# 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:

### 9 2/5 ÷ 1 3/10 = 94/13 = 7 3/13 ≅ 7.2307692

Spelled result in words is ninety-four thirteenths (or seven and three thirteenths).### How do we solve fractions step by step?

- Conversion a mixed number 9 2/5 to a improper fraction: 9 2/5 = 9 2/5 = 9 · 5 + 2/5 = 45 + 2/5 = 47/5

To find a new numerator:

a) Multiply the whole number 9 by the denominator 5. Whole number 9 equally 9 * 5/5 = 45/5

b) Add the answer from the previous step 45 to the numerator 2. New numerator is 45 + 2 = 47

c) Write a previous answer (new numerator 47) over the denominator 5.

Nine and two fifths is forty-seven fifths. - Conversion a mixed number 1 3/10 to a improper fraction: 1 3/10 = 1 3/10 = 1 · 10 + 3/10 = 10 + 3/10 = 13/10

To find a new numerator:

a) Multiply the whole number 1 by the denominator 10. Whole number 1 equally 1 * 10/10 = 10/10

b) Add the answer from the previous step 10 to the numerator 3. New numerator is 10 + 3 = 13

c) Write a previous answer (new numerator 13) over the denominator 10.

One and three tenths is thirteen tenths. - Divide: 47/5 : 13/10 = 47/5 · 10/13 = 47 · 10/5 · 13 = 470/65 = 5 · 94 /5 · 13 = 94/13

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 13/10 is 10/13) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 5 gives 94/13.

In other words - forty-seven fifths divided by thirteen tenths is ninety-four thirteenths.

#### 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:

- Anesa

Anesa ate 3/4 of her pizza, and Eman ate 1/4 of her pizza. Who ate the greater part of the pizza? - From least to greatest

Which set of rational numbers is arranged from least to greatest? A) -3.5, negative 1 over 4, 2, 1 over 3 B) -3.5, negative 1 over 4, 1 over 3, 2 C) 2, 1 over 3, negative 1 over 4, -3.5 D) negative 1 over 4, 1 over 3, 2, -3.5 - Compare two fractions

Find which is the larger of the two fractions: 11/32, 7/24, by expressing the numbers as a) fractions with the same denominator, b) decimals. - Rhea answered

Rhea answered 5/11 of the questions correctly, and Precious answered 7/11 of them correctly. Who got the higher score if each problem is worth the same amount? - One quarter

Which of the following has a sum of 3/4? A. 1/2+1/4 B. 1/2+1/3 C. 1/4+1/8 D. 1/9+1/12 - Sort fractions

Which of the following fractions is the largest? 29/36 5/6 7/9 3/4 - Equivalent fractions

Are these two fractions -4/9 and 11/15 equivalent? - Playing games

In a school, 9/10 of the students take part. 2/3 of these play football. What fraction of the students play football? - Same fractions

I remember that 2/2 is equal to 1. 3/3 is equal to 1. Where is the fraction 4/4 located on the number line? - Place 2

Place the correct symbol, < or >, between the two numbers: 4/7? 5/6 - Order fractions

Arrange in ascending order 1 5/6, 11/9, 5/16, 3 - Which 15

Which is larger, 1 2/7 or 10/4? - Andy and Mike

Mike and Andy are each reading the same book. Mike read 2/4 of the book on Tuesday and 1/3 of the book on Wednesday. Andy read 1/2 of the book on Tuesday and 1/5 of the book on Wednesday. Andy says that altogether he read more of the book on Tuesday and W - Three friends

You and your friends are playing basketball. You make 7 out of 15 shots. Your first friend makes 6 out of 10 shots, and your second friend makes 5 out of 12 shots. Who is the better shooter (write a, b, c)? How would you solve the problem using what you k - A student 4

A student knows that ¾ x 4 is the same as 4 x ¾ The student assumes that 4 ÷ ¾ is the same as ¾ ÷ 4 Is the student correct?

more math problems »