# Fraction calculator

This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

## The result:

### 7 3/25 - 6 4/15 = 64/75 ≅ 0.8533333

The spelled result in words is sixty-four seventy-fifths.### How do we solve fractions step by step?

- Conversion a mixed number 7 3/25 to a improper fraction: 7 3/25 = 7 3/25 = 7 · 25 + 3/25 = 175 + 3/25 = 178/25

To find a new numerator:

a) Multiply the whole number 7 by the denominator 25. Whole number 7 equally 7 * 25/25 = 175/25

b) Add the answer from the previous step 175 to the numerator 3. New numerator is 175 + 3 = 178

c) Write a previous answer (new numerator 178) over the denominator 25.

Seven and three twenty-fifths is one hundred seventy-eight twenty-fifths. - Conversion a mixed number 6 4/15 to a improper fraction: 6 4/15 = 6 4/15 = 6 · 15 + 4/15 = 90 + 4/15 = 94/15

To find a new numerator:

a) Multiply the whole number 6 by the denominator 15. Whole number 6 equally 6 * 15/15 = 90/15

b) Add the answer from the previous step 90 to the numerator 4. New numerator is 90 + 4 = 94

c) Write a previous answer (new numerator 94) over the denominator 15.

Six and four fifteenths is ninety-four fifteenths. - Subtract: 178/25 - 94/15 = 178 · 3/25 · 3 - 94 · 5/15 · 5 = 534/75 - 470/75 = 534 - 470/75 = 64/75

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(25, 15) = 75. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 25 × 15 = 375. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one hundred seventy-eight twenty-fifths minus ninety-four fifteenths is sixty-four seventy-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

• square root of a fraction: sqrt(1/16)

• 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:

- Subtract and compare

1-5/8 is the same as 11/8, true or false? - The bucket

Anna and Joey share an 18-ounce bucket of clay. By the end of the week, Anna has used 1/3 of the bucket, and Joey has used 2/3 of the bucket of clay. How many ounces are left in the bucket? - Dive Attempt

Dive Attempt ; Fraction of the distance to the pool bottom Dive 1; 1/4 Dive 2; 2/3 Dive 3; 5/6 Tony's second dive was deeper than his first dive by what fraction of the pool? - Her garden

Lira harvested 135 different flowers in her garden. Two-ninths of them are roses, and the rest are tulips. How many tulips are?

- Negative fractions

I am a number that is equal to -3/4 subtracted from the sum of 3/5 and -1/3. What number am I? - Three cakes

There are three cakes an ice cream cake, chocolate, and a sponge cake. We ate 3/4 of the ice cream cake. We cut the chocolate cake into twelve equal pieces, of which We ate nine. The sponge cake was divided into eight equal pieces, with only one remaining - Jojo ordered

Jojo ordered 36 cupcakes for the party. He ordered red velvet and vanilla cupcakes. ¾ of the cupcakes are vanilla. How many are red velvet?

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Last Modified: June 4, 2024