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:

• Compare ratios
  Is ratios 4:7 and 16:19 equivalent?
• David 4
  David made 4/3 of a quart of fruit juice. Each mug he has holds 1/3 of a quart. How many mugs will David be able to fill?
• Integer add to fraction
  Seven is added to the sum of 4/5 and 6/7
• Well-known 10731
  The well-known Candle Collector, Antonín, had half of the blue candles in his collection, a third of the candles with a colored motif, and 128 green candles. How many candles does Antonín have in his collection?
• Equation 20
  In the given equation: 8/9-4/5=2/9+x, find x
• Two numbers at a ratio
  If 1.5x = 0.04y, then find the value of {(y - x)/(y + x)}.
• 6 cups of strawberries
  Mr. Hunter decided to make a healthy snack for the 20 students in his class. He gave each student a dish of yogurt and divided 6 cups of strawberries equally among the dishes. How many cups of strawberries did each student get in their yogurt? Write your

more math problems »