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:
5 4/7 - 2 1/2 = 43/14 = 3 1/14 ≅ 3.0714286
Spelled result in words is forty-three fourteenths (or three and one fourteenth).How do we solve fractions step by step?
- Conversion a mixed number 5 4/7 to a improper fraction: 5 4/7 = 5 4/7 = 5 · 7 + 4/7 = 35 + 4/7 = 39/7
To find a new numerator:
a) Multiply the whole number 5 by the denominator 7. Whole number 5 equally 5 * 7/7 = 35/7
b) Add the answer from the previous step 35 to the numerator 4. New numerator is 35 + 4 = 39
c) Write a previous answer (new numerator 39) over the denominator 7.
Five and four sevenths is thirty-nine sevenths. - Conversion a mixed number 2 1/2 to a improper fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2
To find a new numerator:
a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2 = 4/2
b) Add the answer from the previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
c) Write a previous answer (new numerator 5) over the denominator 2.
Two and one half is five halfs. - Subtract: 39/7 - 5/2 = 39 · 2/7 · 2 - 5 · 7/2 · 7 = 78/14 - 35/14 = 78 - 35/14 = 43/14
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 2) = 14. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 2 = 14. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirty-nine sevenths minus five halfs is forty-three fourteenths.
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:
- A man 9
A man earns $2400 in his monthly salary. He spends 3/5 of his salary on food and rent. This month he decided to buy his family presents. What fraction of his money does he spend on presents? - Peter's calculation
Peter wrote the following: 7 1/4 - 3 3/4 = 4 2/4 = 4 1/2 . Is Peter's calculation correct? Using words (math vocabulary) and numbers to explain why he is correct or incorrect. - The cat
The cat starts with 4/6 of a cup in his bowl. It eats 1/4 of a cup of food. How much food is left? - Before 4
Before a journey, the petrol gauge showed my car's tank was half full. When I returned home, it was one-third full. What fraction of a tank of petrol had I used? - Paul ate
Paul ate 2/8 of a cake and his brother 3/8. What fraction of the cake is left for the parents?
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