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:
- 3/8 * -4/9 = 1/6 ≅ 0.1666667
Spelled result in words is one sixth.How do we solve fractions step by step?
- Unary minus: -3/8 = -3/8
- Multiple: the result of step No. 1 * (-4) = -3/8 * (-4) = -3 · (-4)/8 · 1 = 12/8 = 3 · 4/2 · 4 = 3/2
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(12, 8) = 4. In the following intermediate step, cancel by a common factor of 4 gives 3/2.
In other words - minus three eighths multiplied by minus four is three halfs. - Divide: the result of step No. 2 : 9 = 3/2 : 9 = 3/2 · 1/9 = 3 · 1/2 · 9 = 3/18 = 3 · 1 /3 · 6 = 1/6
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 9/1 is 1/9) 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 1/6.
In other words - three halfs divided by nine is one sixth.
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:
- Peter's calculation
Peter wrote the following: 7 1/4 - 3 3/4 = 4 2/4 = 4 1/2 . Is Peter's calculation correct? Using words (math vocabulary) and numbers to explain why he is correct or incorrect. - A man 9
A man earns $2400 in his monthly salary. He spends 3/5 of his salary on food and rent. This month he decided to buy his family presents. What fraction of his money does he spend on presents? - A chocolate 2
A chocolate cake is cut into twelve equal pieces. Mr. Greedy eats five pieces at break time with his mug of tea. What fraction of the cake is left? - Paul ate
Paul ate 2/8 of a cake and his brother 3/8. What fraction of the cake is left for the parents? - Sadie
Sadie practiced her spelling words for 3/4 of an hour, and Max practiced his spelling words for 5/12 of an hour. In the simplest form, how much longer did Sadie practice than Max? - Difference between fractions
What is the difference when you take away 1/6 from 2/8? - A cake
A cake has 46 slices. Harry ate 16 slices, and Jack ate 26 slices, Dave ate 0 & Mary ate 1 slice. What fraction of the cake is remaining? - The bread 2
Sandra and Tylar baked two loaves of bread. On Monday, they ate 1/2 of one loaf. On Tuesday, they ate 1/3 of one loaf of bread. How much bread is left? - Subtract 19
Subtract as indicated. 11/10 - (- 2/5) - Unload truck
Andy has just moved and is beginning to unload his boxes. The truck is currently 11/12 of the way full. He unloads 1/4 more of it. How much more does he have to unload? - The entity
What is the difference between seven-tenths of an entity and seven-fifteenths of the same entity? Please solve it for me. - Fraction subtraction
Find the difference. Reduce the answer to the simplest form: 1.) ¾ - 1/8 = 2.) ½ - 1/8 = 3.) ½ - 1/6 = 4.) 7/8 - ¾ = 5.) 1/5 - 1/10 - Before 4
Before a journey, the petrol gauge showed my car's tank was half full. When I returned home, it was one-third full. What fraction of a tank of petrol had I used? - A housewife
A housewife spent 3/7 of her money in the market and 1/2 of the remainder in the shop. What fraction of her money is left? - Shopper
Eva spent 1/4 in one store and 1/3 in another. What fraction is left?
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