# 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:

### 5/6 + 1/9 = 17/18 ≅ 0.9444444

Spelled result in words is seventeen eighteenths.### How do we solve fractions step by step?

- Add: 5/6 + 1/9 = 5 · 3/6 · 3 + 1 · 2/9 · 2 = 15/18 + 2/18 = 15 + 2/18 = 17/18

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, 9) = 18. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 9 = 54. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - five sixths plus one ninth is seventeen eighteenths.

#### 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:

- Evaluate expression

Calculate the value of the expression z/3 - 2 z/9 + 1/6, for z = 2 - A quarter

A quarter of the number 72 is: - Oranges

There are 50 oranges in a bag. If ten of these oranges are bad, what fraction of them are good? - Using money

Out of 575,000.00 given to a school, an amount of 25,000.00 was used. What fraction of the total amount was used? - Fraction and a decimal

Write as a fraction and a decimal. One and two plus three and five hundredths - Fractions 80134

There are 420 pupils in the school. Two hundred fifty-two pupils go to the 1st level. Write as a fraction what part of the pupils goes to the 1st grade and what part to the 2nd grade. Shorten both fractions to their basic form. - Simplify 12

Simplify {1/3 + 1/12} ÷ {2/3 - 5/8} - Unsatisfactory 5604

In 1995, 360 fish samples were tested for contamination with foreign substances, and 138 samples were unsatisfactory. Write a fraction of what part of the fish did not meet the limits. - Lowest terms 2

We can write the expression 4/12 in its lowest term as 1/3. What is 3/15 expressed in its lowest term? - Dea makes

Dea makes 18 out of 27 shots in a basketball game. Which decimal represents the fraction of shots Dea makes? - Fraction to decimal

Write the fraction 3/22 as a decimal. - Mathew

Mathew has eight pencils. Three of them do not have erasers on end. What fraction of the pencils do not have erasers on end? - Equations

Solve following equations without fractions: a) 5 (x-1) -7 = 17-3 (1-x) b) 3 (y-2) -4y = 2- (1 + 2y) - A class IV.A

In a class, there are 15 girls and 30 boys. What fraction of the class represents the boys? - The parsley

Milka's grandmother planted 12 rows of vegetables. 1/6 of the rows are carrots. The rest is parsley. How many rows are planted with parsley?

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