# 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:

### 1/4 + 1/5 = 9/20 = 0.45

Spelled result in words is nine twentieths.

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

1. Add: 1/4 + 1/5 = 1 · 5/4 · 5 + 1 · 4/5 · 4 = 5/20 + 4/20 = 5 + 4/20 = 9/20
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(4, 5) = 20. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 5 = 20. In the following intermediate step, the fraction result cannot be further simplified by canceling.
In other words - one quarter plus one fifth = nine twentieths.

#### 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:

• Divide 13 Divide. Simplify your answer and write as an improper fraction or whole number. 14÷8/3 7 is added to the sum of 4/5 and 6/7
• Teacher Teacher Rem bought 360 pieces of cupcakes for the outreach program of their school. 5/9 of the cupcakes were chocolate flavor and 1/4 wete pandan flavor and the rest were a vanilla flavor. How much more pandan flavor cupcakes than vanilla flavor? Max is working out 2/3+7/9. He says the answer is 9/12. What mistake have Max made?
• The recipe The recipe they are following requires 7/8 cups of milk, Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe?
• Paper clips Mrs. Bright is organizing her office supplies. There are 5 open boxes of paper clips in her desk drawer. Each box has 1/2 of the paper clips remaining. How many boxes of paper clips are left?
• King King had four sons. First inherit 1/2, second 1/4, third 1/5 of property. What part of the property was left to the last of the brothers?
• A korean A korean mart sells banana milk, strawberry milk, and melon milk. 65% of the milks sold is banana and 14% is strawberry. What percentage is melon milk?
• Bricklayers 8 bricklayers build a house for 630 days. How many bricklayers have to add after 150 days to complete the whole building in (next) 320 days?
• Fruits Amy bought a basket of fruits 1/5 of them were apples,1/4 were oranges, and the rest were 33 bananas. How many fruits did she buy in all?
• Dividends The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least?
• Boys and girls There are 28 girls in the hall. 5/7 of all children are boys. How many children and how many boys are there?
• Michael Michael had a bar of chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?