Fraction calculator



The calculator performs basic and advanced operations with fractions, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. Solve problems with two, three, or more fractions and numbers in one expression.

Result:

6 1/4 - 3 5/8 = 21/8 = 2 5/8 = 2.625

Spelled result in words is twenty-one eighths (or two and five eighths).

How do you solve fractions step by step?

  1. Conversion a mixed number 6 1/4 to a improper fraction: 6 1/4 = 6 1/4 = 6 · 4 + 1/4 = 24 + 1/4 = 25/4

    To find a new numerator:
    a) Multiply the whole number 6 by the denominator 4. Whole number 6 equally 6 * 4/4 = 24/4
    b) Add the answer from previous step 24 to the numerator 1. New numerator is 24 + 1 = 25
    c) Write a previous answer (new numerator 25) over the denominator 4.

    Six and one quarter is twenty-five quarters
  2. Conversion a mixed number 3 5/8 to a improper fraction: 3 5/8 = 3 5/8 = 3 · 8 + 5/8 = 24 + 5/8 = 29/8

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8
    b) Add the answer from previous step 24 to the numerator 5. New numerator is 24 + 5 = 29
    c) Write a previous answer (new numerator 29) over the denominator 8.

    Three and five eighths is twenty-nine eighths
  3. Subtract: 25/4 - 29/8 = 25 · 2/4 · 2 - 29/8 = 50/8 - 29/8 = 50 - 29/8 = 21/8
    For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(4, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 8 = 32. In the following intermediate step, the fraction result cannot be further simplified by canceling.
    In other words - twenty-five quarters minus twenty-nine eighths = twenty-one eighths.

Rules for expressions with fractions:

Fractions - simply use a forward slash between the numerator and denominator, i.e., for five-hundredths, enter 5/100. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.
The slash separates the numerator (number above a fraction line) and denominator (number below).

Mixed numerals (mixed fractions or mixed numbers) write as integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, we recommended use colon (:) as the operator of division fractions i.e., 1/2 : 3.

Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

The colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.
An asterisk * or × is the symbol for multiplication.
Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.
The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2


Examples:

• adding fractions: 2/4 + 3/4
• subtracting fractions: 2/3 - 1/2
• multiplying fractions: 7/8 * 3/9
• dividing Fractions: 1/2 : 3/4
• exponentiation of fraction: 3/5^3
• fractional exponents: 16 ^ 1/2
• adding fractions and mixed numbers: 8/5 + 6 2/7
• dividing integer and fraction: 5 ÷ 1/2
• complex fractions: 5/8 : 2 2/3
• decimal to fraction: 0.625
• Fraction to Decimal: 1/4
• Fraction to Percent: 1/8 %
• comparing fractions: 1/4 2/3
• multiplying a fraction by a whole number: 6 * 3/4
• square root of a fraction: sqrt(1/16)
• reducing or simplifying the fraction (simplification) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22
• expression with brackets: 1/3 * (1/2 - 3 3/8)
• compound fraction: 3/4 of 5/7
• fractions multiple: 2/3 of 3/5
• divide to find the quotient: 3/5 ÷ 2/3

The calculator follows well-known rules for order of operations. The most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
Be careful, always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.

Fractions in word problems:

  • Fractions and mixed numerals
    mixed_fractions (a) Convert the following mixed numbers to improper fractions. i. 3 5/8 ii. 7 7/6 (b) Convert the following improper fraction to a mixed number. i. 13/4 ii. 78/5 (c) Simplify these fractions to their lowest terms. i. 36/42 ii. 27/45 2. evaluate the follow
  • Ali bought 2
    milk Ali bought 5/6 litre of milk. He drank 1/2 litre and his brother drank 1/6 litre. How much litre of milk left?
  • Benhur
    water2 Benhur boiled 1 1/4 liters of water in a kettle. After 10 1/2 minutes he measured the water again. It had 3/4 liters left in the kettle. What is the amount of water that evaporates every minutes?
  • Cherries 2
    cherry If a farmer reaped 636 cherries and he sold one third to a shop keeper, how many did he retain?
  • From a 2
    rope From a rope that is 11 m long, two pieces of lengths 13/5 m and 33/10 m are cut off. What is the length of the remaining rope?
  • Leo hiked
    tourist Leo hiked 6/7 of a kilometer. Jericho hiked 2/3 kilometer. Who covered a longer distance? How much longer?
  • Square metal sheet
    plech We cut out four squares of 300 mm side from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.
  • There 17
    kolac There is 3/4 of a cake on a plate in Maria's kitchen.  Silvia sees the cake and eats 1/5 of the cake.  Then Franca takes 1/3 of what was there and shares half of her portion with Antonella.  What fraction of the cake is left?
  • Jose studied
    clocks Jose studied for 4 and 1/2 hours on Saturday and another 6 and 1/4 hours on Sunday. How many subjects did he study if he has alloted 1 and 1/2 hours per subject on Saturday and 1 and 1/4 hours per subject on Sunday?
  • Savings
    savings Eva borrowed 1/3 of her savings to her brother, 1/2 of savings spent in the store and 7 euros left. How much did she save?
  • Mixed numbers
    mixed Five and two-thirds minus 2 and one-half equals what number? A three and one-sixth B three and two-thirds C three and one-half D three and five-sixths
  • Sundar
    chocholate Sundar has 50 chocolates. He gave 2/5 of these chocolates to Ram and he ate 1/5 of them. How many chocolates are left with Sundar?
  • Equation with mixed 2
    mixed A number, X, is subtracted from 8 1/4. The result is 12 3/5. What is the value of X?


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