Fraction calculator
This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.
The result:
4 1/3 - 2 2/3 = 5/3 = 1 2/3 ≅ 1.6666667
The spelled result in words is five thirds (or one and two thirds).How do we solve fractions step by step?
- Conversion a mixed number 4 1/3 to a improper fraction: 4 1/3 = 4 1/3 = 4 · 3 + 1/3 = 12 + 1/3 = 13/3
To find a new numerator:
a) Multiply the whole number 4 by the denominator 3. Whole number 4 equally 4 * 3/3 = 12/3
b) Add the answer from the previous step 12 to the numerator 1. New numerator is 12 + 1 = 13
c) Write a previous answer (new numerator 13) over the denominator 3.
Four and one third is thirteen thirds. - Conversion a mixed number 2 2/3 to a improper fraction: 2 2/3 = 2 2/3 = 2 · 3 + 2/3 = 6 + 2/3 = 8/3
To find a new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
b) Add the answer from the previous step 6 to the numerator 2. New numerator is 6 + 2 = 8
c) Write a previous answer (new numerator 8) over the denominator 3.
Two and two thirds is eight thirds. - Subtract: 13/3 - 8/3 = 13 - 8/3 = 5/3
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 3) = 3. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 3 = 9. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirteen thirds minus eight thirds is five thirds.
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
• square root of a fraction: sqrt(1/16)
• 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:
- Orchard 5421
The orchard has 600 apple trees. On the first day, they cut 1/5 and 2/8 of the total number of trees on the second day. How many more trees do they have to harvest? - Second 82446
Petr read ⅜ of the book in the first week, ¼ of the book in the second week, and ⅒ of the book in the third week. The book has 240 pages. How many pages does Peter have left to read? - Candy
You stop at hasty to buy candy. You give half of the bag to one friend. Then give a quarter to another friend. Later two more friends come, and you give each of them a third of what is in the bag. How many candies did you start with? - Five-eighths 5694
The car's tank was two-twelfths full. When Dad filled the tank with gas, the volume of gas increased by five-eighths of the tank's volume. What fraction of gasoline did the car use when the tank is now 1/3 full?
- Gingerbread house
Janka and Marienka calculated that there were 210 gingerbreads on the gingerbread house. Janko ate one-seventh of all gingerbreads, and Marienka ate a third less than Janko. How many gingerbreads remained in the gingerbread house? - Felipe
Felipe is planning a party. He has $50.00 to spend on sandwiches that cost $2.50 per person, $25.00 to spend on drinks that cost $1.50 per person, and $25.00 to spend on gift bags that cost $3.00 per person. Which expression could be used to show the amou - Mrs. Susan 2
Mrs. Susan received a shipment of 60 novelty baseball caps. Of the caps, 1/3 had bug antennae, 2/5 had moose antlers, and the rest had plastic propellers. How many of the caps had plastic propellers?
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Last Modified: October 9, 2024