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:
4/7 / 1 3/4 = 16/49 ≅ 0.3265306
The result spelled out in words is sixteen forty-ninths.How do we solve fractions step by step?
- Conversion a mixed number 1 3/4 to a improper fraction: 1 3/4 = 1 3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4
To find a new numerator:
a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4
b) Add the answer from the previous step 4 to the numerator 3. New numerator is 4 + 3 = 7
c) Write a previous answer (new numerator 7) over the denominator 4.
One and three quarters is seven quarters. - Divide: 4/7 : 7/4 = 4/7 · 4/7 = 4 · 4/7 · 7 = 16/49
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 7/4 is 4/7) 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, four sevenths divided by seven quarters equals sixteen forty-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:
- Divide 42
Divide. Write your answer in the lowest terms as a proper or improper fraction. (8/25)÷(-4/5)
- Expression with powers
Which expression is equivalent to 2.1 raised to the fifth power divided by 0.9 raised to the fourth power, all raised to the third power?
- A pizza 3
A pizza shop charges $2.00 for a slice that is one-eighth of a pizza and $3.00 for a slice that is one-fourth of a pizza. One day the pizza shop makes six pizzas. How much more money will they make if they slice all the pizzas into eighths than if they sl
- Pupils - boys and girls
5/8 of the pupils in a hall were boys. 7/10 of the boys wore glasses. 48 boys didn't wear glasses. How many pupils were there in the hall?
- Six friends
Six friends who live inland decide to take a road trip to the closest beach, which is 661 1/2 kilometers away. They decided to share the driving equally. How many kilometers will each person have to drive
- Jacob 4
Jacob is dividing 5 aquariums into 1/8 of aquarium sections for his different animals. How many 1/8s are there in Jacobs 5 aquariums?
- Jana mixing
Jana mix is 1/4 gallon of orange juice and 1/2 gallon of pineapple juice to make punch. Each serving is 1/16 gallon. How many servings can go in? Make sure you work.
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Last Modified: June 23, 2025