# 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:

### 28/9 - 3/7 = 155/63 = 2 29/63 ≅ 2.4603175

Spelled result in words is one hundred fifty-five sixty-thirds (or two and twenty-nine sixty-thirds).

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

1. Conversion a mixed number 2 8/9 to a improper fraction: 2 8/9 = 2 8/9 = 2 · 9 + 8/9 = 18 + 8/9 = 26/9

To find new numerator:
a) Multiply the whole number 2 by the denominator 9. Whole number 2 equally 2 * 9/9 = 18/9
b) Add the answer from previous step 18 to the numerator 8. New numerator is 18 + 8 = 26
c) Write a previous answer (new numerator 26) over the denominator 9.

Two and eight ninths is twenty-six ninths
2. Subtract: 26/9 - 3/7 = 26 · 7/9 · 7 - 3 · 9/7 · 9 = 182/63 - 27/63 = 182 - 27/63 = 155/63
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(9, 7) = 63. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 7 = 63. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - twenty-six ninths minus three sevenths = one hundred fifty-five sixty-thirds.

#### 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:

• School There are 150 pupils in grade 5 . 2/3 of them are female. By what fractions are the males?
• Mixed numbers Rewrite mixed numbers, so the fractions have the same denominator: 5 1/5 - 2 2/3
• Hussein Hussein owns 450000 crowns (local currency). He spent at the bookstore 2 over 9 to buy some books and tales. He paid 3 over 5 of his money to buy his math book. a. Calculate the remaining amount of money with Hussein? b. Hussein lost 3 over 4 of the remai
• Erica Erica bought 3 1/2 yards of fabric. If she uses 2/3 of the fabric, how much will she have left?
• Wood 11 Father has 12 1/5 meters long wood. Then I cut the wood into two pieces. One part is 7 3/5 meters long. Calculate the length of the other wood?
• Simplify 3 Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
• Square metal sheet 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. Sadie practiced her spelling words for 3/4 of an hour, and Max practiced his spelling words for 5/12 of an hour. In the simplest form, how much longer did Sadie practice than Max? Erika’s career consists of filing, typing and answering phones. She spends 1/6 of her time filing and 5/8 of her time typing. What fraction of her time does she spend answering phone calls? Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed? Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante The teacups in Tea Stop 55 are `2/5` green and `3/10` yellow. What fraction of the teacups are neither green nor yellow? Of all 360 employees, there are 11/12 women. How many men work in a company?