Calculator complex fractions
This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.
5/8 : 2 2/3 = 15/64 = 0.234375
The result spelled out in words is fifteen sixty-fourths.How do we solve fractions step by step?
- Conversion a mixed number 2 2/3 to a improper fraction: 2 2/3 = 2 2/3 = 2 · 3 + 2/3 = 6 + 2/3 = 8/3
To find a new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
b) Add the answer from the previous step 6 to the numerator 2. New numerator is 6 + 2 = 8
c) Write a previous answer (new numerator 8) over the denominator 3.
Two and two thirds is eight thirds. - Divide: 5/8 : 8/3 = 5/8 · 3/8 = 5 · 3/8 · 8 = 15/64
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 8/3 is 3/8) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, five eighths divided by eight thirds equals fifteen sixty-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) |
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:
- Boxes of wafers
Wafers measuring 11 3/4 cm, 4 2/5 cm, and 1 2/3 cm are packed in rectangular boxes measuring 23 1/2 cm, 26 2/5 cm, and 6 2/3 cm. What part of the volume of the box does one wafer make up? - Equivalent - reciprocal
Which of these equations is equivalent to 2/3x3 1/4 select all that apply. Answers: ... - Divide mixed numbers
Divide the following fractions and reduce your answers to its simplest form if possible: 1. 2 3/4 ÷ 3 1/12 2. 3 2/3 ÷ 4 1/2 3. 5 3/7 ÷ 2 3/9 4. 6 2/3 ÷ 1 1/5 - Divide 42
Divide. Write your answer in the lowest terms as a proper or improper fraction. (8/25)÷(-4/5) - Pieces of wood
How many pieces of wood can each student have if there are 12 pieces and each student needs 1/4 of a piece? - Soup 4 Cornell makes 11/12 of a gallon of soup. He eats equal portions of soup for 5 days, with no soup remaining after the 5th day. How many gallons of soup did Cornell eat each day?
- David 4
David made 4/3 of a quart of fruit juice. Each mug he has holds 1/3 of a quart. How many mugs will David be able to fill?
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Last Modified: August 28, 2025
