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:
3 4/9 - 1 6/9 = 16/9 = 1 7/9 ≅ 1.7777778
Spelled out: sixteen ninths (or one and seven ninths).How do we solve fractions step by step?
- Conversion a mixed number 3 4/9 to an improper fraction: 3 4/9 = 3 4/9 = 3 · 9 + 4/9 = 27 + 4/9 = 31/9
To find a new numerator:
a) Multiply the whole number 3 by the denominator 9. Whole number 3 equals 3 ·9/9 = 27/9
b) Add the answer from the previous step 27 to the numerator 4. New numerator is 27 + 4 = 31
c) Write a previous answer (new numerator 31) over the denominator 9.
Three and four ninths is thirty-one ninths. - Conversion a mixed number 1 6/9 to an improper fraction: 1 6/9 = 1 6/9 = 1 · 9 + 6/9 = 9 + 6/9 = 15/9
To find a new numerator:
a) Multiply the whole number 1 by the denominator 9. Whole number 1 equals 1 ·9/9 = 9/9
b) Add the answer from the previous step 9 to the numerator 6. New numerator is 9 + 6 = 15
c) Write a previous answer (new numerator 15) over the denominator 9.
One and six ninths is fifteen ninths. - Subtract: 31/9 - 15/9 = 31 - 15/9 = 16/9
Both fractions have the same denominator, which is then the common denominator in the subtracting them. In the following intermediate step, the fraction cannot be simplified further by cancelling.
In other words, thirty-one ninths minus fifteen ninths equals sixteen ninths.
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:
- Tim had
Tim had $360. He spent 1/4 on CD's and 2/3 of the remainder on snacks. What was left in his piggy bank? - 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)? - A book 4
A book has 280 pages. I read 2/7 of the book yesterday, while I read 1/4 of it today. How many pages did I read in 2 days? - A farmer 9
A farmer has 3 hectares of an orchard. ½ of the land is occupied by apples, ⅙ of the remainder is occupied by lemon trees, and tree tomatoes occupy the rest of it. Find the fraction of the land occupied by tree tomatoes. - The bread 2
Sandra and Tylar baked two loaves of bread. On Monday, they ate 1/2 of one loaf. On Tuesday, they ate 1/3 of one loaf of bread. How much bread is left? - Peter's calculation
Peter wrote the following: 7 1/4 - 3 3/4 = 4 2/4 = 4 1/2. Is Peter's calculation correct? Using words (math vocabulary) and numbers to explain why he is correct or incorrect. - Muffins 2
Shayla is baking muffins that require 1/2 cup of vegetable oil. She only has 1/3 cup left. How much more does she need?
more math problems »
Last Modified: October 31, 2026
