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:
2 1/6 - 1 2/8 = 11/12 ≅ 0.9166667
Spelled result in words is eleven twelfths.How do we solve fractions step by step?
- Conversion a mixed number 2 1/6 to a improper fraction: 2 1/6 = 2 1/6 = 2 · 6 + 1/6 = 12 + 1/6 = 13/6
To find a new numerator:
a) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/6 = 12/6
b) Add the answer from the previous step 12 to the numerator 1. New numerator is 12 + 1 = 13
c) Write a previous answer (new numerator 13) over the denominator 6.
Two and one sixth is thirteen sixths. - Conversion a mixed number 1 2/8 to a improper fraction: 1 2/8 = 1 2/8 = 1 · 8 + 2/8 = 8 + 2/8 = 10/8
To find a new numerator:
a) Multiply the whole number 1 by the denominator 8. Whole number 1 equally 1 * 8/8 = 8/8
b) Add the answer from the previous step 8 to the numerator 2. New numerator is 8 + 2 = 10
c) Write a previous answer (new numerator 10) over the denominator 8.
One and two eighths is ten eighths. - Subtract: 13/6 - 10/8 = 13 · 4/6 · 4 - 10 · 3/8 · 3 = 52/24 - 30/24 = 52 - 30/24 = 22/24 = 2 · 11/2 · 12 = 11/12
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(6, 8) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 8 = 48. In the following intermediate step, cancel by a common factor of 2 gives 11/12.
In other words - thirteen sixths minus ten eighths is eleven 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 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:
- Closer to one
Here are two sums: A=1/2 + 1/3 and B=1/5 + 1/3. Which of the two sums is closer in value to 1? You must show your work and state clearly whether the answer is A or B. - 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. - 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? - The recipe
The recipe they are following requires 7/8 cups of milk. Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe?
- Students activities
There are 28 students in the class. Twenty-one of them is involved in-ring activities. What part of the class does not attend the circle? - 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? - Mr. Vandar
Mr. Vandar washed 1/4 of his laundry. His son washed 2/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed? - Whole pie
If you have one whole pie, 1/2 is given away, and 1/4 is eaten, how much do you have left? - Sarah 5
Sarah had ten cookies and ate one-half of a cookie. How much would she have left?
- Sundar
Sundar has 50 chocolates. He gave 2/5 of these chocolates to Ram and ate 1/5 of them. How many chocolates are left with Sundar? - Cherries 2
If a farmer reaped 636 cherries and he sold one-third to a shopkeeper, how many did he retain? - Fraction expression
Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis - Subtract 19
Subtract as indicated. 11/10 - (- 2/5) - Difference between fractions
What is the difference when you take away 1/6 from 2/8?
more math problems »