Fraction calculator

Rules for expressions with fractions:

Fractions - write a forward slash to separate the numerator and 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 whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . 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
• square root of a fraction: sqrt(1/16)
• 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 are:

• PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
  
• BEDMAS: Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
  
• BODMAS: Brackets, Order (or "Of"), Division, Multiplication, Addition, Subtraction.
  
• GEMDAS: Grouping symbols (brackets: `(){}`), Exponents, Multiplication, Division, Addition, Subtraction.
  
• MDAS: Multiplication and Division (same precedence), Addition and Subtraction (same precedence). MDAS is a subset of PEMDAS.

Important Notes:
1. Multiplication/Division vs. Addition/Subtraction: Always perform multiplication and division *before* addition and subtraction.
2. Left-to-Right Rule: Operators with the same precedence (e.g., `+` and `-`, or `*` and `/`) must be evaluated from left to right.

Fractions in word problems:

• Pizza 16
  Kevin ate 5/12 of his pizza. Which is a better estimate for the amount of pizza that he ate: A. about half of the pizza or B. almost all of the pizza?
• 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?
• Ten fractions
  Write ten fractions between 1/3 and 2/3
• Students 34
  Students were surveyed as part of a Statistics project to determine if younger adults are more likely to have tattoos. The results are listed in the two-way table below: age; At least one tattoo; No tattoo; Row totals Age 18 - 29; 165 ; 342; 507 Age 30 -

• Taylor
  Taylor filled eight 5 oz glasses with orange juice ⅔ full. Emeline filled five 9 oz glasses with orange juice ¾ full. Who used more juice?
• Score on tests
  On the first six tests in his Mathematics subject, his scores were 92, 82, 86, 93, 96, and 91. If he took the seventh test and raised the mean of his scores by exactly one point, what is his score on the 7th test?
• Aquarium 7098
  The zoo has an aquarium with a length of 2.5 m, a width of 1.5 m, and a depth of 2 m. The water reaches 3/4 of the height of the aquarium. Can we put a 2 m³ stone in the aquarium without the water spilling out of the aquarium? (1=Yes, 0=No)

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