# Fraction calculator

The calculator performs basic and advanced operations with fractions, expressions with fractions combined with integers, decimals, and mixed numbers. Also shows detailed step-by-step information about fraction calculation procedure. Solve problems with two, three or more fractions and numbers in one expression.

## Result:

### 81/5 + 91/2 = 177/10 = 177/10 = 17.7

Spelled result in words is one hundred seventy-seven tenths (or seventeen and seven tenths).

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

1. Conversion a mixed number 8 15 to a improper fraction: 8 1/5 = 8 15 = 8 · 5 + 15 = 40 + 15 = 415

To find new numerator:
a) Multiply the whole number 8 by the denominator 5. Whole number 8 equally 8 * 55 = 405
b) Add the answer from previous step 40 to the numerator 1. New numerator is 40 + 1 = 41
c) Write previous answer (new numerator 41) over the denominator 5.

Eight and one fifth is forty-one fifths
2. Conversion a mixed number 9 12 to a improper fraction: 9 1/2 = 9 12 = 9 · 2 + 12 = 18 + 12 = 192

To find new numerator:
a) Multiply the whole number 9 by the denominator 2. Whole number 9 equally 9 * 22 = 182
b) Add the answer from previous step 18 to the numerator 1. New numerator is 18 + 1 = 19
c) Write previous answer (new numerator 19) over the denominator 2.

Nine and one half is nineteen halfs
3. Add: 415 + 192 = 41 · 25 · 2 + 19 · 52 · 5 = 8210 + 9510 = 82 + 9510 = 17710
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 the both denominators - LCM(5, 2) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 2 = 10. In the next intermediate step the fraction result cannot be further simplified by cancelling.
In words - forty-one fifths plus nineteen halfs = one hundred seventy-seven tenths.

#### 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 number 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 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.

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

Calculator follows well-known rules for order of operations. 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:

• 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?
• Interior designer To make draperies an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20 yard bolts, how much will be left over after completing both sets of draperies? Add two mixed fractions: 2 4/6 + 1 3/6 3 3/4 + 2 3/5 + 5 1/2 Show your solution.
• Playing Cards 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?
• Pupils Two classes to collect money. Boys are four sevenths pupils. In time did not pay a quarter of the boys and a sixth of girls, which together mean 12 sinners. How many pupils attend this two classes ?
• Master and apprentice Master painted the roof in 3 hours and apprentice for 4 hours. How many of roof they painted in hour and how many in three quarters of an hour?
• Two numbers The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number.
• Chestnuts Three divisions of nature protectors participated in the collection of chestnut trees.1. the division harvested 1250 kg, the 2nd division by a fifth more than the 1st division and the 3rd division by a sixth more than the second division. How many tons of
• Expressions with variable This is algebra. Let n represent an unknown number and write the following expressions: 1. 4 times the sum of 7 and the number x 2. 4 times 7 plus the number x 3. 7 less than the product of 4 and the number x 4. 7 times the quantity 4 more than the number
• Cupcakes In a bowl was some cupcakes. Janka ate one third and Danka ate one quarter of cupcakes. a) How many of cookies ate together? b) How many cookies remain in a bowl? Write the results as a decimal number and in notepad also as a fraction.
• Simplify 3 Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
• The Mayflower The Mayflower traveled for 66 days on the trip from England to America. The weather was storming for many days of their trip. If one and a half of the days at Sea where Sunny with good weather, 1/6 of the days were sunny but very windy and the other days