Fraction calculator
This 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.
Result:
3 5/10 - 1 3/5 = 19/10 = 1 9/10 = 1.9
Spelled result in words is nineteen tenths (or one and nine tenths).How do we solve fractions step by step?
- Conversion a mixed number 3 5/10 to a improper fraction: 3 5/10 = 3 5/10 = 3 · 10 + 5/10 = 30 + 5/10 = 35/10
To find a new numerator:
a) Multiply the whole number 3 by the denominator 10. Whole number 3 equally 3 * 10/10 = 30/10
b) Add the answer from previous step 30 to the numerator 5. New numerator is 30 + 5 = 35
c) Write a previous answer (new numerator 35) over the denominator 10.
Three and five tenths is thirty-five tenths - Conversion a mixed number 1 3/5 to a improper fraction: 1 3/5 = 1 3/5 = 1 · 5 + 3/5 = 5 + 3/5 = 8/5
To find a new numerator:
a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5
b) Add the answer from previous step 5 to the numerator 3. New numerator is 5 + 3 = 8
c) Write a previous answer (new numerator 8) over the denominator 5.
One and three fifths is eight fifths - Subtract: 35/10 - 8/5 = 35/10 - 8 · 2/5 · 2 = 35/10 - 16/10 = 35 - 16/10 = 19/10
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 5) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 5 = 50. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirty-five tenths minus eight fifths is nineteen tenths.
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 signs 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) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22
• 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 /) has the same priority and then must evaluate from left to right.
Fractions in word problems:
- 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 explain why he is correct or incorrect.
- Package
The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
- Evaluate - lowest terms
Evaluate: 16/25 - 11/25 (Express answer as a fraction reduced to lowest terms. )
- Cherries 2
If a farmer reaped 636 cherries and he sold one third to a shop keeper, how many did he retain?
- Difference between fractions
What is the difference when you take away 1/6 from 2/8?
- Fraction expression
Which expression is equivalent to : minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
- 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?
- 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?
- Whole pie
If you have one whole pie and 1/2 is giving away and 1/4 is eaten and how much do you have left
- Sundar
Sundar has 50 chocolates. He gave 2/5 of these chocolates to Ram and he ate 1/5 of them. How many chocolates are left with Sundar?
- The entity
What is the difference between seven tenths of an entity and seven fifteenths of the same entity? Please solve it for me.
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