# Calculator reciprocal of a fraction

This calculator finds the reciprocal of a fraction. To find the reciprocal of a fraction, exchange the numerator and the denominator. Simply speaking, the reciprocal of a/b is b/a.

### 1 : 3/4 = 4/3 = 1 1/3 ≅ 1.3333333

Spelled result in words is four thirds (or one and one third).### How do we solve fractions step by step?

- Divide: 1 : 3/4 = 1/1 · 4/3 = 1 · 4/1 · 3 = 4/3

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 3/4 is 4/3) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one divided by three quarters is four thirds.

#### 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) |

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:

- In dividing

In dividing fractions, get the reciprocal of the divisor and change the division symbol to the multiplication symbol. 2/3 : 5/6 - Fraction expression

Which expression is equivalent to : minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis - A quotient

What is the quotient of 3/10 divided by 2/4 as a fraction? - Chocolate division

How much would everyone get if I had 4/5 of a chocolate bar and wanted to split it evenly among three people? - How many 24

How many 1/4 cup servings of raisins are in 5/8 cup of raisins? - A baker 3

A baker made three cakes which were cut into eighths, ready for individual sale. A customer bought three slices or ⅜ of one of the eight cakes. How many slices were left for sale? - One half 2

One half pizza will be divide among 3 pupils. Each pupil receive 1/6. Is it true or false? - Mrs. Glover

Mrs. Glover is making brownies for the girls’ tennis team. She took 1/5 of the leftover brownies to school to give to her 3 friends. How much did each friend get? - Candy bars

Sheldon has 4 candy bars and wants to split them among his five friends. If each person gets the same amount, what part of the candy bar will each friend get? Show your work. - Division by reciprocal

What is the corresponding illustration/model of 7÷ 1/3? - Quotient and division

Find the quotient of 3/4 and 1/4.

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