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:
27 1/3 - 14 7/15 = 193/15 = 12 13/15 ≅ 12.8666667
The spelled result in words is one hundred ninety-three fifteenths (or twelve and thirteen fifteenths).How do we solve fractions step by step?
- Conversion a mixed number 27 1/3 to a improper fraction: 27 1/3 = 27 1/3 = 27 · 3 + 1/3 = 81 + 1/3 = 82/3
To find a new numerator:
a) Multiply the whole number 27 by the denominator 3. Whole number 27 equally 27 * 3/3 = 81/3
b) Add the answer from the previous step 81 to the numerator 1. New numerator is 81 + 1 = 82
c) Write a previous answer (new numerator 82) over the denominator 3.
Twenty-seven and one third is eighty-two thirds. - Conversion a mixed number 14 7/15 to a improper fraction: 14 7/15 = 14 7/15 = 14 · 15 + 7/15 = 210 + 7/15 = 217/15
To find a new numerator:
a) Multiply the whole number 14 by the denominator 15. Whole number 14 equally 14 * 15/15 = 210/15
b) Add the answer from the previous step 210 to the numerator 7. New numerator is 210 + 7 = 217
c) Write a previous answer (new numerator 217) over the denominator 15.
Fourteen and seven fifteenths is two hundred seventeen fifteenths. - Subtract: 82/3 - 217/15 = 82 · 5/3 · 5 - 217/15 = 410/15 - 217/15 = 410 - 217/15 = 193/15
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(3, 15) = 15. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 15 = 45. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eighty-two thirds minus two hundred seventeen fifteenths is one hundred ninety-three fifteenths.
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:
- 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?
- You have 2
You have 6/13 of a pie. If you share 9/10, how much will you have left? - Cherries 2
If a farmer reaped 636 cherries and he sold one-third to a shopkeeper, how many did he retain? - Paul ate
Paul ate 2/8 of a cake and his brother 3/8. What fraction of the cake is left for the parents? - Fraction operations
For items - fractions 1/6 - 1/9 perform the indicated operation/s. Write your answer in improper fractions, and it must be in the simplest form. - Evaluate 38
Evaluate the expression shown below and write your answer as a fraction in simplest form. (5)/(6) - (3)/(8) Transcription: start fraction, 5, divided by, 6, end fraction, minus, start fraction, 3, divided by, 8, end fraction
- King
King had four sons. First inherit 1/2, second 1/4, third 1/5 of property. What part of the property was left to the last of the brothers? - Sarah 5
Sarah had ten cookies and ate one-half of a cookie. How much would she have left? - You have 4
You have eaten ⅔ of a pizza. Your friend eats what is left. How much of the original pizza is left? - Unload truck
Andy has just moved and is beginning to unload his boxes. The truck is currently 11/12 of the way full. He unloads 1/4 more of it. How much more does he have to unload? - Difference between fractions
What is the difference when you take away 1/6 from 2/8?
What is 3/5 less than 11/12? (Answer should be in proper or improper only: Example 1/2, -1/2, 3/2, and -3/2)more math problems »