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:
(5 1/4) : 12 = 7/16 = 0.4375
Spelled result in words is seven sixteenths.How do we solve fractions step by step?
- Conversion a mixed number 5 1/4 to a improper fraction: 5 1/4 = 5 1/4 = 5 · 4 + 1/4 = 20 + 1/4 = 21/4
To find a new numerator:
a) Multiply the whole number 5 by the denominator 4. Whole number 5 equally 5 * 4/4 = 20/4
b) Add the answer from the previous step 20 to the numerator 1. New numerator is 20 + 1 = 21
c) Write a previous answer (new numerator 21) over the denominator 4.
Five and one quarter is twenty-one quarters. - Divide: 21/4 : 12 = 21/4 · 1/12 = 21 · 1/4 · 12 = 21/48 = 3 · 7 /3 · 16 = 7/16
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 12/1 is 1/12) 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 3 gives 7/16.
In other words - twenty-one quarters divided by twelve is seven sixteenths.
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 evaluate from left to right.
Fractions in word problems:
- Soup 4
Cornell makes 11/12 of a gallon of soup. He eats equal portions of soup for 5 days, with no soup remaining after the 5th day. How many gallons of soup did Cornell eat each day?
- 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?
- Divide 42
Divide. Write your answer in lowest terms as a proper or improper fraction. (8/25)÷(-4/5)
- Why is
Why is three divided by one-fifth different from one-fifth divided by three?
- Jaenette
Janette served 3/4 of a pizza to her friends. Each visitor was given 1/4 of the pizza. How many visitors shared the pizza?
- 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?
- In dividing
In dividing fractions, get the reciprocal of the divisor and change the division symbol to the multiplication symbol. 2/3 : 5/6
- One half 2
One-half pizza will be divided among three pupils. Each pupil receives 1/6. Is it true or false?
- Julian 2
Julian and two of his friends will share 1/4 of a pizza. How much will each person get?
- 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?
- Divide 6677
How do we call one part when we divide the whole into 5 (6,7,8,9,10) equal parts?
- Solve 21
Solve the following problem and write the answer as a mixed number in the lowest terms: 8/11 ÷ 4/9.
- Division by reciprocal
What is the corresponding illustration/model of 7÷ 1/3?
- Three 210
Three friends share 4/5 of a pizza. What fraction of pizza does each person get?
- Larry 2
Larry spends half of his workday teaching piano lessons. He sees six students and gives the same amount of time to each. What fraction of his workday is spent with each student?
more math problems »