# 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:

### 12 : (1 1/5) = 10/1 = 10

Spelled result in words is ten.### How do you solve fractions step by step?

- 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: 12 : 6/5 = 12/1 · 5/6 = 12 · 5/1 · 6 = 60/6 = 6 · 10 /6 · 1 = 10

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 6 gives 10/1.

In other words - twelve divided by six fifths = ten.

#### 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 shopkeeper

A shopkeeper cuts a wheel of cheese into 10 equal wedges. A customer buys one-fifth of the wheel. How many wedges does the customer buy? Use the number line to help find the solution. - Red Riding Hood

Red Riding Hood is making her special banana pudding recipe. She is looking for her cup measure, but can only find her quarter cup measure. How many quarter cups does she need for 2 cups of sour cream? - 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? - Dividing walnuts into crates

There are 8 and 2 over 3 pounds of walnuts in a container, which will be divided equally into containers that hold 1 and 1 over 5 pounds. This would fill n and 4 over 18 containers. What is n? - Statues

Diana is painting statues. She has 7/8 of a liter of paint remaining. Each statue requires 1/20 of a liter of paint. How many statues can she paint? - Divide in ratio

Line segment AB 12 cm long divide in a ratio of 5: 3. How long are the individual parts? - Scale of the map

Determine the map's scale, which is the actual distance of 120 km l represented by a segment long 6 cm. - The cost 2

The cost of 5 apples is $3.45, and 5 oranges are $1.23. If Rachel buys one apple and one orange, then how much must she pay? - Tape

Video is 153% more expensive than tape recorder. How many percent is tape recorder less expensive than video? - Cathy

Cathy has 5 cups of peanuts to share with her family. If each family member gets 1/2 cup of peanuts, how many family members can have some? - 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: - Unit rate

Find unit rate: 6,840 customers in 45 days - Strawberry-rhubarb pie

Larry had 3/7 of a strawberry-rhubarb pie left over. He split the leftover pie evenly between his 3 children. What fraction of a pie did each child get?

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