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:
(3 1/3) : 4 = 5/6 ≅ 0.8333333
Spelled result in words is five sixths.How do we solve fractions step by step?
- Conversion a mixed number 3 1/3 to a improper fraction: 3 1/3 = 3 1/3 = 3 · 3 + 1/3 = 9 + 1/3 = 10/3
To find a new numerator:
a) Multiply the whole number 3 by the denominator 3. Whole number 3 equally 3 * 3/3 = 9/3
b) Add the answer from the previous step 9 to the numerator 1. New numerator is 9 + 1 = 10
c) Write a previous answer (new numerator 10) over the denominator 3.
Three and one third is ten thirds. - Divide: 10/3 : 4 = 10/3 · 1/4 = 10 · 1/3 · 4 = 10/12 = 2 · 5 /2 · 6 = 5/6
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 4/1 is 1/4) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 2 gives 5/6.
In other words - ten thirds divided by four is five sixths.
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:
- In dividing
In dividing fractions, get the reciprocal of the divisor and change the division symbol to the multiplication symbol. 2/3 : 5/6 - Marshall 2
Marshall Track team. After the race, the team goes to Connor's Pizza Palace. The pizza slices served at the Pizza Palace are ¼ of a whole pizza. There are 2 pizzas ready to be served. Nine students come in for lunch. Is there enough pizza for every studen - Julian 3
Julian had 7 cookies and gave half of them to a friend. How many cookies did his friend get? - 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? - Divide 6677
How do we call one part when we divide the whole into 5 (6,7,8,9,10) equal parts? - A quotient
What is the quotient of 3/10 divided by 2/4 as a fraction? - One half 2
One-half pizza will be divided among three pupils. Each pupil receives 1/6. Is it true or false? - Divide 42
Divide. Write your answer in the lowest terms as a proper or improper fraction. (8/25)÷(-4/5) - 4 friends
Four friends share 5/6 of a pizza. What fraction of the pizza does each person get? - 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? - Pie division
5/8 of a pie divided into six pieces. Each friend got 1/6. What fraction of the whole pie does each person receive? - 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? - Divide with remainder
Mrs. Diaz has 4 brownies left. She wants to share the brownies equally among her 5 children. Which of the following shows the amount of brownies each child can receive? - 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? - Pieces of wood
How many pieces of wood can each student have if there are 12 pieces and each student needs 1/4 of a piece?
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