# 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:

### 2/6 + 1/3 + 1/2 = 7/6 = 1 1/6 ≅ 1.1666667

Spelled result in words is seven sixths (or one and one sixth).

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

1. Add: 2/6 + 1/3 = 2/6 + 1 · 2/3 · 2 = 2/6 + 2/6 = 2 + 2/6 = 4/6 = 2 · 2/2 · 3 = 2/3
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(6, 3) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 3 = 18. In the next intermediate step, , cancel by a common factor of 2 gives 2/3.
In words - two sixths plus one third = two thirds.
2. Add: the result of step No. 1 + 1/2 = 2/3 + 1/2 = 2 · 2/3 · 2 + 1 · 3/2 · 3 = 4/6 + 3/6 = 4 + 3/6 = 7/6
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(3, 2) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 2 = 6. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - two thirds plus one half = seven sixths.

#### 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:

• Fraction to decimal Write the fraction 3/22 as a decimal.
• Fraction and a decimal Write as a fraction and a decimal. One and two plus three and five hundredths
• Pears There were pears in the basket, I took two-fifths of them, and left six in the basket. How many pears did I take?
• Simple equation 5 Solve equation with fractions: X × 3/8 = 1/2
• Unknown number I think the number - its sixth is 3 smaller than its third.
• Rolls Mom bought 13 rolls. Dad ate 3.5 rolls. How many rolls left when Peter yet put two at dinner?
• Product of two fractions Product of two fractions is 9 3/5 . If one of the fraction is 9 3/7. Find the other fraction.
• Withdrawal If I withdrew 2/5 of my total savings and spent 7/10 of that amount. What fraction do I have in left in my savings?
• Cupcakes 2 Susi has 25 cupcakes. She gives 4/5. How much does she have left?
• Simple equation 6 Solve equation with one variable: X/2+X/3+X/4=X+4
• New bridge Thanks to the new bridge, the road between A and B has been cut to one third and is now 10km long. How much did the road between A and B measure before?
• One-third 2 One-third of the people in a barangay petitioned the council to allow them to plant in vacant lots, and another 1/5 of the people petitioned to have a regular garbage collection. What FRACTION of the barangay population made the petition?
• Pizza 5 You have 2/4 of a pizza, and you want to share it equally between 2 people. How much pizza does each person get?