# 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:

### 23/7 * 13/7 = 170/49 = 3 23/49 ≅ 3.4693878

Spelled result in words is one hundred seventy forty-ninths (or three and twenty-three forty-ninths).

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

1. Conversion a mixed number 2 3/7 to a improper fraction: 2 3/7 = 2 3/7 = 2 · 7 + 3/7 = 14 + 3/7 = 17/7

To find a new numerator:
a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7
b) Add the answer from previous step 14 to the numerator 3. New numerator is 14 + 3 = 17
c) Write a previous answer (new numerator 17) over the denominator 7.

Two and three sevenths is seventeen sevenths
2. Conversion a mixed number 1 3/7 to a improper fraction: 1 3/7 = 1 3/7 = 1 · 7 + 3/7 = 7 + 3/7 = 10/7

To find a new numerator:
a) Multiply the whole number 1 by the denominator 7. Whole number 1 equally 1 * 7/7 = 7/7
b) Add the answer from previous step 7 to the numerator 3. New numerator is 7 + 3 = 10
c) Write a previous answer (new numerator 10) over the denominator 7.

One and three sevenths is ten sevenths
3. Multiple: 17/7 * 10/7 = 17 · 10/7 · 7 = 170/49
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(170, 49) = 1. In the following intermediate step, the fraction result cannot be further simplified by canceling.
In other words - seventeen sevenths multiplied by ten sevenths = one hundred seventy forty-ninths.

#### 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: Rhea answered 5/11 in the questions correctly and Precious answered 7/11 of it correctly. If each problem is worth the same amount, who got the higher score?
• Sort fractions Which of the following fractions is the largest? 29/36 5/6 7/9 3/4
• 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?
• Ten fractions Write ten fractions between 1/3 and 2/3
• Equivalent fractions Are these two fractions equivalent -4/9 and 11/15?
• A laundry Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
• Luke Luke, Seth, and Anja have empty glasses. Mr. Gabel pours 3/6 cup of orange juice in Seth's glass. Then he pouts 1/6 cup of orange juice in Luke's glass and 2/6 cup of orange juice in Anja's glass. Who gets the MOST orange juice?
• Roma ate Roma ate 2/5 of a cake while Somya ate 3/7 of the same cake. Who ate more and by how much?
• A small A small book took one-sixth of a ream of paper to make. The team said they could make nine books from 3 whole reams of paper. Are they correct?
• Sort fractions Which is larger 3/7, 3/8, 3/9, 3/6 =
• Simplest form of a fraction Which one of the following fraction after reducing in simplest form is not equal to 3/2? a) 15/20 b) 12/8 c) 27/18 d) 6/4
• Buing Brother got to buy 240 CZK and could buy for 1/8 what he wanted. Could he pay the rest of the purchase for 200 CZK?
• Paper collecting At the paper collecting contest gathered Franta 2/9 ton, Karel 1/4 ton, and Patrick 19/36 tons of paper. Who has gathered the most and the least?