# Fraction calculator

This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

## The result:

### 1 1/3 - 3/4 = 7/12 ≅ 0.5833333

The spelled result in words is seven twelfths.### How do we solve fractions step by step?

- Conversion a mixed number 1 1/3 to a improper fraction: 1 1/3 = 1 1/3 = 1 · 3 + 1/3 = 3 + 1/3 = 4/3

To find a new numerator:

a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/3 = 3/3

b) Add the answer from the previous step 3 to the numerator 1. New numerator is 3 + 1 = 4

c) Write a previous answer (new numerator 4) over the denominator 3.

One and one third is four thirds. - Subtract: 4/3 - 3/4 = 4 · 4/3 · 4 - 3 · 3/4 · 3 = 16/12 - 9/12 = 16 - 9/12 = 7/12

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - four thirds minus three quarters is seven twelfths.

### Rules for expressions with fractions:

**Fractions**- use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter

**5/100**. If you use mixed numbers, leave a space between the whole and fraction parts.

**Mixed numerals**(mixed numbers or fractions) keep one space between the integer and

fraction and use a forward slash to input fractions i.e.,

**1 2/3**. An example of a negative mixed fraction:

**-5 1/2**.

Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e.,

**1/2 : 1/3**.

Decimals (decimal numbers) enter with a decimal point

**.**and they are automatically converted to fractions - i.e.

**1.45**.

### Math Symbols

Symbol | Symbol name | Symbol Meaning | Example |
---|---|---|---|

+ | plus sign | addition | 1/2 + 1/3 |

- | minus sign | subtraction | 1 1/2 - 2/3 |

* | asterisk | multiplication | 2/3 * 3/4 |

× | times sign | multiplication | 2/3 × 5/6 |

: | division sign | division | 1/2 : 3 |

/ | division slash | division | 1/3 / 5 |

: | colon | complex fraction | 1/2 : 1/3 |

^ | caret | exponentiation / power | 1/4^3 |

() | parentheses | calculate expression inside first | -3/5 - (-1/4) |

#### 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

• reciprocal of a fraction: 1 : 3/4

• square of a fraction: 2/3^2

• cube of a fraction: 2/3^3

• exponentiation of a fraction: 1/2^4

• 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) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction

• 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

**the 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.

**MDAS**- Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.

Be careful; always do

**multiplication and division**before

**addition and subtraction**. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to right.

## Fractions in word problems:

- The entity

What is the difference between seven-tenths of an entity and seven-fifteenths of the same entity? Please solve it for me. - My mother 2

My mother ate 1/8 of the cake, and my father ate 3/8 of the cake. How much cake has been eaten, and how much is left? - A football 2

A football team wins 2/5 of their matches and draws 1/3. What fraction of their matches are lost? - Two cakes

Two cakes were each cut into eight slices. Maria ate 1/8 of the chocolate cake and one slice of carrot cake. Julia ate 1/2 of the carrot cake. Mark ate one slice of each. Thomas ate three slices of chocolate cake. How many slices were left?

- Farmer Peter

Farmer Peter paints 12 chicken coops. He started painting this day morning. He only has 1/4 of the chicken coop left to paint this afternoon. How many chicken coops did farmer Peter paint this morning? - Charlie 2

Charlie has $10 1/2; she went to the store and bought a chap-stick for $1.75. How much money does she have now? - Chicken supermarket

Nela bought 5 3/4 kilos of chicken and gave 2 1/2 to her friend. How many chicken was left? - The row

The row of shrubs will be 20 feet long. Maya planted three sets of shrubs. One shrub needs to be 7 1/2 feet from the other shrub. How can you use fractions to show how far apart each shrub is from each other? - Tim had

Tim had $360. He spent 1/4 on CD's and 2/3 of the remainder on snacks. What was left in his piggy bank?

- Mother 16

Mother cooks food in 1 3/4 hours and prepares the children's snack in 4/6 of an hour. How much longer does she cook the food than prepare the children's snacks? - Difference and sum

If the difference of 19/13 and his answer is 6/7, Bruno's answer is: If the sum of his answer and 6/7 is 1/2, Bruno's answer is: If his answer is the sum of 19/13 and 6/7, Bruno's answer is : - Eighty 2

Eighty children went on a field trip. If three-fifths of them were boys, how many were girls? - The boy

The boy scouts spent 10/12 hours doing their daily exercises. They only used 1/4 hour in hiking. How much time did they use for other body exercises? - Spending

Peter spends 1/5 of his earnings on his rent, and he saves 2/7. What fraction of his earnings is left?

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