Fraction Calculator - Calculation: 3 2/3

Fraction calculator Enter fraction expression: 3 2/3 This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.

The result:

3 2/3 = 3 2/3 = 3 · 3 + 2/3 = 9 + 2/3 = 11/3 = 3 2/3 ≅ 3.6666667

The result spelled out in words is eleven thirds (or three and two thirds).

How do we solve fractions step by step?

1. Conversion a mixed number 3 2/3 to a improper fraction: 3 2/3 = 3 2/3 = 3 · 3 + 2/3 = 9 + 2/3 = 11/3To find a new numerator: a) Multiply the whole number 3 by the denominator 3. Whole number 3 equally 3 * 3/3 = 9/3 b) Add the answer from the previous step 9 to the numerator 2. New numerator is 9 + 2 = 11 c) Write a previous answer (new numerator 11) over the denominator 3.Three and two thirds is eleven thirds.

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 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.
• Subtract and compare 1-5/8 is the same as 11/8, true or false?
• Small and large bread Kipton's aunt bakes a large loaf of bread and a small loaf of bread. She cuts each loaf into tenths and gives Kipton 2 tenths of each loaf to take home. Kipton writes the equation 2/10 + 2/10 = 4/10 to show the amount of bread he takes home. Explain Kipto
• The cost 7 The cost of a pen is Rs. 20/3, and that of a pencil is 25/6. Which costs more and by how much?
• 1/12 fraction Which statement about determining the quotient 1/12÷3 is true? A. Because 1/36×3=1/12, 1/12 divided by 3 is 1/36. B. Because 1/4×3=1/12, 1/12 divided by 3 is 1/4. C. Because 3/4×3=1/12, 1/12 divided by 3 is 3/4. D. Because 4/3×3=1/12, 1/12 divided by 3 is
• The fuel The car's fuel was ¾ full at the beginning of the week. At the end of the week, there was ⅛ of a tank left. a. Did the car use more or less than ½ of a fuel tank? How do you know? b. How much more or less than ½ of a tank did it use? Show your work using
• Dividends The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most, and which got the least?

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Last Modified: November 19, 2025

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