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:
5 1/2 * 3 3/4 = 165/8 = 20 5/8 = 20.625
Spelled result in words is one hundred sixty-five eighths (or twenty and five eighths).How do you solve fractions step by step?
- Conversion a mixed number 5 1/2 to a improper fraction: 5 1/2 = 5 1/2 = 5 · 2 + 1/2 = 10 + 1/2 = 11/2
To find a new numerator:
a) Multiply the whole number 5 by the denominator 2. Whole number 5 equally 5 * 2/2 = 10/2
b) Add the answer from previous step 10 to the numerator 1. New numerator is 10 + 1 = 11
c) Write a previous answer (new numerator 11) over the denominator 2.
Five and one half is eleven halfs - Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4
To find a new numerator:
a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4
b) Add the answer from previous step 12 to the numerator 3. New numerator is 12 + 3 = 15
c) Write a previous answer (new numerator 15) over the denominator 4.
Three and three quarters is fifteen quarters - Multiple: 11/2 * 15/4 = 11 · 15/2 · 4 = 165/8
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(165, 8) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eleven halfs multiplied by fifteen quarters = one hundred sixty-five eighths.
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:
- Rhea answered
Rhea answered 5/11 in the questions correctly and Precious answered 7/11 of it correctly. If each problem is worth the same amount, who got the higher score?
- Daniel
Daniel ate 4/5 of his pizza and Shawn ate 5/6 of his pizza. Who ate more?
- One quarter
Which of the following has a sum of 3/4? A. 1/2+1/4 B. 1/2+1/3 C. 1/4+1/8 D. 1/9+1/12
- Equivalent fractions
Are these two fractions -4/9 and 11/15 equivalent?
- Sort fractions
Which of the following fractions is the largest? 29/36 5/6 7/9 3/4
- Roma ate
Roma ate 2/5 of a cake while Somya ate 3/7 of the same cake. Who ate more and by how much?
- 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?
- Ten fractions
Write ten fractions between 1/3 and 2/3
- Luke
Luke, Seth, and Anja have empty glasses. Mr. Gabel pours 3/6 cup of orange juice in Seth's glass. Then he pouts 1/6 cup of orange juice in Luke's glass and 2/6 cup of orange juice in Anja's glass. Who gets the MOST orange juice?
- Paper collecting
At the paper collecting contest gathered Franta 2/9 ton, Karel 1/4 ton, and Patrick 19/36 tons of paper. Who has gathered the most and the least?
- Math test
Brayden was solving some math problems for the math team. He answered 2 math problems. Matthew answered 3, John answered 1 reasoning. Matthew 1/2 times as many. Brayden said that 2/6. Is he correct? Why or why not? Be sure to explain your answer.
more math problems »