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 2/3 : 4 3/8 = 8/21 ≅ 0.3809524
Spelled result in words is eight twenty-firsts.How do we solve fractions step by step?
- Conversion a mixed number 1 2/3 to a improper fraction: 1 2/3 = 1 2/3 = 1 · 3 + 2/3 = 3 + 2/3 = 5/3
To find a new numerator:
a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/3 = 3/3
b) Add the answer from the previous step 3 to the numerator 2. New numerator is 3 + 2 = 5
c) Write a previous answer (new numerator 5) over the denominator 3.
One and two thirds is five thirds. - Conversion a mixed number 4 3/8 to a improper fraction: 4 3/8 = 4 3/8 = 4 · 8 + 3/8 = 32 + 3/8 = 35/8
To find a new numerator:
a) Multiply the whole number 4 by the denominator 8. Whole number 4 equally 4 * 8/8 = 32/8
b) Add the answer from the previous step 32 to the numerator 3. New numerator is 32 + 3 = 35
c) Write a previous answer (new numerator 35) over the denominator 8.
Four and three eighths is thirty-five eighths. - Divide: 5/3 : 35/8 = 5/3 · 8/35 = 5 · 8/3 · 35 = 40/105 = 5 · 8 /5 · 21 = 8/21
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 35/8 is 8/35) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 5 gives 8/21.
In other words - five thirds divided by thirty-five eighths is eight twenty-firsts.
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:
- Why is
Why is three divided by one-fifth different from one-fifth divided by three? - Julian 2
Julian and two of his friends will share 1/4 of a pizza. How much will each person get? - Convert 6
Convert to a decimal 15/100. - Solve 21
Solve the following problem and write the answer as a mixed number in the lowest terms: 8/11 ÷ 4/9. - Larry 2
Larry spends half of his workday teaching piano lessons. He sees six students and gives the same amount of time to each. What fraction of his workday is spent with each student?
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