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:
8 1/2 = 17/2 = 8 1/2 = 8.5
Spelled result in words is seventeen halfs (or eight and one half).How do we solve fractions step by step?
- Conversion a mixed number 8 1/2 to a improper fraction: 8 1/2 = 8 1/2 = 8 · 2 + 1/2 = 16 + 1/2 = 17/2
To find a new numerator:
a) Multiply the whole number 8 by the denominator 2. Whole number 8 equally 8 * 2/2 = 16/2
b) Add the answer from the previous step 16 to the numerator 1. New numerator is 16 + 1 = 17
c) Write a previous answer (new numerator 17) over the denominator 2.
Eight and one half is seventeen halfs.
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
• 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 /) have the same priority and 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?
- Which 14
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
- 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?
- 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.
- 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?
- 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?
- Roma ate
Roma ate 2/5 of the cake while Somya ate 3/7 of the same cake. Who ate more, and by how much?
- Equivalent fractions
Are these two fractions -4/9 and 11/15 equivalent?
- The cost 7
The cost of a pen is Rs. 20/3, and that of a pencil is 25/6. Which costs more and by how much?
- 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
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