Fraction calculator
This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.
The result:
1/3 * 3/5 = 1/5 = 0.2
Spelled result in words is one fifth.How do we solve fractions step by step?
- Multiple: 1/3 * 3/5 = 1 · 3/3 · 5 = 3/15 = 1 · 3/5 · 3 = 1/5
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 15) = 3. In the following intermediate step, cancel by a common factor of 3 gives 1/5.
In other words - one third multiplied by three fifths is one fifth.
Rules for expressions with fractions:
Fractions - use a forward slash to divide the numerator by 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 integer and
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . 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
• multiplying a fraction by a whole number: 6 * 3/4
• square root of a fraction: sqrt(1/16)
• reducing or simplifying the fraction (simplification) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction
• 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 of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to right.
Fractions in word problems:
- Puzzle game
In a letter puzzle game, John can use every alphabet only once. He used only 8 alphabets to solve the puzzle. What fraction of the 26 alphabets did he use? Express your answer as a fraction in the simplest form. - Denominator 2
The denominator of a fraction is five, and the numerator is 7. Write the fraction. - Someone
Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake left, how much of a whole cake will you have eaten? - A quarter
A quarter of the number 72 is: - Evaluate expression
Calculate the value of the expression z/3 - 2 z/9 + 1/6, for z = 2 - Out 550,000.00
Out of 550,000.00, an amount of 325,000.00 was used. What fraction of the total amount was used? - Children 9
There are 11 children in a room. Six of the children are girls. What fraction of the children are girls? - Dea makes
Dea makes 18 out of 27 shots in a basketball game. Which decimal represents the fraction of shots Dea makes? - A class IV.A
In a class, there are 15 girls and 30 boys. What fraction of the class represents the boys? - A company
A company has 860 employees, of which 500 are female. Write a fraction to represent the female employees in the company. - In the cafeteria
There are 18 students in Jacob's homeroom. Six students bring their lunch to school. The rest eat lunch in the cafeteria. In the simplest form, what fraction of students eat lunch in the cafeteria? - Fruit basket
If there are seven apples and five oranges in the basket, what fraction of oranges are in the fruit basket? - The following 3
The following fraction is reduced to its lowest terms except one. Which of these: A.98/99 B.73/179 C.1/250 D.81/729 - Reduce 9 Reduce the fraction 16/24 to the lowest terms.
- Fractions 80134
There are 420 pupils in the school. Two hundred fifty-two pupils go to the 1st level. Write as a fraction what part of the pupils goes to the 1st grade and what part to the 2nd grade. Shorten both fractions to their basic form.
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