Fraction calculator
This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.
The result:
6 2/3 - 4 3/4 = 23/12 = 1 11/12 ≅ 1.9166667
The spelled result in words is twenty-three twelfths (or one and eleven twelfths).How do we solve fractions step by step?
- Conversion a mixed number 6 2/3 to a improper fraction: 6 2/3 = 6 2/3 = 6 · 3 + 2/3 = 18 + 2/3 = 20/3
To find a new numerator:
a) Multiply the whole number 6 by the denominator 3. Whole number 6 equally 6 * 3/3 = 18/3
b) Add the answer from the previous step 18 to the numerator 2. New numerator is 18 + 2 = 20
c) Write a previous answer (new numerator 20) over the denominator 3.
Six and two thirds is twenty thirds. - Conversion a mixed number 4 3/4 to a improper fraction: 4 3/4 = 4 3/4 = 4 · 4 + 3/4 = 16 + 3/4 = 19/4
To find a new numerator:
a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/4 = 16/4
b) Add the answer from the previous step 16 to the numerator 3. New numerator is 16 + 3 = 19
c) Write a previous answer (new numerator 19) over the denominator 4.
Four and three quarters is nineteen quarters. - Subtract: 20/3 - 19/4 = 20 · 4/3 · 4 - 19 · 3/4 · 3 = 80/12 - 57/12 = 80 - 57/12 = 23/12
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, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty thirds minus nineteen quarters is twenty-three twelfths.
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
• square root of a fraction: sqrt(1/16)
• 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:
- The entity
What is the difference between seven-tenths of an entity and seven-fifteenths of the same entity? Please solve it for me. - A football 2
A football team wins 2/5 of their matches and draws 1/3. What fraction of their matches are lost? - Tim had
Tim had $360. He spent 1/4 on CD's and 2/3 of the remainder on snacks. What was left in his piggy bank? - Eighty 2
Eighty children went on a field trip. If three-fifths of them were boys, how many were girls?
- Johnny 2
Johnny spends 1/2 of his salary on his family, 1/6 on personal expenses, and 1/9 on convenience, and he saves the rest. What fraction of his salary does he have? How much money does he save from his salary of $180? - Square metal sheet
We cut out four squares with a 300 mm side from a square sheet metal plate with a side of 0.7 m. Express the fraction and the percentage of waste from the square metal sheet. - Flags 2
1/4 are white and another 1/4 are yellow. What fraction of the flags are either white or yellow?
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Last Modified: October 9, 2024