# 3 Ways to Calculate the Fraction of a Quantity

Knowing how to calculate the fraction of a value is a very useful knowledge for solving everyday mathematical problems in the real world. For example, to find a discounted price, or to determine what part of something you are (or what part you are missing), you need to know how to find the fraction of an amount. In these types of problems, you need to know how to multiply a fraction by a whole number, or how to calculate a fraction based on the information provided. You may find that the hardest part of these types of problems is determining what the problem question is.

## Steps

### Method 1 of 3: Calculating a Value

#### Step 1. Defining the problem

When the question in the problem is what is the fraction of a whole number, the problem is one of multiplication, and you must multiply the fraction by the whole number. Search for the keyword of. When you find de in the words of a problem, you need to multiply it.

• For example, if the problem question is: "How much is 56{displaystyle {frac {5}{6}}}

de 294{displaystyle 294}

#### Step 2. Converting an integer to a fraction

To do this, put denominator 1 on it. Remember, the denominator is the number below the fraction bar.

• For example, you convert 294{displaystyle 294}

em 2941{displaystyle {frac {294}{1}}}

. E o novo problema fica 56×2941{displaystyle {frac {5}{6}}\times {frac {294}{1}}}

#### Step 3. Multiply the numerators

Remember that numerators are the numbers above the fraction bars.

• For example, 5×294=1, 470{displaystyle 5\times 294=1,470}

#### Step 4. Multiply the denominators

Place the denominator under the product of numerators.

• For example, 6×1=6{displaystyle 6\times 1=6}

, logo 56×2941=1, 4706{displaystyle {frac {5}{6}}\times {frac {294}{1}}={frac {1, 470}{6}}}

#### Step 5. Simplify a fraction

To do this, divide the numerator by the denominator. This will result in a whole number or a decimal number as the final answer. If the result is not a whole number and you need the answer in fraction form, reduce the fraction by dividing the numerator and denominator by their greatest common factor. For complete instructions on simplifying a fraction, read Simplifying a Fraction.

• For example, 1, 470÷6=245{displaystyle 1, 470\div 6=245}

, logo 56{displaystyle {frac {5}{6}}}

de 294=245{displaystyle 294=245}

### Método 2 de 3: Calculando uma fração

#### Step 1. Understand the problem question

When the question in the problem is: which fraction of a whole number matches another whole number, you need to create a fraction and reduce it. Look for the key phrases "fraction of" or "resulting from".

• For example, if the problem question is, “What fraction of 294{displaystyle 294}

equivale a245{displaystyle 245}

,” você precisa criar uma fração resultante dos dois números inteiros dados.

#### Step 2. Determine the numerator and denominator

The numerator is the fraction of the whole. It will often be the smallest number, but not always, so please read the problem carefully. The denominator is the number corresponding to the "whole". Look for the key phrase “fraction of x{displaystyle x}

.” A variavel x{displaystyle x}

• Por exemplo, se a pergunta do problema for, “Qual fração de 294{displaystyle 294}
• corresponde a 245{displaystyle 245}

,” você sabe que 245{displaystyle 245}

é o denominador, porque esse é o número que corresponde a uma parte de, ou fração de 294{displaystyle 294}

. Logo, a fração é equivalente a245294{displaystyle {frac {245}{294}}}

#### Step 3. Simplify the fraction

To do this, find the largest common factor between the numerator and denominator and divide each by that factor. For complete instructions on simplifying fractions, read Simplifying a Fraction.

• For example, the biggest common factor among 245{displaystyle 245}

e 294{displaystyle 294}

é 49{displaystyle 49}

:

245÷49=5{displaystyle 245\div 49=5}

, logo, o numerador reduzido é 5{displaystyle 5}

294÷49=6{displaystyle 294\div 49=6}

, e o denominador reduzido é 6{displaystyle 6}

Então, 245{displaystyle 245}

é 56{displaystyle {frac {5}{6}}}

de 294{displaystyle 294}

### Método 3 de 3: Alterando um valor por uma fração

#### Step 1. Understand what the problem is asking

If the problem is determining how much is left of something, or reducing an amount, or quantifying a discount, you will first have to multiply to find the fractional amount, then subtract the fractional amount from the original integer. If the problem is to determine how much came out of something after an increase, you will first have to multiply to find the fractional value, then add the fractional value to the original integer.

• For example, if the problem question is, “If you have $294{displaystyle \$294}

, e dá 56{displaystyle {frac {5}{6}}}

desse valor, quanto sobra?” Nesse caso, você terá que multiplicar, e depois subtrair.

#### Step 2. Equate the multiplication problem

To do this, convert the integer to a fraction by placing it over a denominator of 1{displaystyle 1}

• Por exemplo, para encontrar o valor de 294×56{displaystyle 294\times {frac {5}{6}}}
• , você tem que converter o problema para 2941×56{displaystyle {frac {294}{1}}\times {frac {5}{6}}}

#### Step 3. Multiply the numerators

This will give you a new numerator.

• For example, 294×5=1, 470{displaystyle 294\times 5=1, 470}

#### Step 4. Multiply the denominators

This will give you a new denominator. Rewrite the new fraction.

• For example, 1×6=6{displaystyle 1\times 6=6}

. Então, a nova fração fica 1, 4706{displaystyle {frac {1, 470}{6}}}

#### Step 5. Simplify the fraction

First divide the numerator by the denominator to see if the result is an integer. If the result is not an integer, you must simplify the fraction by dividing the numerator and denominator by the greatest common factor. For complete instructions on simplifying a fraction, read Simplifying a Fraction.

• For example, 1, 470÷6=245{displaystyle 1, 470\div 6=245}

, logo 56{displaystyle {frac {5}{6}}}

of 294=245{displaystyle 294=245}

. Este é o valor fracionado que você está diminuindo.

#### Step 6. Change the original value by adding or subtracting the fractional value

By doing this, you will get the final result.

• For example, 294−245=49{displaystyle 294-245=49}

. portanto, se tiver $294{displaystyle \$294}

, e der 56{displaystyle {frac {5}{6}}}

, terá $49{displaystyle \$49}

sobrando.