# 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:

### 2/3 * 2/3 = 4/9 ≅ 0.4444444

Spelled result in words is four ninths.### How do we solve fractions step by step?

- Multiple: 2/3 * 2/3 = 2 · 2/3 · 3 = 4/9

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(4, 9) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - two thirds multiplied by two thirds is four ninths.

#### 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? - A pie 6

There was 5/8 of a pie left in the fridge. Daniel ate 1/4 of the leftover pie. How much of the pie did he have? - Pencils

You have 36 pencil crayons. How many pencil crayons makeup 1/2 of the total? - 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? - Peter 15

Peter try to calculate: 3/4 x 2/3 He did 3x3 to get 9 and 4 x 2 to get 8. The final answer is 8/9. Can you explain the error and how to help? What is the correct answer? - Write 3

Write a real-world problem involving the multiplication of a fraction and a whole number with a product between 8 and 10, then solve the problem. - 100/4700 66704

What is 1/8 of 100/4700? - Beth wants

Beth wants to give 1/4 pizza to each of her 6 friends. Which choice does not show the number of pizzas Beth needs? - 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? - 10 children

Ten children in the park, four-tenths are wearing a red shirt. How many children in the park are wearing a red shirt? - There 31

There are 600 students in the plaza. 2/5 of them are from USC. How many students are from USC? - Shoes

Jim and Dora are collecting shoes for a yard sale. Dora collected 1/2 as many shoes as Jim did. Jim collected 3/7 of a bag of shoes. How many bags of shoes did Dora collect? - One-third 2

One-third of the people in a barangay petitioned the council to allow them to plant in vacant lots, and another 1/5 of the people petitioned to have a regular garbage collection. What FRACTION of the barangay population made the petition? - Jennifer

Jennifer has 10 pets. Two-fifths of the pets are cats, one-half are fish, and one-tenth are dogs. How many of each pet does she have?

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