# Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## The result:

### 5 1/2 - 3 3/4 = 7/4 = 1 3/4 = 1.75

Spelled result in words is seven quarters (or one and three quarters).### How do we solve fractions step by step?

- Conversion a mixed number 5 1/2 to a improper fraction: 5 1/2 = 5 1/2 = 5 · 2 + 1/2 = 10 + 1/2 = 11/2

To find a new numerator:

a) Multiply the whole number 5 by the denominator 2. Whole number 5 equally 5 * 2/2 = 10/2

b) Add the answer from the previous step 10 to the numerator 1. New numerator is 10 + 1 = 11

c) Write a previous answer (new numerator 11) over the denominator 2.

Five and one half is eleven halfs. - Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4

To find a new numerator:

a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4

b) Add the answer from the previous step 12 to the numerator 3. New numerator is 12 + 3 = 15

c) Write a previous answer (new numerator 15) over the denominator 4.

Three and three quarters is fifteen quarters. - Subtract: 11/2 - 15/4 = 11 · 2/2 · 2 - 15/4 = 22/4 - 15/4 = 22 - 15/4 = 7/4

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(2, 4) = 4. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 4 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - eleven halfs minus fifteen quarters is seven quarters.

#### 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:

- Peter's calculation

Peter wrote the following: 7 1/4 - 3 3/4 = 4 2/4 = 4 1/2 . Is Peter's calculation correct? Using words (math vocabulary) and numbers to explain why he is correct or incorrect. - A man 9

A man earns $2400 in his monthly salary. He spends 3/5 of his salary on food and rent. This month he decided to buy his family presents. What fraction of his money does he spend on presents? - The bread 2

Sandra and Tylar baked two loaves of bread. On Monday, they ate 1/2 of one loaf. On Tuesday, they ate 1/3 of one loaf of bread. How much bread is left? - Fraction expression

Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis - Students 4252

Out of 35 pupils in class 15, they went on a trip. What part of the students went on a journey, and what remained at school? - Evaluate 38

Evaluate the expression shown below and write your answer as a fraction in simplest form. (5)/(6) - (3)/(8) Transcription: start fraction, 5, divided by, 6, end fraction, minus, start fraction, 3, divided by, 8, end fraction - Unload truck

Andy has just moved and is beginning to unload his boxes. The truck is currently 11/12 of the way full. He unloads 1/4 more of it. How much more does he have to unload? - Flags 2

1/4 are white and another 1/4 are yellow. What fraction of the flags are either white or yellow? - A less than B

What is 3/5 less than 11/12? (Answer should be in proper or improper only: Example 1/2, -1/2, 3/2, and -3/2) - A cake

A cake has 46 slices. Harry ate 16 slices, and Jack ate 26 slices, Dave ate 0 & Mary ate 1 slice. What fraction of the cake is remaining? - Terrell

Terrell goes apple-picking. He uses 3/10 of his apples. Then he uses 5/10. What fraction of his apples does he have left? - Difference of two fractions

What is the difference between 1/2 and 1/6? (Write the answer as a fraction in the lowest terms. ) - Cherries 2

If a farmer reaped 636 cherries and he sold one-third to a shopkeeper, how many did he retain? - Subtract 19

Subtract as indicated. 11/10 - (- 2/5) - A housewife

A housewife spent 3/7 of her money in the market and 1/2 of the remainder in the shop. What fraction of her money is left?

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