# Fraction calculator

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

## The result:

### 1/2 * 2/3 = 1/3 ≅ 0.3333333

Spelled result in words is one third.### How do we solve fractions step by step?

- Multiple: 1/2 * 2/3 = 1 · 2/2 · 3 = 2/6 = 1 · 2/3 · 2 = 1/3

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(2, 6) = 2. In the following intermediate step, cancel by a common factor of 2 gives 1/3.

In other words - one half multiplied by two thirds is one third.

#### 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 signs 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) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22

• 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 /) has the same priority and then must evaluate from left to right.

## Fractions in word problems:

- 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? - Pencils

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

Mrs. Bright is organizing her office supplies. There are five open boxes of paper clips in her desk drawer. Each box has 1/2 of the paper clips remaining. How many boxes of paper clips are left? - 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? - Learnes

There are 800 learners in a school 7/8 of the learners walk to school. How many learners walk in school? - Multiplying fractions

What is 1/3 of 5? - 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? - 100/4700 66704

What is 1/8 of 100/4700? - Trent

Trent operates a hot dog stand. On Wednesday, he used two bags of hot dog buns. On Thursday, he used 1/5 as many hot dog buns as Wednesday. How many bags of hot dog buns used Trent on Thursday? - Pupils 13

If ⅜ of the pupils in year 9 say, their favorite color is red. There are 112 pupils in year 9. How many students said red is their favorite color? - 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.

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