Fraction calculator
This calculator divides fractions. The first step makes the reciprocal value of the second fraction - exchange numerator and denominator of 2nd fraction. Then multiply both numerators and place the result over the product of both denominators. Then simplify the result to the lowest terms or a mixed number.
The result:
2/3 / 4/5 = 5/6 ≅ 0.8333333
Spelled result in words is five sixths.How do we solve fractions step by step?
- Divide: 2/3 : 4/5 = 2/3 · 5/4 = 2 · 5/3 · 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 4/5 is 5/4) 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 - two thirds divided by four fifths 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) - 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:
- 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?
- Frac answer
What is the answer to 1/2 ÷ 5/7?
- Fractions 4
How many 2/3s are in 6?
- 4 friends
Four friends share 5/6 of a pizza. What fraction of the pizza does each person get?
- Solve 21
Solve the following problem and write the answer as a mixed number in lowest terms: 8/11 ÷ 4/9.
- How many 29
How many 5/8s's are in 1? (To write a whole number and fraction: 2 3/4)
- Quotient and division
Find the quotient of 3/4 and 1/4.
- 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?
- One fourth
One-fourth of an apple pie is left for two family members to share equally. What fraction of the original pie will each member get?
- Candy bars
Sheldon has four candy bars and wants to split them among his five friends. If each person gets the same amount, what part of the candy bar will each friend get? Show your work.
- Fraction expression
Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
more math problems »