Fraction Calculator - Calculation: 3 4/6+9/18

Fraction Calculator Enter fraction expression: 3 4/6+9/18 This fraction calculator performs all basic fraction operations – addition, subtraction, multiplication, and division – and evaluates expressions with fractions. Each calculation includes a detailed step-by-step explanation.

The result:

3 4/6 + 9/18 = 25/6 = 4 1/6 ≅ 4.1666667

Spelled out: twenty-five sixths (or four and one sixth).

How do we solve fractions step by step?

1. Conversion a mixed number 3 4/6 to a improper fraction: 3 4/6 = 3 4/6 = 3 · 6 + 4/6 = 18 + 4/6 = 22/6To find a new numerator: a) Multiply the whole number 3 by the denominator 6. Whole number 3 equally 3 * 6/6 = 18/6 b) Add the answer from the previous step 18 to the numerator 4. New numerator is 18 + 4 = 22 c) Write a previous answer (new numerator 22) over the denominator 6.Three and four sixths is twenty-two sixths.
2. Add: 22/6 + 9/18 = 22 · 3/6 · 3 + 9/18 = 66/18 + 9/18 = 66 + 9/18 = 75/18 = 3 · 25/3 · 6 = 25/6 It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 18) = 18. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 18 = 108. In the following intermediate step, cancel by a common factor of 3 gives 25/6. In other words, twenty-two sixths plus nine eighteenths equals twenty-five sixths.

Rules for expressions with fractions:

Fractions - Use a forward slash to separate the numerator and denominator. For example, for five-hundredths, enter 5/100. Mixed numbers Leave one space between the whole number and the fraction part, and use a forward slash for the fraction. For example, enter 1 2/3 . For negative mixed numbers, write the negative sign before the whole number, such as -5 1/2. Division of fractions - Since the forward slash is used for both fraction lines and division, use a colon (:) to divide fractions. For example, to divide 1/2 by 1/3, enter 1/2 : 1/3. Decimals Enter decimal numbers using a decimal point (.), and they will be automatically converted to fractions. For example, enter 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• multiplying fractions: 2/3 of 3/5• divide to find the quotient: 3/5÷2/3 Order of Operations Ever wondered why calculators don't just work left to right? This calculator follows the mathematical order of operations — a set of rules that ensures everyone solves expressions the same way, every time. Popular Memory Tricks Different regions use different mnemonics to remember this order: * 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 (parentheses, brackets, braces: (){}), Exponents, Multiplication, Division, Addition, Subtraction The Golden Rules Rule 1: Multiplication and division always come before addition and subtraction. Think of them as the VIPs that skip to the front of the line! Rule 2: When operations have equal priority (like × and ÷, or + and −), work from left to right—just like reading a book. Rule 3: Parentheses change the natural order of evaluation of operations.

Fractions in word problems:

• Which 15 Which is larger, 1 2/7 or 10/4?
• What number 2 What number is between 3 1/4 and 3 1/8? Write at least three numbers.
• Equivalent fractions Are these two fractions -4/9 and 11/15 equivalent?
• 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?
• The numerator The numerator of the fraction is 5 more than its denominator. If 4 is added to the numerator and denominator, the fraction obtained is 6/5. What is that fraction?
• Comparing by height Ira is 1 2/5 m tall. Her mother is 4/5 m as tall as Ira. How many times is Ira's mother taller than her?
• Even Integers Number Line Which even integers are greater than -1 1/4 and less than 7 1/4? The mark is on the number axis.

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Last Modified: March 6, 2026

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