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 4/9 - 1 6/9 = 16/9 = 1 7/9 ≅ 1.7777778
The result spelled out in words is sixteen ninths (or one and seven ninths).How do we solve fractions step by step?
- Conversion a mixed number 3 4/9 to a 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 equally 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 a 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 equally 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, it cannot further simplify the fraction result by canceling.
In other words, thirty-one ninths minus fifteen ninths equals sixteen ninths.
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:
- Nida had
Nida had 1/12 of a pizza. She gave 1/8 of it to her friend Madeeha. Find what part of the whole pizza did Madeeha get.
- Adeline
Adeline helped her mother make 7/9 liters of lemonade to treat their guests. She poured the lemonade into cups. Each cup had a capacity of 1/6 liters. She filled some cups entirely except for 1 cup. How much was lemonade in the cup that was not filled?
- Akpan
Akpan spent 3/8 of his time in school during the week. What fraction of his time does he spend at home during the week?
- Balloons 2
One balloon is 3 7/10 meters above the ground. A second balloon 2 3/5 meters higher. How far above the ground is the second balloon? Complete the addition equation and a related subtraction equation to model the problem. Use x to represent the height of t
- The recipe 2
The recipe needs 3/4 cups of flour. How many cups of flour will be left if you have 4 cups of flour in the container?
- Blank number
5/2 + blank =1/3 What is the blank number?
- One large
One large pizza is cut into 12 pieces. The pizza has sausage, mushrooms, and cheese on it. Michelle ate 1/6 of the pizza, Natalie ate 1/4 of the pizza, Bridgette ate 1/8 of the pizza, and Brenda ate 1/3 of the pizza. How much of the whole pizza is left, a
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Last Modified: June 23, 2025