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:

6/7 - 3/4 = 3/280.1071429

Spelled result in words is three twenty-eighths.

How do you solve fractions step by step?

  1. Subtract: 6/7 - 3/4 = 6 · 4/7 · 4 - 3 · 7/4 · 7 = 24/28 - 21/28 = 24 - 21/28 = 3/28
    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(7, 4) = 28. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 4 = 28. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - six sevenths minus three quarters = three twenty-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:

  • Human 3
    Human bones are 3/10 living tissues 9/20 minerals, and the rest water. What fraction of human bone is water?
  • Mountain
    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?
  • Pizza fractions
    Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
  • Plums
    In the bag was to total 136 plums. Igor took 3 plums and Mary took 4/7 from the rest. How many plums remained in the bag?
  • Bitoo and Reena
    Bitoo ate 3/5 part of an apple and the remaining part was eaten by his sister Reena. How much part of an apple did Renna eat? Who had the larger share? By how much?
  • Mike buys
    Mike buys flowers to plant around his trees. 3/8 of the flowers are red. 1/3 of the flowers are pink. The rest of the flowers are white. Find the fraction of flowers that are white.
  • Cake fractions
    Thomas ate 1/3 of cake, Bohouš of the rest of the cake ate 2/5. What fraction of cake left over for others?
  • A rectangle 7
    A rectangle that has been split into 24 parts, set in 4 rows of 6 pieces each. The parts in the top 3 rows have been shaded blue. The parts in the left 5 columns have been shaded purple. The first 5 parts in the top 3 rows are striped to show they are sha
  • Tree planting
    The trapezoidal garden has bases 44 m and 16 m long. Their distance is 25 m. How many square meters of its area will remain for tree planting if we use 1/5 of the entire site to construct a cottage, backyard, and road. Is it possible to determine the leng
  • Leo hiked
    Leo hiked 6/7 of a kilometer. Jericho hiked 2/3 kilometer. Who covered a longer distance? How much longer?
  • Estimate
    Estimate the answer by rounding each fraction to the nearest whole number and then subtracting. 9/15 - 2 7/8
  • Difference mixed fractions
    What is the difference between 4 2/3 and 3 1/6?
  • What is 13
    What is the number sentence? * 1 point 1/2 + 3/4 + 1/4 = A 1/2 - 3/4 - 1/4 = B 1/2 x 3/4 x 1/4 = C 1/2 ÷ 3/4 ÷ 1/4 = D


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