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:
(1/6) : (1/9) = 3/2 = 1 1/2 = 1.5
Spelled result in words is three halfs (or one and one half).How do we solve fractions step by step?
- Divide: 1/6 : 1/9 = 1/6 · 9/1 = 1 · 9/6 · 1 = 9/6 = 3 · 3 /3 · 2 = 3/2
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 1/9 is 9/1) 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 3/2.
In other words - one sixth divided by one ninth is three halfs.
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:
- Divide 13
Divide. Simplify your answer and write it as an improper fraction or whole number. 14÷8/3
- 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?
- 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?
- Three 210
Three friends share 4/5 of a pizza. What fraction of pizza does each person get?
- 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?
- 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.
- 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?
- Pizza 5
You have 2/4 of a pizza, and you want to share it equally between 2 people. How much pizza does each person get?
- 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?
- A lawn
Sean and his sister, Betty, equally mowed 8/9th of the total area of a lawn. What fraction of the total area did each of them mow?
- Julian 2
Julian and two of his friends will share 1/4 of a pizza. How much will each person get?
- 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?
- 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?
- Fraction expression
Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis
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