# 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:

### 41/7 + 21/3 - 3/4 = 481/84 = 5 61/84 ≅ 5.7261905

Spelled result in words is four hundred eighty-one eighty-fourths (or five and sixty-one eighty-fourths).

### How do you solve fractions step by step?

1. Conversion a mixed number 4 1/7 to a improper fraction: 4 1/7 = 4 1/7 = 4 · 7 + 1/7 = 28 + 1/7 = 29/7

To find a new numerator:
a) Multiply the whole number 4 by the denominator 7. Whole number 4 equally 4 * 7/7 = 28/7
b) Add the answer from previous step 28 to the numerator 1. New numerator is 28 + 1 = 29
c) Write a previous answer (new numerator 29) over the denominator 7.

Four and one seventh is twenty-nine sevenths
2. Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 · 3 + 1/3 = 6 + 1/3 = 7/3

To find a new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7
c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one third is seven thirds
3. Add: 29/7 + 7/3 = 29 · 3/7 · 3 + 7 · 7/3 · 7 = 87/21 + 49/21 = 87 + 49/21 = 136/21
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, 3) = 21. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 3 = 21. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty-nine sevenths plus seven thirds = one hundred thirty-six twenty-firsts.
4. Subtract: the result of step No. 3 - 3/4 = 136/21 - 3/4 = 136 · 4/21 · 4 - 3 · 21/4 · 21 = 544/84 - 63/84 = 544 - 63/84 = 481/84
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(21, 4) = 84. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 21 × 4 = 84. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one hundred thirty-six twenty-firsts minus three quarters = four hundred eighty-one eighty-fourths.

#### 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:

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:

• Fraction Fraction frac(0, overline(38))(0,38) write as fraction a/b, a, b is integers numerator/denominator.
• Jo walks Jo walks 3/4 of km to a friends home, 1/2 km to mall, and 2/3 km home. What total distance that joy covers?
• Simplify 9 Simplify and express the result as a rational number in its simplest form 1/2+ 1/5+ 6.25+0.25
• Weigh in total I put 3/5 kg of grapes into a box which is 1/4kg in weight. How many kilograms do the grapes and the box weigh in total? 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?
• Math homework It took Jose two-thirds of an hour to complete his math homework on Monday, three-fourths of an hour on Tuesday, any two-fifths of an hour on Wednesday. How many hours did it take Jose to complete his homework altogether?
• Area and perimeter 2 Find the area and the perimeter of a rectangle of length 45 1/2 cm and breadth 16 2/3 cm.
• Sum of fractions What is the sum of 2/3+3/5? 3 3/4 + 2 3/5 + 5 1/2 Show your solution. Kara has 2 times more cards than Dana, Dana has 4× less than Mary. Together they have 728 cards. How many cards has each of them? 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? Carrie picked 2/5 of the raspberries from the garden, and Robin picked some too.  When they were finished, 1/3 of the raspberries still needed to be picked.  What fraction of the raspberries did Robin pick? Use pictures, numbers or words and write your fi The sum of two rational numbers is (-2). If one of them is 3/5, find the other.