Fraction calculator
This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.
The result:
4 1/8 + 2 1/16 = 99/16 = 6 3/16 = 6.1875
The result spelled out in words is ninety-nine sixteenths (or six and three sixteenths).How do we solve fractions step by step?
- Conversion a mixed number 4 1/8 to a improper fraction: 4 1/8 = 4 1/8 = 4 · 8 + 1/8 = 32 + 1/8 = 33/8
To find a new numerator:
a) Multiply the whole number 4 by the denominator 8. Whole number 4 equally 4 * 8/8 = 32/8
b) Add the answer from the previous step 32 to the numerator 1. New numerator is 32 + 1 = 33
c) Write a previous answer (new numerator 33) over the denominator 8.
Four and one eighth is thirty-three eighths. - Conversion a mixed number 2 1/16 to a improper fraction: 2 1/16 = 2 1/16 = 2 · 16 + 1/16 = 32 + 1/16 = 33/16
To find a new numerator:
a) Multiply the whole number 2 by the denominator 16. Whole number 2 equally 2 * 16/16 = 32/16
b) Add the answer from the previous step 32 to the numerator 1. New numerator is 32 + 1 = 33
c) Write a previous answer (new numerator 33) over the denominator 16.
Two and one sixteenth is thirty-three sixteenths. - Add: 33/8 + 33/16 = 33 · 2/8 · 2 + 33/16 = 66/16 + 33/16 = 66 + 33/16 = 99/16
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(8, 16) = 16. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 16 = 128. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, thirty-three eighths plus thirty-three sixteenths equals ninety-nine sixteenths.
Rules for expressions with fractions:
Fractions - write a forward slash to separate the numerator and the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts.Mixed numerals (mixed numbers or fractions) - keep one space between the whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . and they are automatically converted to fractions - i.e. 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
• fractions multiple: 2/3 of 3/5
• divide to find the quotient: 3/5÷2/3
The calculator follows well-known rules for the order of operations. The most common mnemonics for remembering this order are:
- 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 (brackets: (){}), Exponents, Multiplication, Division, Addition, Subtraction.
- MDAS: Multiplication and Division (same precedence), Addition and Subtraction (same precedence). MDAS is a subset of PEMDAS.
1. Multiplication/Division vs. Addition/Subtraction: Always perform multiplication and division *before* addition and subtraction.
2. Left-to-Right Rule: Operators with the same precedence (e.g., + and -, or * and /) must be evaluated from left to right.
Fractions in word problems:
- Add two fractions
What is the sum of 2/3 and 3/10?
- Matthew
Matthew is saving up for a car. Last year he saved 3/5 of the total amount. In addition to what he saved last year, he saved 3/10 of the total amount in the summer. If the car costs 15 000$, how much has he saved so far?
- Mary spent
Mary spent 3/4 hour doing science and 1/8 hour reading. How much time did she spend studying?
- Rachel 2
Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?
- A biology
A biology experiment required pouring 2/9 liter of nutrient solution and 2/3 liter of pure water into a tank. At the end of the experiment, 3/10 liter of fluid had evaporated. How much fluid was left in the tank?
- Paul spent
Paul spent 2/5 of his money on new shirts and a ½ of his money on new shoes. What fraction of his money has been spent? What fraction is still left?
- Wednesday 67114
Emil and Erika are playing a board game. a) on Monday, they started playing at 17:36 and played for 45 minutes. What time was it when they finished? b) on Tuesday, they played from 4:47 p.m. Until half past six. How many minutes did they play? c) they pla
more math problems »
Last Modified: June 23, 2025