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:
16 3/9 - 10 2/5 = 89/15 = 5 14/15 ≅ 5.9333333
Spelled result in words is eighty-nine fifteenths (or five and fourteen fifteenths).How do we solve fractions step by step?
- Conversion a mixed number 16 3/9 to a improper fraction: 16 3/9 = 16 3/9 = 16 · 9 + 3/9 = 144 + 3/9 = 147/9
To find a new numerator:
a) Multiply the whole number 16 by the denominator 9. Whole number 16 equally 16 * 9/9 = 144/9
b) Add the answer from the previous step 144 to the numerator 3. New numerator is 144 + 3 = 147
c) Write a previous answer (new numerator 147) over the denominator 9.
Sixteen and three ninths is one hundred forty-seven ninths. - Conversion a mixed number 10 2/5 to a improper fraction: 10 2/5 = 10 2/5 = 10 · 5 + 2/5 = 50 + 2/5 = 52/5
To find a new numerator:
a) Multiply the whole number 10 by the denominator 5. Whole number 10 equally 10 * 5/5 = 50/5
b) Add the answer from the previous step 50 to the numerator 2. New numerator is 50 + 2 = 52
c) Write a previous answer (new numerator 52) over the denominator 5.
Ten and two fifths is fifty-two fifths. - Subtract: 147/9 - 52/5 = 147 · 5/9 · 5 - 52 · 9/5 · 9 = 735/45 - 468/45 = 735 - 468/45 = 267/45 = 3 · 89/3 · 15 = 89/15
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(9, 5) = 45. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 5 = 45. In the following intermediate step, cancel by a common factor of 3 gives 89/15.
In other words - one hundred forty-seven ninths minus fifty-two fifths is eighty-nine fifteenths.
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) : 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:
- 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 - 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. - Anesa
Anesa ate 3/4 of her pizza, and Eman ate 1/4 of her pizza. Who ate the greater part of the pizza? - A student 4
A student knows that ¾ x 4 is the same as 4 x ¾ The student assumes that 4 ÷ ¾ is the same as ¾ ÷ 4 Is the student correct? - 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 k - Four children
Father saved a certain amount of money in the bank. He divided this amount equally among his four children. One of the daughters donated 3/7 of the amount she received to her son and 4/9 of it to her daughter. What part of the total amount saved did the s - 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? - Place 2
Place the correct symbol, < or >, between the two numbers: 4/7? 5/6 - Ten fractions
Write ten fractions between 1/3 and 2/3 - Which 15
Which is larger, 1 2/7 or 10/4? - 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? - Small and large bread
Kipton's aunt bakes a large loaf of bread and a small loaf of bread. She cuts each loaf into tenths and gives Kipton 2 tenths of each loaf to take home. Kipton writes the equation 2/10 + 2/10 = 4/10 to show the amount of bread he takes home. Explain Kipto - Order fractions
Arrange in ascending order 1 5/6, 11/9, 5/16, 3
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