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:
12 5/8 ÷ 3 19/24 = 303/91 = 3 30/91 ≅ 3.3296703
Spelled result in words is three hundred three ninety-firsts (or three and thirty ninety-firsts).How do we solve fractions step by step?
- Conversion a mixed number 12 5/8 to a improper fraction: 12 5/8 = 12 5/8 = 12 · 8 + 5/8 = 96 + 5/8 = 101/8
To find a new numerator:
a) Multiply the whole number 12 by the denominator 8. Whole number 12 equally 12 * 8/8 = 96/8
b) Add the answer from the previous step 96 to the numerator 5. New numerator is 96 + 5 = 101
c) Write a previous answer (new numerator 101) over the denominator 8.
Twelve and five eighths is one hundred one eighths. - Conversion a mixed number 3 19/24 to a improper fraction: 3 19/24 = 3 19/24 = 3 · 24 + 19/24 = 72 + 19/24 = 91/24
To find a new numerator:
a) Multiply the whole number 3 by the denominator 24. Whole number 3 equally 3 * 24/24 = 72/24
b) Add the answer from the previous step 72 to the numerator 19. New numerator is 72 + 19 = 91
c) Write a previous answer (new numerator 91) over the denominator 24.
Three and nineteen twenty-fourths is ninety-one twenty-fourths. - Divide: 101/8 : 91/24 = 101/8 · 24/91 = 101 · 24/8 · 91 = 2424/728 = 8 · 303 /8 · 91 = 303/91
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 91/24 is 24/91) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 8 gives 303/91.
In other words - one hundred one eighths divided by ninety-one twenty-fourths is three hundred three ninety-firsts.
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:
- 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.
- 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
- 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 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?
- What number 2
What number is between 3 1/4 and 3 1/8? Write at least three numbers.
- Playing games
In a school, 9/10 of the students take part. 2/3 of these play football. What fraction of the students play football?
- Three friends
You and your friends are playing basketball. You make 7 out of 15 shots. Your first friend makes 6 out of 10 shots and your second friend makes 5 out of 12 shots. Who is the better shooter (write a, b, c)? How would you solve the problem using what you kn
- Andy and Mike
Mike and Andy are each reading the same book. Mike read 2/4 of the book on Tuesday and 1/3 of the book on Wednesday. Andy read 1/2 of the book on Tuesday and 1/5 of the book on Wednesday. Andy says that altogether he read more of the book on Tuesday and W
- Place 2
Place the correct symbol, < or > between the twos numbers: 4/7? 5/6
- The fuel
The car's fuel was ¾ full at the beginning of the week. At the end of the week, there was ⅛ of a tank left. a. Did the car use more or less than ½ of a fuel tank? How do you know? b. How much more or less than ½ of a tank did it use? Show your work using
- 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?
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