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:
3/8 + 7 5/6 = 197/24 = 8 5/24 ≅ 8.2083333
The result spelled out in words is one hundred ninety-seven twenty-fourths (or eight and five twenty-fourths).How do we solve fractions step by step?
- Conversion a mixed number 7 5/6 to a improper fraction: 7 5/6 = 7 5/6 = 7 · 6 + 5/6 = 42 + 5/6 = 47/6
To find a new numerator:
a) Multiply the whole number 7 by the denominator 6. Whole number 7 equally 7 * 6/6 = 42/6
b) Add the answer from the previous step 42 to the numerator 5. New numerator is 42 + 5 = 47
c) Write a previous answer (new numerator 47) over the denominator 6.
Seven and five sixths is forty-seven sixths. - Add: 3/8 + 47/6 = 3 · 3/8 · 3 + 47 · 4/6 · 4 = 9/24 + 188/24 = 9 + 188/24 = 197/24
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, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 6 = 48. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, three eighths plus forty-seven sixths equals one hundred ninety-seven twenty-fourths.
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:
- A cake 2
Karen sliced a cake into 10 slices. She ate 2/10 of it and after some time she ate another 4/10 of it. How much of the cake did Karen eat?
- Work out 2
Work out the sum of 2/6 and 1/6. Give your answer in its simplest form.
- My whole
My whole number is 88 if you add 5 thousandths, 8 tenths, and 7 thousandths. What number will I be?
- Mary read
Mary read 2/9 books in the morning and 5/9 in the evening. What fraction of books has she read?
- Hardware store
At the hardware store, 1/4 of the nails are size 2d, and 3/8 of the nails are size 4d. What fraction of the nails are either size 2d or 4d?
- There 22
There is 5/8 of a pizza in one box and 9/12 of a pizza in another box. How much do you have altogether?
- Party pizza
At a party, there were some pizzas of the same size. Amelia ate 1/3 of a pizza. Chris ate 1/3 of a pizza. Miguel ate 5/12 of a pizza. How many pizzas did the three children eat?
more math problems »
Last Modified: April 16, 2025