# 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:

### 47/9 - 3/15 = 206/45 = 4 26/45 ≅ 4.5777778

Spelled result in words is two hundred six forty-fifths (or four and twenty-six forty-fifths).

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

1. Conversion a mixed number 4 7/9 to a improper fraction: 4 7/9 = 4 7/9 = 4 · 9 + 7/9 = 36 + 7/9 = 43/9

To find a new numerator:
a) Multiply the whole number 4 by the denominator 9. Whole number 4 equally 4 * 9/9 = 36/9
b) Add the answer from previous step 36 to the numerator 7. New numerator is 36 + 7 = 43
c) Write a previous answer (new numerator 43) over the denominator 9.

Four and seven ninths is forty-three ninths
2. Subtract: 43/9 - 3/15 = 43 · 5/9 · 5 - 3 · 3/15 · 3 = 215/45 - 9/45 = 215 - 9/45 = 206/45
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, 15) = 45. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 15 = 135. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - forty-three ninths minus three fifteenths = two hundred six forty-fifths.

#### 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:

• Farmer Peter Farmer Peter paints 12 chicken coop. He started painting this day morning. Now he only has 1/4 of the chicken coop left to paint this afternoon. How many chicken coops did farmer Peter paint this morning?
• Cups of punch Cyka made 6 19/20 cups of punch punch at two different types of juice in it. If the punch had 4 1/5 cups of one type of juice how many cups of the other type of juice did it have?
• In bucket In bucket of 87 oranges 1/3 are spoiled ones and the remaining are eaten by the member of a family. How many oranges are eaten by the member of family?
• 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?
• Lunch time In a cafeteria, 3/10 of the students are eating salads, and 3/5 are eating sandwiches. There are 30 students in the cafeteria. How many students are eating lunches other than salads or sandwiches?
• Pounds Three pounds subtract 1/3 of a pound.
• Pupils 7 There are 40 pupils in a certain class. 3/5 of the class are boys. How many are girls?
• Curtain Mrs. Lazo bought 9 1/8 m curtain cloth. She used 3 5/6 m to make a curtain for their bedroom. How many meters of cloth were not used?
• Length subtracting Express in mm: 5 3/10 cm - 2/5 mm
• Martin Martin is making a model of a Native American canoe. He has 5 1/2 feet of wood. He uses 2 3/4 feet for the hull and 1 1/4 feet for a paddle. How much wood does he have left? Martin has feet of wood left.
• Pediatrician Pediatrician this month of 20 working days takes 8 days holidays. What is the probability that on Monday it will be at work?
• Sum of 18 Sum of two fractions is 4 3/7. If one of the fractions is 2 1/5 find the other one .
• Difference mixed fractions What is the difference between 4 2/3 and 3 1/6?