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:
2/5 * 1/4 = 1/10 = 0.1
Spelled result in words is one tenth.How do we solve fractions step by step?
- Multiple: 2/5 * 1/4 = 2 · 1/5 · 4 = 2/20 = 1 · 2/10 · 2 = 1/10
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(2, 20) = 2. In the following intermediate step, cancel by a common factor of 2 gives 1/10.
In other words - two fifths multiplied by one quarter is one tenth.
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) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22
• 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 evaluate from left to right.
Fractions in word problems:
- 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?
- 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?
- 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?
- Two fractions multiply
What is 4/5 when multiplied by 9/10?
- Doughnuts
2/3 of the doughnuts in a box have frosting. 1/2 of the doughnuts with frosting have sprinkles. What fraction of the doughnuts in the box have frosting and sprinkles?
- Peter 15
Peter try to calculate: 3/4 x 2/3 He did 3x3 to get 9 and 4 x 2 to get 8. The final answer is 8/9. Can you explain the error and how to help? What is the correct answer?
- 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?
- One third 2
One-third of all students in class live in a house. If there are 42 students in a class, how many of them live in a house?
- Pencils
You have 36 pencil crayons. How many pencil crayons makeup 1/2 of the total?
- Puppies
At an animal rescue, 5/6 of the animals are dogs. Three-fourths of the dogs are puppies. This model represents the fraction of the animals at the rescue that is puppies. What fraction of the animals at the rescue are puppies?
- Task 7
Multiply the following fractions. Change the answer to the lowest term if needed. 1. 8/12 × 1/5= 2. 3/9 × 1/11= 3. 2/7 × 7/9 = 4. 8/10 × 4/7= 5. 4/5 × 3/8=
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