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 × 2 1/7 = 55/7 = 7 6/7 ≅ 7.8571429
Spelled result in words is fifty-five sevenths (or seven and six sevenths).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 2 1/7 to a improper fraction: 2 1/7 = 2 1/7 = 2 · 7 + 1/7 = 14 + 1/7 = 15/7
To find a new numerator:
a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7
b) Add the answer from previous step 14 to the numerator 1. New numerator is 14 + 1 = 15
c) Write a previous answer (new numerator 15) over the denominator 7.
Two and one seventh is fifteen sevenths - Multiple: 11/3 * 15/7 = 11 · 15/3 · 7 = 165/21 = 55 · 3/7 · 3 = 55/7
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(165, 21) = 3. In the following intermediate step, cancel by a common factor of 3 gives 55/7.
In other words - eleven thirds multiplied by fifteen sevenths = fifty-five sevenths.
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:
- Daniel
Daniel ate 4/5 of his pizza and Shawn ate 5/6 of his pizza. Who ate more?
- 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?
- Equivalent fractions
Are these two fractions -4/9 and 11/15 equivalent?
- 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
- Ten fractions
Write ten fractions between 1/3 and 2/3
- 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?
- 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 small
A small book took one-sixth of a ream of paper to make. The team said they could make nine books from 3 whole reams of paper. Are they correct?
- Comparing mixed numbers
Which of the following expression will give a sum of 7 and 3/10? A. 3 and 1/5+ 4 and 2/2 B. 3 and 1/10+4 and 2/10 C. 1/10+ 7 and 2/5 D. 2 and 1/10+ 5 and 3/10
- Dividends
The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least?
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