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:
(1/3) : (5/8) = 8/15 ≅ 0.5333333
Spelled result in words is eight fifteenths.How do we solve fractions step by step?
- Divide: 1/3 : 5/8 = 1/3 · 8/5 = 1 · 8/3 · 5 = 8/15
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 5/8 is 8/5) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one third divided by five eighths is eight fifteenths.
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:
- A seller
A seller sliced some pizza into eights. After selling 57 slices, seven slices were left. How many whole pizzas did the vendor slice?
- Two boxes 3
Two boxes of pizza of the same size are left on the table. One box has 1/2 of a pizza, and the other has 3/4 of a pizza left in it. Then, Mother divides all the pizzas into 1/8 each. How many were many slices of pizza left?
- Divide 42
Divide. Write your answer in the lowest terms as a proper or improper fraction. (8/25)÷(-4/5)
- Divide mixed numbers
Divide the following fractions and reduce your answers to its simplest form if possible: 1. 2 3/4 ÷ 3 1/12 2. 3 2/3 ÷ 4 1/2 3. 5 3/7 ÷ 2 3/9 4. 6 2/3 ÷ 1 1/5
- David 4
David made 4/3 of a quart of fruit juice. Each mug he has holds 1/3 of a quart. How many mugs will David be able to fill?
- Birthday party
You are having a birthday party and are inviting 6 friends. You have 9 cupcakes, and you are going to share the cupcakes fairly among you and your 6 friends. How many cupcakes each friend will receive?
- Two-thirds 15
Two-thirds of a pie has already been eaten. What fraction of the pie would still leave if John ate 1/2 of what of the remaining pie?
- Julian 2
Julian and two of his friends will share 1/4 of a pizza. How much will each person get?
- Solve 21
Solve the following problem and write the answer as a mixed number in the lowest terms: 8/11 ÷ 4/9.
- One half 2
One-half pizza will be divided among three pupils. Each pupil receives 1/6. Is it true or false?
- Mrs. Glover
Mrs. Glover is making brownies for the girls' tennis team. She took 1/5 of the leftover brownies to school to give to her three friends. How much did each friend get?
- Frac answer
What is the answer to 1/2 ÷ 5/7?
- Convert 6
Convert to a decimal 15/100.
- There 20
There is 1/2 of a pizza left for four friends to share. What fraction of a pizza will each friend get to eat?
- Chocolate division
How much would everyone get if I had 4/5 of a chocolate bar and wanted to split it evenly among three people?
more math problems »