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:
6 + 0.413 + 0.173 = 3293/500 = 6 293/500 = 6.586
Spelled result in words is three thousand two hundred ninety-three five-hundredths (or six and two hundred ninety-three five-hundredths).How do we solve fractions step by step?
- Conversion a decimal number to a fraction: 0.413 = 413/1000 = 413/1000
a) Write down the decimal 0.413 divided by 1: 0.413 = 0.413/1
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.)
0.413/1 = 4.13/10 = 41.3/100 = 413/1000
Note: 413/1000 is called a decimal fraction.
c) Simplify and reduce the fraction
413/1000 = 413 * 1/1000 * 1 = 413* 1/1000* 1 - Add: 6 + 0.413 = 6/1 + 413/1000 = 6 · 1000/1 · 1000 + 413/1000 = 6000/1000 + 413/1000 = 6000 + 413/1000 = 6413/1000
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(1, 1000) = 1000. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 1000 = 1000. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - six plus four hundred thirteen one-thousandths is six thousand four hundred thirteen one-thousandths. - Conversion a decimal number to a fraction: 0.173 = 173/1000 = 173/1000
a) Write down the decimal 0.173 divided by 1: 0.173 = 0.173/1
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.)
0.173/1 = 1.73/10 = 17.3/100 = 173/1000
Note: 173/1000 is called a decimal fraction.
c) Simplify and reduce the fraction
173/1000 = 173 * 1/1000 * 1 = 173* 1/1000* 1 - Add: the result of step No. 2 + 0.173 = 6413/1000 + 0.173 = 6413/1000 + 173/1000 = 6413 + 173/1000 = 6586/1000 = 2 · 3293/2 · 500 = 3293/500
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(1000, 1000) = 1000. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1000 × 1000 = 1000000. In the following intermediate step, cancel by a common factor of 2 gives 3293/500.
In other words - six thousand four hundred thirteen one-thousandths plus one hundred seventy-three one-thousandths is three thousand two hundred ninety-three five-hundredths.
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:
- Fraction and a decimal
Write as a fraction and a decimal. One and two plus three and five hundredths - Dea makes
Dea makes 18 out of 27 shots in a basketball game. Which decimal represents the fraction of shots Dea makes? - Equations
Solve following equations without fractions: a) 5 (x-1) -7 = 17-3 (1-x) b) 3 (y-2) -4y = 2- (1 + 2y) - Children 9
There are 11 children in a room. Six of the children are girls. What fraction of the children are girls?
- Fraction to decimal
Write the fraction 3/22 as a decimal. - Extinction 5552
Of the 65 freshwater fish species in Europe, 45 are at risk of extinction. In the basic form, express which parts of the fish are in danger of extinction. - A quarter
A quarter of the number 72 is: - 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? - In the cafeteria
There are 18 students in Jacob's homeroom. Six students bring their lunch to school. The rest eat lunch in the cafeteria. In the simplest form, what fraction of students eat lunch in the cafeteria?
- Out 550,000.00
Out of 550,000.00, an amount of 325,000.00 was used. What fraction of the total amount was used? - Value of Z
For x = -9, what is the value of Z, where Z equals fraction numerator x minus 17 over denominator 6.5 end fraction. Give your answer to 2 decimal places. - 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. - Oranges
There are 50 oranges in a bag. If ten of these oranges are bad, what fraction of them are good? - Simplify 12
Simplify {1/3 + 1/12} ÷ {2/3 - 5/8}
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