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:

1 1/3 - 3/4 = 7/120.5833333

Spelled result in words is seven twelfths.

How do you solve fractions step by step?

  1. Conversion a mixed number 1 1/3 to a improper fraction: 1 1/3 = 1 1/3 = 1 · 3 + 1/3 = 3 + 1/3 = 4/3

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/3 = 3/3
    b) Add the answer from previous step 3 to the numerator 1. New numerator is 3 + 1 = 4
    c) Write a previous answer (new numerator 4) over the denominator 3.

    One and one third is four thirds
  2. Subtract: 4/3 - 3/4 = 4 · 4/3 · 4 - 3 · 3/4 · 3 = 16/12 - 9/12 = 16 - 9/12 = 7/12
    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(3, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, the fraction result cannot be further simplified by canceling.
    In other words - four thirds minus three quarters = seven twelfths.

Rules for expressions with fractions:

Fractions - use the 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 non-zero 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:

  • Mountain
    manga_parbat Mountain has an elevation of 7450 meters and in the morning is the middle portion thereof in the clouds. How many meters of height is in the sky if below the clouds are 2,000 meters, and above clouds are two-fifths of the mountain's elevation?
  • 5 2/5
    time 5 2/5 hours a week  mathematics,  3 3/4 hours a week   Natural sciences, 4 3/8 hours a week  Technology . how many hours does  he spend on social sciences if he spend 17 1/2 hours a week for the four subject?
  • Leo hiked
    tourist Leo hiked 6/7 of a kilometer. Jericho hiked 2/3 kilometer. Who covered a longer distance? How much longer?
  • 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?
  • 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?
  • 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?
  • Cherries 2
    cherry If a farmer reaped 636 cherries and he sold one third to a shop keeper, how many did he retain?
  • Sixth graders
    skola About 6/9 of the sixth- grade pupils will be going to the parents' seminar. If 1/6 of the participants are girls, what part of the portion of sixth graders are boys?
  • Hotel 4
    manderlak A 360 room hotel has 1/3 of its rooms occupied at present. How many rooms are empty?
  • Translate 2
    three_circles_inside_one Translate the given phrases to mathematical phrases. Thrice the sum of three fifths and two thirds less one half is what number?
  • 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.
  • Half of halves
    sequence_geo Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the content of the original square is the content of the cut part?
  • Mother 7
    mangoes Mother bought 18 fruits. 1/3 were pineapple and the rest  were mangoes . how many were mangoes


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