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:
0.9289 - 0.7493 = 449/2500 = 0.1796
Spelled result in words is four hundred forty-nine over two thousand five hundred.How do we solve fractions step by step?
- Conversion a decimal number to a fraction: 0.9289 = 9289/10000 = 9289/10000
a) Write down the decimal 0.9289 divided by 1: 0.9289 = 0.9289/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
0.9289/1 = 9.289/10 = 92.89/100 = 928.9/1000 = 9289/10000
Note: 9289/10000 is called a decimal fraction.
c) Simplify and reduce the fraction
9289/10000 = 9289 * 1/10000 * 1 = 9289* 1/10000* 1 - Conversion a decimal number to a fraction: 0.7493 = 7493/10000 = 7493/10000
a) Write down the decimal 0.7493 divided by 1: 0.7493 = 0.7493/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
0.7493/1 = 7.493/10 = 74.93/100 = 749.3/1000 = 7493/10000
Note: 7493/10000 is called a decimal fraction.
c) Simplify and reduce the fraction
7493/10000 = 7493 * 1/10000 * 1 = 7493* 1/10000* 1 - Subtract: 0.9289 - 0.7493 = 9289/10000 - 7493/10000 = 9289 - 7493/10000 = 1796/10000 = 4 · 449/4 · 2500 = 449/2500
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(10000, 10000) = 10000. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10000 × 10000 = 100000000. In the following intermediate step, cancel by a common factor of 4 gives 449/2500.
In other words - nine thousand two hundred eighty-nine over ten thousand minus seven thousand four hundred ninety-three over ten thousand is four hundred forty-nine over two thousand five hundred.
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:
- Simplify 12
Simplify {1/3 + 1/12} ÷ {2/3 - 5/8} - Unsatisfactory 5604
In 1995, 360 fish samples were tested for contamination with foreign substances, and 138 samples were unsatisfactory. Write a fraction of what part of the fish did not meet the limits. - Reduce fractions
The following fraction is reduced to its lowest terms except one. Which of these: A. 98/99 B. 73/179 C. 1/250 D. 81/729 - Puzzle game
In a letter puzzle game, John can use every alphabet only once. He used only 8 alphabets to solve the puzzle. What fraction of the 26 alphabets did he use? Express your answer as a fraction in the simplest form. - A class IV.A
In a class, there are 15 girls and 30 boys. What fraction of the class represents the boys? - Children 9
There are 11 children in a room. Six of the children are girls. What fraction of the children are girls? - Andy gets
Andy gets five out of 15 questions wrong in his math test. What fraction of the question does andy answer correctly? - Fraction 4070
Petr reads 12 pages of the book in 1 hour. Express a fraction of what part of the book it will read in 5 hours if it has 280 pages. - Fraction and a decimal
Write as a fraction and a decimal. One and two plus three and five hundredths - Mathew
Mathew has eight pencils. Three of them do not have erasers on end. What fraction of the pencils do not have erasers on end? - A farm 6
A farm has 20 animals. There are four chickens. What fraction of the animals are chickens? Express your answer as a fraction in the simplest form. - A company
A company has 860 employees, of which 500 are female. Write a fraction to represent the female employees in the company. - Denominator 2
The denominator of a fraction is five, and the numerator is 7. Write the fraction. - Samantha
Samantha took 72 pictures on her beach vacation. 3/4 of those pictures are on the beach. How many pictures from her vacation are on the beach? - Evaluate expression
Calculate the value of the expression z/3 - 2 z/9 + 1/6, for z = 2
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