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:
6 4/7 + 5/6 = 311/42 = 7 17/42 = 7.4047619
The result spelled out in words is three hundred eleven forty-seconds (or seven and seventeen forty-seconds).How do we solve fractions step by step?
- Conversion a mixed number 6 4/7 to a improper fraction: 6 4/7 = 6 4/7 = 6 · 7 + 4/7 = 42 + 4/7 = 46/7
To find a new numerator:
a) Multiply the whole number 6 by the denominator 7. Whole number 6 equally 6 * 7/7 = 42/7
b) Add the answer from the previous step 42 to the numerator 4. New numerator is 42 + 4 = 46
c) Write a previous answer (new numerator 46) over the denominator 7.
Six and four sevenths is forty-six sevenths. - Add: 46/7 + 5/6 = 46 · 6/7 · 6 + 5 · 7/6 · 7 = 276/42 + 35/42 = 276 + 35/42 = 311/42
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(7, 6) = 42. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 6 = 42. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, forty-six sevenths plus five sixths equals three hundred eleven forty-seconds.
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:
- My mother 2
My mother ate 1/8 of the cake, and my father ate 3/8 of the cake. How much cake has been eaten, and how much is left?
- A city
A city received 11/4 cm of rainfall on Sunday and 11/2 cm on Monday. Find the total rain in the city on these two days.
- A football 2
A football team wins 2/5 of their matches and draws 1/3. What fraction of their matches are lost?
- Adding 11
You are adding numbers. Which of the following numbers to 3/5 will give a whole number? a. 2 b. 2/5 c. 5/3 d. 3/5
- How many 3
How many hours do the Andersons watch TV in all Wednesday 3/1 hr Thursdays 2/3 hr Friday 4/5 hr Saturday 3/4 hr
- Difference and sum
If the difference of 19/13 and his answer is 6/7, Bruno's answer is: If the sum of his answer and 6/7 is 1/2, Bruno's answer is: If his answer is the sum of 19/13 and 6/7, Bruno's answer is :
- Mr. Ofori
Mr. Ofori starts a job with an annual salary of 6400, which increases by 240 every year. After working for eight years, Mr. Ofori was promoted to a new post with an annual salary of 9500, which increased by 360 yearly. Find I. Mr. Ofori's salary in the fi
more math problems »
Last Modified: June 23, 2025