# Fraction calculator

This calculator adds two fractions. First, all fractions are converted to a common denominator when fractions have different denominators. Find the Least Common Denominator (LCD) or multiply all denominators to find a common denominator. When all denominators are the same, subtract the numerators and place the result over the common denominator. Then, simplify the result to the lowest terms or a mixed number.

## The result:

### 7/6 + 3/4 = 23/12 = 1 11/12 ≅ 1.9166667

The spelled result in words is twenty-three twelfths (or one and eleven twelfths).### How do we solve fractions step by step?

- Add: 7/6 + 3/4 = 7 · 2/6 · 2 + 3 · 3/4 · 3 = 14/12 + 9/12 = 14 + 9/12 = 23/12

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(6, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 4 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seven sixths plus three quarters is twenty-three 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:

- 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 city

A city received 11/4 cm of rainfall on Sunday and 11/2 cm on Monday. Find the total rain in the city on these two days. - A football 2

A football team wins 2/5 of their matches and draws 1/3. What fraction of their matches are lost? - Adding 11

You are adding numbers. Which of the following numbers to 3/5 will give a whole number? a. 2 b. 2/5 c. 5/3 d. 3/5

- How many 3

How many hours do the Andersons watch TV in all Wednesday 3/1 hr Thursdays 2/3 hr Friday 4/5 hr Saturday 3/4 hr - 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 : - Mr. Ofori

Mr. Ofori starts a job with an annual salary of 6400, which increases by 240 every year. After working for eight years, Mr. Ofori was promoted to a new post with an annual salary of 9500, which increased by 360 every year. Find I. Mr. Ofori's salary in th - Spending

Peter spends 1/5 of his earnings on his rent, and he saves 2/7. What fraction of his earnings is left? - Expeditions 6119

There are 99 athletes on the American team. There were 35 more athletes in the Japanese expedition than in the American one. There is an eighth less in the Czech expedition than in the Japanese expedition. How many athletes are there on individual expedit

- 3 gifts

Chad had 30 dollars to spend on 3 gifts. He spent 9 1/4 dollars on gift A and 3 4/5 dollars on gift B. How much money did he have left for gift C? - Cement and sand

Rasmus mixes cement with sand for some repair work. He used 3 5/6 kg of cement and 1/2 kg more sand than cement. In all, he needs 10 kg of the mixture. Does he have enough mixture? If yes, then how much more does it have? If not, then how much more does h - School time

If Martin started school at 8:30. If he spent 6 3/4 hours in school, what time did he leave school? - Evaluate 17

Evaluate 2x+6y when x=- 4/5 and y=2/5. Write your answer as a fraction or mixed number in the simplest form. - Complicated sum minus product

What must be subtracted from the sum of 3/8 and 5/16 to get a difference equal to the product of 5/8 and 3/16?

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