# Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## The result:

### 14 5/10 - 12 9/10 = 8/5 = 1 3/5 = 1.6

The spelled result in words is eight fifths (or one and three fifths).### How do we solve fractions step by step?

- Conversion a mixed number 14 5/10 to a improper fraction: 14 5/10 = 14 5/10 = 14 · 10 + 5/10 = 140 + 5/10 = 145/10

To find a new numerator:

a) Multiply the whole number 14 by the denominator 10. Whole number 14 equally 14 * 10/10 = 140/10

b) Add the answer from the previous step 140 to the numerator 5. New numerator is 140 + 5 = 145

c) Write a previous answer (new numerator 145) over the denominator 10.

Fourteen and five tenths is one hundred forty-five tenths. - Conversion a mixed number 12 9/10 to a improper fraction: 12 9/10 = 12 9/10 = 12 · 10 + 9/10 = 120 + 9/10 = 129/10

To find a new numerator:

a) Multiply the whole number 12 by the denominator 10. Whole number 12 equally 12 * 10/10 = 120/10

b) Add the answer from the previous step 120 to the numerator 9. New numerator is 120 + 9 = 129

c) Write a previous answer (new numerator 129) over the denominator 10.

Twelve and nine tenths is one hundred twenty-nine tenths. - Subtract: 145/10 - 129/10 = 145 - 129/10 = 16/10 = 2 · 8/2 · 5 = 8/5

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(10, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 8/5.

In other words - one hundred forty-five tenths minus one hundred twenty-nine tenths is eight 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) |

#### 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:

- From least to greatest

Which set of rational numbers is arranged from least to greatest? A) -3.5, negative 1 over 4, 2, 1 over 3 B) -3.5, negative 1 over 4, 1 over 3, 2 C) 2, 1 over 3, negative 1 over 4, -3.5 D) negative 1 over 4, 1 over 3, 2, -3.5 - What number 2

What number is between 3 1/4 and 3 1/8? Write at least three numbers. - If you 4

If you take away 1 ¾ from 3 1/3, the answer is 2 2/3. Is this correct? - A small

A small book took one-sixth of a ream of paper to make. The team said they could make nine books from 3 whole reams of paper. Are they correct?

- Buing

Brother got to buy 240 CZK and could buy for 1/8 what he wanted. Could he pay the rest of the purchase for 200 CZK? - Leo hiked

Leo hiked 6/7 of a kilometer. Jericho hiked 2/3 kilometers. Who covered a longer distance? How much longer? - Statements 17733

There are 24 students in the class, and 5/8 of them are girls. Which of the following statements is true: And there are 15 boys in the class, B there are more boys than girls in the class, There are 9 boys and 15 girls in C's class - Cody states

Cody states that 1/4 + ( - 6/8 ) = 1 whole, while Eddie says that it is - 1/2. Who is correct? Justify your answer and explain your thinking. - True or false?

Which of the following is true? A. Three and three ninths plus seven and six-elevenths equal ten and eighty-seven ninety ninths. B. two and three-eighths plus six and four-fifths equals eight and twelve fortieth C. three and three sevenths plus four and t

- Stephan - cookies

Stephan is making cookies for the class. He has a recipe that calls for 3 and 1/2 cups of flour. He has 7/8 a cup of wheat flour and 2 and 1/2 cups white flour. Does Mr. Stephan have enough flour to make the cookies? - Colored blocks

Tucker and his classmates placed colored blocks on a scale during a science lab. The brown block weighed 8.94 pounds, and the red block weighed 1.87 pounds. How much more did the brown block weigh than the red block? - Janet

Janet walks 7/10 miles in 1/4 hour. Ian walks 9/10 miles in 1/3 hour; who walks at the faster rate and why? - Performance 7682

They produced 8,892 cans in the production hall. Their performance is in the ratio 11:12:13. Which workshop was the hardest, and how many cans did it make? - Sort fractions

Which is larger 3/7, 3/8, 3/9, 3/6 =

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