# Calculator adding fractions and mixed numbers

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

### 8/5 + 6 2/7 = 276/35 = 7 31/35 ≅ 7.8857143

The spelled result in words is two hundred seventy-six thirty-fifths (or seven and thirty-one thirty-fifths).### How do we solve fractions step by step?

- Conversion a mixed number 6 2/7 to a improper fraction: 6 2/7 = 6 2/7 = 6 · 7 + 2/7 = 42 + 2/7 = 44/7

To find a new numerator:

a) Multiply the whole number 6 by the denominator 7. Whole number 6 equally 6 * 7/7 = 42/7

b) Add the answer from the previous step 42 to the numerator 2. New numerator is 42 + 2 = 44

c) Write a previous answer (new numerator 44) over the denominator 7.

Six and two sevenths is forty-four sevenths. - Add: 8/5 + 44/7 = 8 · 7/5 · 7 + 44 · 5/7 · 5 = 56/35 + 220/35 = 56 + 220/35 = 276/35

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(5, 7) = 35. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 7 = 35. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - eight fifths plus forty-four sevenths is two hundred seventy-six thirty-fifths.

### 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) |

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

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Last Modified: July 23, 2024