# Fraction calculator

This calculator multiplies fractions. Multiplies all numerators and places the result over the product of all denominators. Then simplify the result to the lowest terms or a mixed number.

## The result:

### 3/4 * 1/2 = 3/8 = 0.375

Spelled result in words is three eighths.### How do we solve fractions step by step?

- Multiple: 3/4 * 1/2 = 3 · 1/4 · 2 = 3/8

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 8) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - three quarters multiplied by one half is three eighths.

#### 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:

- Samantha

Samantha took 72 pictures on her beach vacation. 3/4 of those pictures are on the beach. How many pictures from her vacation are on the beach? - Someone

Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake left, how much of a whole cake will you have eaten? - 19 boy

Nineteen boys in section 1 and 23 boys in section 2. If 2/6 of them are boy Scouts, how many boy scouts are them? - Ms. Sheppard

Ms. Sheppard cuts ½ of a piece of construction paper. She uses ⅙ of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower? - Slices of pizza

Maria ate 1/4 of a pizza. If there were 20 slices of pizza, how many slices did Maria eat? - Roy harvested

Roy harvested 3/4 crate of guavas. He sold 1/2 of them in the neighborhood. What part of a crate of guavas sold? - Watching TV

One evening 2/3 of students watch TV. Of those students, 3/8 watched a reality show. Of the students that watched the show, 1/4 of them recorded it. What fraction of the students watched and recorded reality TV? - Puppies

At an animal rescue, 5/6 of the animals are dogs. Three-fourths of the dogs are puppies. This model represents the fraction of the animals at the rescue that is puppies. What fraction of the animals at the rescue are puppies? - A newspaper's

A newspaper's cover page is 3/8 text, and photographs fill the rest. If 2/5 of the text is an article about endangered species, what fraction of the whole cover page is the article about endangered species? - Scouts 4

4/7 out of the students in a school are boys. If 3/8 of the boys are scouts, how many scouts are there in a school of 1878 students? - A store

A store received a shipment of 240 skateboards. In three weeks, it sold 1/3 of those skateboards. How many skateboards did the store sell? - A total 2

A total of 42 candies if divided among boys and girls. If boys receive 3/7, then how much will girls receive? - A quarter 2

A quarter of the 72 sandwiches contain cheese. The rest contain ham. How many are ham sandwiches? - Bryce

Bryce collected 1/4 of a bin of glass bottles to recycle. Megan collected 5 times as many bins as Bryce. How many bins of bottles did Megan collect? - Doughnuts

2/3 of the doughnuts in a box have frosting. 1/2 of the doughnuts with frosting have sprinkles. What fraction of the doughnuts in the box have frosting and sprinkles?

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