# Fraction calculator

This calculator subtracts two fractions. First, convert all fractions to a common denominator when fractions have different denominators. Find Least Common Denominator (LCD) or multiply all denominators to find a common denominator. When all denominators are the same, simply 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:

### 1/2 - 3/7 = 1/14 ≅ 0.07142857

The spelled result in words is one fourteenth.### How do we solve fractions step by step?

- Subtract: 1/2 - 3/7 = 1 · 7/2 · 7 - 3 · 2/7 · 2 = 7/14 - 6/14 = 7 - 6/14 = 1/14

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(2, 7) = 14. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 7 = 14. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half minus three sevenths is one fourteenth.

### 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:

- Closer to one

Here are two sums: A=1/2 + 1/3 and B=1/5 + 1/3. Which of the two sums is closer in value to 1? You must show your work and state clearly whether the answer is A or B. - Shopping 7

I went into a shop with 210.00 and spent 1/7 of it on eggs and 1/2 of it on fruits. How much did I have left? - 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? - Ahsan

Ahsan has a large pizza. He gives 1/3 to his sister and 1/4 to his mother. What fraction of the pizza does Ahsan have left?

- Tourists 82400

On the first day, tourists covered 3/14 of the planned route, on the second day 1/3 of the route, and on the third day 8/21 of the route. On which day did they walk the longest part of the route (1,2,3)? - A book 4

A book has 280 pages. I read 2/7 of the book yesterday, while I read 1/4 of it today. How many pages did I read in 2 days? - Cupcakes

In a bowl were some cupcakes. Janka ate one-third, and Danka ate one-quarter of the cupcakes. a) How many cookies ate together? b) How many cookies remain in a bowl? Write the results as a decimal number and notepad as a fraction. - A farmer 9

A farmer has 3 hectares of an orchard. ½ of the land is occupied by apples, ⅙ of the remainder is occupied by lemon trees, and tree tomatoes occupy the rest of it. Find the fraction of the land occupied by tree tomatoes. - Square metal sheet

We cut out four squares of 300 mm side from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.

- Peter's calculation

Peter wrote the following: 7 1/4 - 3 3/4 = 4 2/4 = 4 1/2 . Is Peter's calculation correct? Using words (math vocabulary) and numbers to explain why he is correct or incorrect. - Shopper

Eva spent 1/4 in one store and 1/3 in another. What fraction is left? - Evaluate - lowest terms

Evaluate: 16/25 - 11/25 (Express answer as a fraction reduced to lowest terms. ) - Difference of two fractions

What is the difference between 1/2 and 1/6? (Write the answer as a fraction in the lowest terms. ) - Orchard 5421

The orchard has 600 apple trees. On the first day, they cut 1/5 and 2/8 of the total number of trees on the second day. How many more trees do they have to harvest?

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