Fraction Calculator
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:
12 5/8 ÷ 3 19/24 = 303/91 = 3 30/91 ≅ 3.3296703
Spelled out: three hundred three ninety-firsts (or three and thirty ninety-firsts).How do we solve fractions step by step?
- Conversion a mixed number 12 5/8 to a improper fraction: 12 5/8 = 12 5/8 = 12 · 8 + 5/8 = 96 + 5/8 = 101/8
To find a new numerator:
a) Multiply the whole number 12 by the denominator 8. Whole number 12 equally 12 * 8/8 = 96/8
b) Add the answer from the previous step 96 to the numerator 5. New numerator is 96 + 5 = 101
c) Write a previous answer (new numerator 101) over the denominator 8.
Twelve and five eighths is one hundred one eighths. - Conversion a mixed number 3 19/24 to a improper fraction: 3 19/24 = 3 19/24 = 3 · 24 + 19/24 = 72 + 19/24 = 91/24
To find a new numerator:
a) Multiply the whole number 3 by the denominator 24. Whole number 3 equally 3 * 24/24 = 72/24
b) Add the answer from the previous step 72 to the numerator 19. New numerator is 72 + 19 = 91
c) Write a previous answer (new numerator 91) over the denominator 24.
Three and nineteen twenty-fourths is ninety-one twenty-fourths. - Divide: 101/8 : 91/24 = 101/8 · 24/91 = 101 · 24/8 · 91 = 2424/728 = 8 · 303 /8 · 91 = 303/91
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 91/24 is 24/91) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 8 gives 303/91.
In other words, one hundred one eighths divided by ninety-one twenty-fourths equals three hundred three ninety-firsts.
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:
- Closer to one
Here are two sums: A=1/2 + 1/3 and B=1/5 + 1/3. Which of the two sums is closer in value to 1? You must show your work and state clearly whether the answer is A or B. - Compare operators
Place the correct symbol, < or >, between the two numbers: 4/7 and 5/6. - 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?
- Tourist route longest
On the first day, tourists covered 3/14 of the planned route, on the second day 1/3 of the route, and on the third day 8/21 of the route. On which day did they walk the longest part of the route (1,2,3)? - Fractions
Sort fractions z1 = (20)/(9); z2 = (10)/(21); z3 = (15)/(14) by their size. The result writes as three serial numbers 1,2,3. - 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? - A laundry
Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
more math problems »
Last Modified: March 10, 2026
