# 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:

### 3/8 + 3/7 = 45/56 ≅ 0.8035714

The spelled result in words is forty-five fifty-sixths.### How do we solve fractions step by step?

- Add: 3/8 + 3/7 = 3 · 7/8 · 7 + 3 · 8/7 · 8 = 21/56 + 24/56 = 21 + 24/56 = 45/56

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(8, 7) = 56. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 7 = 56. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - three eighths plus three sevenths is forty-five fifty-sixths.

### 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:

- Work out 2

Work out the sum of 2/6 and 1/6. Give your answer in its simplest form. - My whole

My whole number is 88 if you add 5 thousandths, 8 tenths, and 7 thousandths. What number will I be? - Adding denominators

Max is working out 2/3+7/9. He says the answer is 9/12. What mistake has Max made? - Integer add to fraction

Seven is added to the sum of 4/5 and 6/7

- 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. - Chocolate buyer

Peter bought 1/2 a pound of chocolate at rocky mountain chocolate factory. Later, he went to the sweet shop and bought 6/9 of a pound more chocolate. How much chocolate did he buy that day? - Students 82194

Out of 30 students in the class, 2 thirds of the children were on a trip, and all the others were at home. How many students stayed at home? - Arithmetic 81795

In which arithmetic sequence is S5=S6=60? - Fraction multiplied by the sum

Find the three-fifths of the sum of 18 and 17.

- Rebecca

Rebecca needs to make a quilt. She has two pieces of fabric. One piece has 3 3/4 yards of fabric, and the other piece has 5 1/2 yards of fabric. How many yards of fabric does Rebecca currently have? - Fitness center

Monica works out for 3/4 of an hour every Wednesday at the fitness center. Every Saturday, he goes to the fitness center again and exercises for three times as long. How much time does Wayne spend at the fitness center each week? - Expressions

Let k represent an unknown number, express the following expressions: 1. The sum of the numbers n and two 2. The quotient of the numbers n and nine 3. Twice the number n 4. The difference between nine and the number n 5. Nine less than the number n - Paving Company Ltd

Roadster's Paving Company used 6 6/8 tons of cement to pave Hunter's street and 9 5/8 tons of cement to pave Jayden's street. How much cement did Roadster's Paving Company use in all? - Sum of AP members

Find the sum of all the numbers between 8 and 258 that are divisible by 5.

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