# 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:

### 1/7 + 5/14 + 3/7 = 13/14 ≅ 0.9285714

Spelled result in words is thirteen fourteenths.

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

1. Add: 1/7 + 5/14 = 1 · 2/7 · 2 + 5/14 = 2/14 + 5/14 = 2 + 5/14 = 7/14 = 7 · 1/7 · 2 = 1/2
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, 14) = 14. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 14 = 98. In the next intermediate step, , cancel by a common factor of 7 gives 1/2.
In words - one seventh plus five fourteenths = one half.
2. Add: the result of step No. 1 + 3/7 = 1/2 + 3/7 = 1 · 7/2 · 7 + 3 · 2/7 · 2 = 7/14 + 6/14 = 7 + 6/14 = 13/14
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 next intermediate step, the fraction result cannot be further simplified by canceling.
In words - one half plus three sevenths = thirteen 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:

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:

• Cupcakes 2
Susi has 25 cupcakes. She gives 4/5. How much does she have left?
• Unknown number
I think the number - its sixth is 3 smaller than its third.
• Trees
From the total number of trees in the orchard, there are two-fifths pearls and apples are three eighty. The rest of the trees are 9 ceremonial. How many trees are in the set?
• Brick
Isosceles scale has on one side all brick and second weight 1 kg and 1/4 of brick. The balance is in equilibrium. What is the weight of a brick?
• One sixth
How many sixths are two thirds?
• Class 8.A
Three quarters of class 8.A went skiing. Of those who remained at home one third was ill and the remaining six were on math olympic. How many students have class 8.A?
• Sales tax
A sales tax on a Php 10,800 appliance is Php.1,620. What is the rate of sales tax?
• PC disks
Peter has 45 disks in three colors. One-fifth of the disks are blue, red are twice more than the white. How much is blue, red and white disks?
• The quotient
The quotient of g and 55 is the same as 279. What is g?
• Trip
On the trip drank 3/10 of pupils tea, 2/5 cola, 1/4 mineral water and remaining 3 juice. How many students were on the trip?
• A man
A man spends 5/9 of his money on rent, and 5/16 of the remainder on electricity. If the final balance remaining is 550 find how much was spent on rent
• On a farm
On a farm, there are 90 rabbits, 700 sheep, 300 cattle and 500 pigs. What percentage of the total number of animals are rabbits?