Fraction Calculator - Calculation: 5/8:2 2/3

Fraction Calculator Enter fraction expression: 5/8:2 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:

5/8 : 2 2/3 = 15/64 = 0.234375

Spelled out: fifteen sixty-fourths.

How do we solve fractions step by step?

1. Conversion a mixed number 2 2/3 to a improper fraction: 2 2/3 = 2 2/3 = 2 · 3 + 2/3 = 6 + 2/3 = 8/3To find a new numerator: a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3 b) Add the answer from the previous step 6 to the numerator 2. New numerator is 6 + 2 = 8 c) Write a previous answer (new numerator 8) over the denominator 3.Two and two thirds is eight thirds.
2. Divide: 5/8 : 8/3 = 5/8 · 3/8 = 5 · 3/8 · 8 = 15/64 Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 8/3 is 3/8) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, the fraction cannot be simplified further by canceling.In other words, five eighths divided by eight thirds equals fifteen sixty-fourths.

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:

• Money - parts What part of €24 is €12, €4, €8, €1, €18, €20?
• 7 athletes Seven athletes run a combined total of 4 miles. How many miles did each athlete run?
• A ribbon Bree has a piece of ribbon that is 6 inches long. She needs to cut it into equal pieces measuring 3/4 of an inch. How many pieces will she have? Answer in simplest form
• My fraction My fraction is not a mixed number. My fraction is equivalent to 1/2. When my fraction is divided by 1/3, the answer is 1 1/2. The numerator of the fraction is 4. What is my fraction?
• Ciara’s Ciara's father bought a big bar of chocolate at the grocery. He divided it into two equal pieces and gave one piece to Ciara. Ciara then shared her piece with her and her two friends. What fraction of the big bar of chocolate did one of Ciara's friends ge
• Lila knows Lila knows that 3/16 means "3 divided by 16." She uses this to find the decimal equivalent for 3/16. Enter a digit into each box to continue her work.
• Unit rate Find unit rate: 6,840 customers in 45 days

more math problems »

Last Modified: March 8, 2026

• Maths calculators
• Math Practice Problems18530
• Worksheets