# 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:

### 3/4 + 4/7 = 37/28 = 1 9/28 ≅ 1.3214286

The spelled result in words is thirty-seven twenty-eighths (or one and nine twenty-eighths).### How do we solve fractions step by step?

- Add: 3/4 + 4/7 = 3 · 7/4 · 7 + 4 · 4/7 · 4 = 21/28 + 16/28 = 21 + 16/28 = 37/28

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(4, 7) = 28. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 7 = 28. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - three quarters plus four sevenths is thirty-seven twenty-eighths.

### 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:

- A cake 2

Karen sliced a cake into 10 slices. She ate 2/10 of it and after some time she ate another 4/10 of it. How much of the cake did Karen eat? - Randy

Randy solved the following problem: 7/8 + 9/16. He said: I can add 7 and 9 to get 16 and add 8 and 15 to get 23. The answer is 16/23. Is randy correct? Explain. - There 22

There is 5/8 of a pizza in one box and 9/12 of a pizza in another box. How much do you have altogether? - Adding two fractions

Find the missing fraction: 2/5 + 7/10 =

- Numbers 5256

What is 4/5 of the sum of numbers (-4.95) and (-11.05)? - Equal slices of pizza

If you have a pizza divided into 6 equal slices and you eat 2/6 of it, what fraction of the pizza is left? - Jiwan

Jiwan Incorrectly Wrote 1+ 1/2 + 1/3 + 1/4 =1 3/9 Show The Correct Working And Write Down The Answer As A Mixed Number. - Benson

Benson spends ⅓ of his pocket money on transport and ⅔ on food I. What fraction of his pocket money did he spend on transport and food? ii. What fraction is left? - Negative mixed 2

What is −4 2/3 + 2 1/2? Write the answer as a mixed number in simplest form.

- The ribbon

Jody had some ribbon. She used 1/4 of it to tie and 1/2 to tie. She had 1/10 of the ribbon left. How much ribbon did she have at first? For your answer, please write as a fraction in the simplest form. - Matthew

Matthew is saving up for a car. Last year he saved 3/5 of the total amount. In addition to what he saved last year, he saved 3/10 of the total amount in the summer. If the car costs 15 000$, how much has he saved so far? - Mel and Lisa

Mel and Lisa used 9/10 of the clay in their art kit. Mel used 1/2 of the clay. How much clay did Lisa use? - Two mixed adding

What is 1 and 1/6 + 1 and 3/6? - The sum

If you add 3/4 and 5/8, what would be the sum? A. more than one B. equal to one C. less than one D. zero

more math problems »