Fraction calculator
This calculator adds two fractions. First, all fractions are converted to a common denominator when fractions have different denominators. Find the Least Common Denominator (LCD) or multiply all denominators to find a common denominator. When all denominators are the same, subtract the numerators and place the result over the common denominator. Then, simplify the result to the lowest terms or a mixed number.
The result:
3/5 + 7/10 = 13/10 = 1 3/10 = 1.3
Spelled result in words is thirteen tenths (or one and three tenths).How do we solve fractions step by step?
- Add: 3/5 + 7/10 = 3 · 2/5 · 2 + 7/10 = 6/10 + 7/10 = 6 + 7/10 = 13/10
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(5, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 10 = 50. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - three fifths plus seven tenths is thirteen 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 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?
- 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. - Fraction to decimal
Write the fraction 3/22 as a decimal. - 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.
- 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? - 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. - 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. - Denominator 2
The denominator of a fraction is five, and the numerator is 7. Write the fraction.
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