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:
2/3 * 1/2 = 1/3 ≅ 0.3333333
The spelled result in words is one third.How do we solve fractions step by step?
- Multiple: 2/3 * 1/2 = 2 · 1/3 · 2 = 2/6 = 1 · 2/3 · 2 = 1/3
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(2, 6) = 2. In the following intermediate step, cancel by a common factor of 2 gives 1/3.
In other words - two thirds multiplied by one half is one third.
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:
- 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? - Someone
Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake left, how much of a whole cake will you have eaten? - In dividing
In dividing fractions, get the reciprocal of the divisor and change the division symbol to the multiplication symbol. 2/3 : 5/6 - 10 children
Ten children in the park, four-tenths are wearing a red shirt. How many children in the park are wearing a red shirt?
- Trent
Trent operates a hot dog stand. On Wednesday, he used two bags of hot dog buns. On Thursday, he used 1/5 as many hot dog buns as Wednesday. How many bags of hot dog buns Trent used on Thursday? - Bryce
Bryce collected 1/4 of a bin of glass bottles to recycle. Megan collected 5 times as many bins as Bryce. How many bins of bottles did Megan collect? - Ms. Sheppard
Ms. Sheppard cuts ½ of a piece of construction paper. She uses ⅙ of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower? - Fraction expression
Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis - Scouts 4
4/7 out of the students in a school are boys. If 3/8 of the boys are scouts, how many scouts are there in a school of 1878 students?
- There 12
There are 42 students in the class, and 2/3 of them are girls. How many girls are there in the class? - Shoes
Jim and Dora are collecting shoes for a yard sale. Dora collected 1/2 as many shoes as Jim did. Jim collected 3/7 of a bag of shoes. How many bags of shoes did Dora collect? - 19 boy
Nineteen boys in section 1 and 23 boys in section 2. If 2/6 of them are boy Scouts, how many boy scouts are them? - Icecreams
Karthik bought 30 icecreams for his birthday. 2/5 of them are chocolate icecreams. Find the number of chocolate icecreams he bought. - A newspaper's
A newspaper's cover page is 3/8 text, and photographs fill the rest. If 2/5 of the text is an article about endangered species, what fraction of the whole cover page is the article about endangered species?
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