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:

1/2 - 1/7 = 5/140.3571429

Spelled result in words is five fourteenths.

How do you solve fractions step by step?

  1. Subtract: 1/2 - 1/7 = 1 · 7/2 · 7 - 1 · 2/7 · 2 = 7/14 - 2/14 = 7 - 2/14 = 5/14
    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(2, 7) = 14. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 7 = 14. In the following intermediate step, the fraction result cannot be further simplified by canceling.
    In other words - one half minus one seventh = five fourteenths.

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:

  • 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
  • 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?
  • 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?
  • 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
  • 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.
  • Mother 7
    mangoes Mother bought 18 fruits. 1/3 were pineapple and the rest  were mangoes . how many were mangoes
  • 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?
  • 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?
  • 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?
  • 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?
  • 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?
  • A basket 2
    mangoes A basket contains three types of fruits weighing 87/4 kg in all. If 23/4 kilograms of these are oranges, 48/7 kg are mangoes, and the rest are apples. What is the weight of the apples in the basket?


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