Fraction calculator
This 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 fraction value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.
Result:
3 2/3 - 5 5/9 = -17/9 = -1 8/9 ≅ -1.8888889
Spelled result in words is minus seventeen ninths (or minus one and eight ninths).How do you solve fractions step by step?
- Conversion a mixed number 3 2/3 to a improper fraction: 3 2/3 = 3 2/3 = 3 · 3 + 2/3 = 9 + 2/3 = 11/3
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 previous step 9 to the numerator 2. New numerator is 9 + 2 = 11
c) Write a previous answer (new numerator 11) over the denominator 3.
Three and two thirds is eleven thirds - Conversion a mixed number 5 5/9 to a improper fraction: 5 5/9 = 5 5/9 = 5 · 9 + 5/9 = 45 + 5/9 = 50/9
To find a new numerator:
a) Multiply the whole number 5 by the denominator 9. Whole number 5 equally 5 * 9/9 = 45/9
b) Add the answer from previous step 45 to the numerator 5. New numerator is 45 + 5 = 50
c) Write a previous answer (new numerator 50) over the denominator 9.
Five and five ninths is fifty ninths - Subtract: 11/3 - 50/9 = 11 · 3/3 · 3 - 50/9 = 33/9 - 50/9 = 33 - 50/9 = -17/9
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 9 = 27. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eleven thirds minus fifty ninths = minus seventeen ninths.
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 are using mixed numbers, leave a space between the whole and fraction part.Mixed numerals (mixed fractions or mixed numbers) 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 signs for fraction line and division, use 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
• exponentiation of fraction: 3/5^3
• 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 /) has the same priority and then must evaluate from left to right.
Fractions in word problems:
- Package
The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
- 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 explain why he is correct or incorrect.
- Whole pie
If you have one whole pie and 1/2 is giving away and 1/4 is eaten and how much do you have left
- Sundar
Sundar has 50 chocolates. He gave 2/5 of these chocolates to Ram and he ate 1/5 of them. How many chocolates are left with Sundar?
- The entity
What is the difference between seven tenths of an entity and seven fifteenths of the same entity? Please solve it for me.
- From a
From a 1 meter ribbon, Ericka cut 2/4 meter for her hat and another 1/4 meter for her bag. How long was the remaining piece?
- Evaluate - lowest terms
Evaluate: 16/25 - 11/25 (Express answer as a fraction reduced to lowest terms. )
- Bucket
Kim and Joey share a 30-ounce bucket of clay. By the end of the week, Kim has used 3/10 of the bucket, and Joey has used 3/5 of the bucket of clay. How many ounces are left in the bucket?
- Mr. Vandar
Mr. Vandar washed 1/4 of his laundry . His son washed 2/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
- The recipe
The recipe they are following requires 7/8 cups of milk, Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe?
- Cherries 2
If a farmer reaped 636 cherries and he sold one third to a shop keeper, how many did he retain?
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