# 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:

### 4 2/5 / 1 1/5 = 11/3 = 3 2/3 ≅ 3.6666667

Spelled result in words is eleven thirds (or three and two thirds).### How do you solve fractions step by step?

- Conversion a mixed number 4 2/5 to a improper fraction: 4 2/5 = 4 2/5 = 4 · 5 + 2/5 = 20 + 2/5 = 22/5

To find a new numerator:

a) Multiply the whole number 4 by the denominator 5. Whole number 4 equally 4 * 5/5 = 20/5

b) Add the answer from previous step 20 to the numerator 2. New numerator is 20 + 2 = 22

c) Write a previous answer (new numerator 22) over the denominator 5.

Four and two fifths is twenty-two fifths - Conversion a mixed number 1 1/5 to a improper fraction: 1 1/5 = 1 1/5 = 1 · 5 + 1/5 = 5 + 1/5 = 6/5

To find a new numerator:

a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5

b) Add the answer from previous step 5 to the numerator 1. New numerator is 5 + 1 = 6

c) Write a previous answer (new numerator 6) over the denominator 5.

One and one fifth is six fifths - Divide: 22/5 : 6/5 = 22/5 · 5/6 = 22 · 5/5 · 6 = 110/30 = 10 · 11 /10 · 3 = 11/3

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 6/5 is 5/6) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 10 gives 11/3.

In other words - twenty-two fifths divided by six fifths = eleven thirds.

#### 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:

• 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:

- A baker

A baker has 5 1/4 pies in her shop. She cut the pies in pieces that are each 1/8 of a whole pie. How many pieces of pie does she have? - Cooks

Four cooks cleaned 5 kg of potatoes for 10 minutes. How many cook would have to work clean 9 kg of potatoes for 12 minutes? - Barbara 2

Barbara get 6 pizzas to divide equally among 4 people. How much of a pizza can each person have? - Fraction expression

Which expression is equivalent to : minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis - Lauren

Lauren is tutoring students at the library on Saturday. If she is at the library for a total of 6 hours and she helps each student, one at a time, for three-fourths of an hour, how many students does she tutor? - Division by zero

Fraction 5 by 2. if 3 is added to numerator and 2 is subtracted from the denominator then the new fraction is: - The Hobson

The Hobson family is on a road trip and their gas tank is 1/10 full. If they can drive 40 more miles, what fraction of the tank does each mile consume? - Francesca

Francesca is growing 1/2 inch each year. How many years will it take for her to grow 6 inches? - What is 13

What is the number sentence? * 1 point 1/2 + 3/4 + 1/4 = A 1/2 - 3/4 - 1/4 = B 1/2 x 3/4 x 1/4 = C 1/2 ÷ 3/4 ÷ 1/4 = D - 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? - Balls

The boys changed stamps, beads and balls. For 9 balls is 3 stamps, 2 balls is 44 stamps. How many beads is for 1 ball? - Cake 7

1/3 of a cake shared with 4 people. What share of the whole cake has each people? - Brooke

Brooke divided 2/3 by 1/6 and got 1/9. Her classmate told her that she isn’t correct. What do you think went wrong with Brooke’s solution? Explain your answer in 2 - 3 sentences.

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