# 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 = 215/84 = 2 47/84 ≅ 2.5595238

Spelled result in words is two hundred fifteen eighty-fourths (or two and forty-seven 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 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 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. Subtract: 29/7 - 7/3 = 29 · 3/7 · 3 - 7 · 7/3 · 7 = 87/21 - 49/21 = 87 - 49/21 = 38/21
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 next intermediate step, the fraction result cannot be further simplified by canceling.
In words - twenty-nine sevenths minus seven thirds = thirty-eight twenty-firsts.
4. Add: the result of step No. 3 + 3/4 = 38/21 + 3/4 = 38 · 4/21 · 4 + 3 · 21/4 · 21 = 152/84 + 63/84 = 152 + 63/84 = 215/84
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 next intermediate step, the fraction result cannot be further simplified by canceling.
In words - thirty-eight twenty-firsts plus three quarters = two hundred fifteen eighty-fourths.

#### 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:

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:

What is the sum of 2/3 and 3/10?
• Series and sequences
Find a fraction equivalent to the recurring decimal? 0.435643564356
• 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?
• 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?
• Sayavong
Sayavong is making cookies for the class. He has a recipe that calls for 3 and 1/2 cups of flour. He has 7/8 of a cup of wheat flour, and 2 and 1/2 cups of white flour. Does Mr. Sayavong have enough flour to make the cookies?
• The cost 2
The cost of 5 apples is \$3.45  and 5 oranges is \$1.23. If Rachel buys one apple and one orange, then how much must she pay?
• Sum of fractions
What is the sum of 2/3+3/5?