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:

2 1/2 - 1 2/7 = 17/14 = 1 3/141.2142857

Spelled result in words is seventeen fourteenths (or one and three fourteenths).

How do you solve fractions step by step?

  1. Conversion a mixed number 2 1/2 to a improper fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2

    To find a new numerator:
    a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2 = 4/2
    b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
    c) Write a previous answer (new numerator 5) over the denominator 2.

    Two and one half is five halfs
  2. Conversion a mixed number 1 2/7 to a improper fraction: 1 2/7 = 1 2/7 = 1 · 7 + 2/7 = 7 + 2/7 = 9/7

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 7. Whole number 1 equally 1 * 7/7 = 7/7
    b) Add the answer from previous step 7 to the numerator 2. New numerator is 7 + 2 = 9
    c) Write a previous answer (new numerator 9) over the denominator 7.

    One and two sevenths is nine sevenths
  3. Subtract: 5/2 - 9/7 = 5 · 7/2 · 7 - 9 · 2/7 · 2 = 35/14 - 18/14 = 35 - 18/14 = 17/14
    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 - five halfs minus nine sevenths = seventeen 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:

  • The recipe
    milk The recipe they are following requires 7/8 cups of milk, Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe?
  • 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?
  • Cherries 2
    cherry If a farmer reaped 636 cherries and he sold one third to a shop keeper, how many did he retain?
  • 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?
  • 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?
  • Mother 7
    mangoes Mother bought 18 fruits. 1/3 were pineapple and the rest  were mangoes . how many were mangoes
  • 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?
  • Mrs. Susan
    textiles Mrs. Susan bought 1/8 m of curtain cloth. She used 3/5 m to make a curtain for the living room window. How many meters of cloth were not used?
  • 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?
  • Hotel 4
    manderlak A 360 room hotel has 1/3 of its rooms occupied at present. How many rooms are empty?
  • 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?
  • 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?
  • Product and sum
    fractions14 What is the product of two fourths  and the sum of three halves and four?


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