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Mixed Numbers Calculator

Mixed Numbers Calculator
= ?
Answer:
\[ = 4 \frac{1}{8} \]
Solution 1 by separating parts
Rewriting our equation with parts separated\[ = 1 + \frac{3}{4} + 2 + \frac{3}{8} \]Solving the whole number parts\[ 1 + 2 = 3 \]Solving the fraction parts\[ \frac{3}{4} + \frac{3}{8}= \; ? \]Find the LCD of 3/4 and 3/8 and rewrite to solve with the equivalent fractions.
LCD = 8
\[ \frac{6}{8} + \frac{3}{8}= \frac{9}{8} \]Simplifying the fraction part, 9/8, \[ \frac{9}{8}= 1 \frac{1}{8} \]Combining the whole and fraction parts\[ 3 + 1 + \frac{1}{8}= 4 \frac{1}{8} \]
Solution by Formulas
converting mixed numbers to fractions, our initial equation becomes,\[ \frac{7}{4} + \frac{19}{8} \]Applying the fractions formula for addition,\[ = \frac{(7 \times 8) + (19 \times 4)}{4 \times 8} \]\[ = \frac{56 + 76}{32} \]\[ = \frac{132}{32} \]Simplifying 132/32, the answer is\[ = 4 \frac{1}{8} \]

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Calculator Use

Do calculations with mixed numbers (mixed fractions), performing operations on fractions, whole numbers, integers, mixed numbers, mixed fractions and improper fractions. We also have a fractions calculator, simplify fractions calculator and fractions comparison calculator. See additional notes below.

Mixed Numbers Calculator (also referred to as Mixed Fractions):

This online calculator handles simple operations on whole numbers, integers, mixed numbers, fractions and improper fractions by adding, subtracting, dividing or multiplying. The answer is provided in a reduced fraction and a mixed number if it exists.

Enter mixed numbers, whole numbers or fractions in the following formats:

  1. Mixed numbers: exactly as 1 1/2 which is one and one half or 25 3/32 which is twenty five and three thirty seconds. Keep exactly one space between the whole number and fraction. You can enter up to 3 digits in length for each whole number, numerator or denominator (123 456/789).
  2. Whole numbers: up to 3 digits in length. (123)
  3. Fractions: as 3/4 which is three fourths or 3/100 which is three one hundredths. You can enter up to 3 digits in length for each the numerators and denominators (456/789).

Adding Mixed Numbers using the Adding Fractions Formula

  • Convert the mixed numbers to improper fractions
  • Use the algebraic formula for addition of fractions: a/b + c/d = (ad + bc) / bd
  • Reduce fractions and simplify if possible

Adding Fractions Formula

\( \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \times d) + (b \times c)}{b \times d} \)

Example

Add 1 2/6 and 2 1/4

\( 1 \dfrac{2}{6} + 2 \dfrac{1}{4} = \dfrac{8}{6} + \dfrac{9}{4} \)
\( = \dfrac{(8 \times 4) + (9 \times 6)}{6 \times 4} \)
\( = \dfrac{32 + 54}{24} = \dfrac{86}{24} = \dfrac{43}{12} \)
\( = 3 \dfrac{7}{12} \)

1 2/6 + 2 1/4 = 8/6 + 9/4 = (8*4 + 9*6) / 6*4 = 86 / 24

so we get 43/12 and simplify to 3 7/12

Subtracting Mixed Numbers using the Subtracting Fractions Formula

  • Convert the mixed numbers to improper fractions
  • Use the algebraic formula for subtraction of fractions: a/b - c/d = (ad - bc) / bd
  • Reduce fractions and simplify if possible

Subtracting Fractions Formula

\( \dfrac{a}{b} - \dfrac{c}{d} = \dfrac{(a \times d) - (b \times c)}{b \times d} \)

Example

subtract 2 1/4 from 1 2/6

1 2/6 - 2 1/4 = 8/6 + 9/4 = (8*4 - 9*6) / 6*4 = -22 / 24

Reduce fractions so we get -11/12

Multiplying Mixed Numbers using the Multiplying Fractions Formula

  • Convert the mixed numbers to improper fractions
  • Use the algebraic formula for multiplying of fractions: a/b * c/d = ac / bd
  • Reduce fractions and simplify if possible

Multiplying Fractions Formula

\( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d} \)

Example

multiply 1 2/6 by 2 1/4

1 2/6 * 2 1/4 = 8/6 * 9/4 = 8*9 / 6*4 = 72 / 24

Reduce fractions so we get 3/1 and simplify to 3

Dividing Mixed Numbers and Dividing Fractions Formula

  • Convert the mixed numbers to improper fractions
  • Use the algebraic formula for division of fractions: a/b ÷ c/d = ad / bc
  • Reduce fractions and simplify if possible

Dividing Fractions Formula

\( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a \times d}{b \times c} \)

Example

divide 1 2/6 by 2 1/4

1 2/6 ÷ 2 1/4 = 8/6 ÷ 9/4 = 8*4 / 9*6 = 32 / 54

Reduce fractions so we get 16/27

 

This script performs the reducing calculation faster than other scripts you might find. The primary reason is that it utilizes Euclid's Theorem for reducing fractions which can be found at The Math Forum: LCD, LCM.



 

Cite this content, page or calculator as:

Furey, Edward "Mixed Numbers Calculator"; from http://www.calculatorsoup.com - Online Calculator Resource.

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