fraction
- Understand what the problem is asking. If the problem is asking you to determine how much of something is left, or to decrease an amount, or to find a discount, you will first multiply to find the fractional amount, then subtract the fractional amount from the original whole number. If the problem is asking you to determine how much of something there is after an increase, you will first multiply to find the fractional amount, then add the fractional amount to the original whole number.
- For example, a problem might ask, “If you have <math>$294</math>, and you give <math>\frac{5}{6}</math> of it away, how much money do you have left?” In this case, you will multiply, then subtract.
- Set up the multiplication problem. To do this, turn the whole number into a fraction by placing it over a denominator of <math>1</math>.
- For example, to find <math>294 \times \frac{5}{6}</math>, you would change the problem to <math>\frac{294}{1} \times \frac{5}{6}</math>.
- Multiply the numerators. This will give you your new numerator.
- For example, <math>294 \times 5 = 1,470</math>.
- Multiply the denominators. This will give you your new denominator. Rewrite the new fraction.
- For example, <math>1 \times 6 = 6</math>. So the new fraction is <math>\frac{1,470}{6}</math>.
- Simplify the fraction. First divide the numerator by the denominator to see if the result is a whole number. If the result is not a whole number, you should reduce the fraction by dividing the numerator and denominator by their greatest common factor. For complete instructions on how to reduce a fraction, read Reduce Fractions.
- For example, <math>1,470 \div 6 = 245</math>, so <math>\frac{5}{6}</math> of <math>294 = 245</math>. This is the fractional amount you are decreasing by.
- Change the original amount by adding or subtracting the fractional amount. This will give you your final answer.
- For example, <math>294 - 245 = 49</math>. So, if you have <math>$294</math>, and you give <math>\frac{5}{6}</math> of it away, you have <math>$49</math> left.
