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:
3 4/5 * 1 5/7 = 228/35 = 6 18/35 ≅ 6.5142857
Spelled result in words is two hundred twenty-eight thirty-fifths (or six and eighteen thirty-fifths).How do we solve fractions step by step?
- Conversion a mixed number 3 4/5 to a improper fraction: 3 4/5 = 3 4/5 = 3 · 5 + 4/5 = 15 + 4/5 = 19/5
To find a new numerator:
a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/5 = 15/5
b) Add the answer from the previous step 15 to the numerator 4. New numerator is 15 + 4 = 19
c) Write a previous answer (new numerator 19) over the denominator 5.
Three and four fifths is nineteen fifths. - Conversion a mixed number 1 5/7 to a improper fraction: 1 5/7 = 1 5/7 = 1 · 7 + 5/7 = 7 + 5/7 = 12/7
To find a new numerator:
a) Multiply the whole number 1 by the denominator 7. Whole number 1 equally 1 * 7/7 = 7/7
b) Add the answer from the previous step 7 to the numerator 5. New numerator is 7 + 5 = 12
c) Write a previous answer (new numerator 12) over the denominator 7.
One and five sevenths is twelve sevenths. - Multiple: 19/5 * 12/7 = 19 · 12/5 · 7 = 228/35
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(228, 35) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - nineteen fifths multiplied by twelve sevenths is two hundred twenty-eight thirty-fifths.
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) |
Fractions in word problems:
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Anesa ate 3/4 of her pizza, and Eman ate 1/4 of her pizza. Who ate the greater part of the pizza?
A student knows that ¾ x 4 is the same as 4 x ¾ The student assumes that 4 ÷ ¾ is the same as ¾ ÷ 4 Is the student correct?more math problems »