# 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 3/7 * 1 3/7 = 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?

- 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 - 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 - 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:

• adding fractions: 2/4 + 3/4• 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

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?

next math problems »