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:
20 3/4 - 18 2/3 = 25/12 = 2 1/12 ≅ 2.0833333
Spelled result in words is twenty-five twelfths (or two and one twelfth).How do we solve fractions step by step?
- Conversion a mixed number 20 3/4 to a improper fraction: 20 3/4 = 20 3/4 = 20 · 4 + 3/4 = 80 + 3/4 = 83/4
To find a new numerator:
a) Multiply the whole number 20 by the denominator 4. Whole number 20 equally 20 * 4/4 = 80/4
b) Add the answer from the previous step 80 to the numerator 3. New numerator is 80 + 3 = 83
c) Write a previous answer (new numerator 83) over the denominator 4.
Twenty and three quarters is eighty-three quarters. - Conversion a mixed number 18 2/3 to a improper fraction: 18 2/3 = 18 2/3 = 18 · 3 + 2/3 = 54 + 2/3 = 56/3
To find a new numerator:
a) Multiply the whole number 18 by the denominator 3. Whole number 18 equally 18 * 3/3 = 54/3
b) Add the answer from the previous step 54 to the numerator 2. New numerator is 54 + 2 = 56
c) Write a previous answer (new numerator 56) over the denominator 3.
Eighteen and two thirds is fifty-six thirds. - Subtract: 83/4 - 56/3 = 83 · 3/4 · 3 - 56 · 4/3 · 4 = 249/12 - 224/12 = 249 - 224/12 = 25/12
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(4, 3) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 3 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eighty-three quarters minus fifty-six thirds is twenty-five twelfths.
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 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:
- Closer to one
Here are two sums: A=1/2 + 1/3 and B=1/5 + 1/3. Which of the two sums is closer in value to 1? You must show your work and state clearly whether the answer is A or B. - From least to greatest
Which set of rational numbers is arranged from least to greatest? A) -3.5, negative 1 over 4, 2, 1 over 3 B) -3.5, negative 1 over 4, 1 over 3, 2 C) 2, 1 over 3, negative 1 over 4, -3.5 D) negative 1 over 4, 1 over 3, 2, -3.5 - Compare two fractions
Find which is the larger of the two fractions: 11/32, 7/24, by expressing the numbers as a) fractions with the same denominator, b) decimals. - Rhea answered
Rhea answered 5/11 of the questions correctly, and Precious answered 7/11 of them correctly. Who got the higher score if each problem is worth the same amount?
- Anesa
Anesa ate 3/4 of her pizza, and Eman ate 1/4 of her pizza. Who ate the greater part of the pizza? - Same fractions
I remember that 2/2 is equal to 1. 3/3 is equal to 1. Where is the fraction 4/4 located on the number line? - Sort fractions
Which of the following fractions is the largest? 29/36 5/6 7/9 3/4 - Identify improper fraction
How do you identify improper fractions? Which is improper: A) 3/4 B) 32/15 C) 3/9 D) 2 2/11 - Ten fractions
Write ten fractions between 1/3 and 2/3
- The sum
If you add 3/4 and 5/8, what would be the sum? A. more than one B. equal to one C. less than one D. zero - What number 2
What number is between 3 1/4 and 3 1/8? Write at least three numbers. - A laundry
Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed? - Pizza 16
Kevin ate 5/12 of his pizza. Which is a better estimate for the amount of pizza that he ate: A. about half of the pizza or B. almost all of the pizza? - Equivalent fractions
Are these two fractions -4/9 and 11/15 equivalent?
more math problems »