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Mixed Number to Decimal Calculator

Convert Mixed Number to Decimal


= ?

Answer:
\[ 2 \frac{5}{8} = 2.625 \]
Solution by Separating the Parts
\[ 2\frac{5}{8} = 2 + \frac{5}{8} \]We know that \[ \frac{5}{8} \]is the same as \[ 5 \div 8 \]Therefore:\[ 2\frac{5}{8} = 2 + (5 \div 8) \]Then using
Long Division for 5 divided by 8
we have\[ = 2 + 0.625 = 2.625 \]
Rounded to a Max of 3 Decimal Places.

Solution by Converting to Improper Fraction
\[ 2\frac{5}{8} = 2 + \frac{5}{8} \]\[ = \frac{2}{1} + \frac{5}{8} \]\[ = \left(\frac{2}{1} \times \frac{8}{8} \right) + \frac{5}{8} \]\[ = \frac{16}{8} + \frac{5}{8} = \frac{21}{8} \]We know that \[ \frac{21}{8} \]is the same as \[ 21 \div 8 \]Then using
Long Division for 21 divided by 8
and rounding to a Max of 3 Decimal Places gives us \[ = 2.625 \]

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Calculator Use

Convert mixed numbers or mixed fractions to decimal numbers. Mixed number to decimal calculator finds the decimal equivalent by converting a mixed number, fraction, integer or whole number to a decimal and shows the work.

How to Convert a Mixed Number to a Decimal

Follow these 2 steps to convert a mixed number to a decimal:

  1. Convert the fraction to a decimal: Divide the numerator by the denominator
  2. Add this decimal number to the whole number part of the mixed number

A mixed number is a whole number plus a fraction. To find the decimal form of a fraction just divide the numerator by the denominator using a calculator or long division. Then add the decimal number to the whole number.

Example: Convert the mixed number 7 1/4 to a decimal

  1. Convert the fraction to a decimal: Divide 1 by 4
    1 ÷ 4 = 0.25
  2. Add 0.25 to the whole number 7:
    7 + 0.25 = 7.25

Note that this solution works even if the fraction part of the mixed number is an improper fraction.

Example: Convert the mixed number 3 9/5 to a decimal

  1. Convert the fraction to a decimal: Divide 9 by 5
    9 ÷ 5 = 1.8
  2. Add 1.8 to the whole number 3:
    3 + 1.8 = 4.8

Secondary Method: Convert a Mixed Number to a Decimal by Fraction Addition

Alternatively you can convert a mixed number to a decimal by first converting the mixed number to two fractions, adding them and simplifying to a decimal.

Example: Convert the mixed number 5 2/3 to a decimal

  • 5 2/3 = 5/1 + 2/3
  • 5 2/3 = (5/1 * 3/3) + 2/3
  • 5 2/3 = 15/3 + 2/3
  • 5 2/3 = 17/3
  • 5 2/3 = 5.667

A mixed number such as 7 1/4 can be converted to a decimal. It is implied that 7 1/4 is really 7 + 1/4 and that 7 = 7/1, therefore we are first adding the fraction 7/1 + 1/4. Since 4 is the denominator in the original fraction part we will use it as our common denominator. 7/1 * 4/4 = 28/4. Then, 28/4 + 1/4 = 29/4. 29/4 = 29 ? 4 = 7.25.

Related Calculators

You can also see our Long Division Calculator with Decimals to convert a fraction to a decimal and see the work involved in the long division.

To convert a decimal to a fraction see the Decimal to Fraction Calculator.

 

Cite this content, page or calculator as:

Furey, Edward "Mixed Number to Decimal Calculator"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculator

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