Fraction Calculator - Calculation: 6 2/5+3 1/8+2/3

Fraction Calculator Enter fraction expression: 6 2/5+3 1/8+2/3 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:

6 2/5 + 3 1/8 + 2/3 = 1223/120 = 10 23/120 ≅ 10.1916667

Spelled out: one thousand two hundred twenty-three one-hundred twentieths (or ten and twenty-three one-hundred twentieths).

How do we solve fractions step by step?

1. Conversion a mixed number 6 2/5 to a improper fraction: 6 2/5 = 6 2/5 = 6 · 5 + 2/5 = 30 + 2/5 = 32/5To find a new numerator: a) Multiply the whole number 6 by the denominator 5. Whole number 6 equally 6 * 5/5 = 30/5 b) Add the answer from the previous step 30 to the numerator 2. New numerator is 30 + 2 = 32 c) Write a previous answer (new numerator 32) over the denominator 5.Six and two fifths is thirty-two fifths.
2. Conversion a mixed number 3 1/8 to a improper fraction: 3 1/8 = 3 1/8 = 3 · 8 + 1/8 = 24 + 1/8 = 25/8To find a new numerator: a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8 b) Add the answer from the previous step 24 to the numerator 1. New numerator is 24 + 1 = 25 c) Write a previous answer (new numerator 25) over the denominator 8.Three and one eighth is twenty-five eighths.
3. Add: 32/5 + 25/8 = 32 · 8/5 · 8 + 25 · 5/8 · 5 = 256/40 + 125/40 = 256 + 125/40 = 381/40 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(5, 8) = 40. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 8 = 40. In the following intermediate step, the fraction cannot be simplified further by canceling.In other words, thirty-two fifths plus twenty-five eighths equals three hundred eighty-one fortieths.
4. Add: the result of step No. 3 + 2/3 = 381/40 + 2/3 = 381 · 3/40 · 3 + 2 · 40/3 · 40 = 1143/120 + 80/120 = 1143 + 80/120 = 1223/120 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(40, 3) = 120. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 40 × 3 = 120. In the following intermediate step, the fraction cannot be simplified further by canceling.In other words, three hundred eighty-one fortieths plus two thirds equals one thousand two hundred twenty-three one-hundred twentieths.

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:

• 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: March 8, 2026

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