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:
7 3/10 + 9 12/15 = 171/10 = 17 1/10 = 17.1
Spelled result in words is one hundred seventy-one tenths (or seventeen and one tenth).How do we solve fractions step by step?
- Conversion a mixed number 7 3/10 to a improper fraction: 7 3/10 = 7 3/10 = 7 · 10 + 3/10 = 70 + 3/10 = 73/10
To find a new numerator:
a) Multiply the whole number 7 by the denominator 10. Whole number 7 equally 7 * 10/10 = 70/10
b) Add the answer from the previous step 70 to the numerator 3. New numerator is 70 + 3 = 73
c) Write a previous answer (new numerator 73) over the denominator 10.
Seven and three tenths is seventy-three tenths. - Conversion a mixed number 9 12/15 to a improper fraction: 9 12/15 = 9 12/15 = 9 · 15 + 12/15 = 135 + 12/15 = 147/15
To find a new numerator:
a) Multiply the whole number 9 by the denominator 15. Whole number 9 equally 9 * 15/15 = 135/15
b) Add the answer from the previous step 135 to the numerator 12. New numerator is 135 + 12 = 147
c) Write a previous answer (new numerator 147) over the denominator 15.
Nine and twelve fifteenths is one hundred forty-seven fifteenths. - Add: 73/10 + 147/15 = 73 · 3/10 · 3 + 147 · 2/15 · 2 = 219/30 + 294/30 = 219 + 294/30 = 513/30 = 3 · 171/3 · 10 = 171/10
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(10, 15) = 30. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 15 = 150. In the following intermediate step, cancel by a common factor of 3 gives 171/10.
In other words - seventy-three tenths plus one hundred forty-seven fifteenths is one hundred seventy-one tenths.
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:
- A man 9
A man earns $2400 in his monthly salary. He spends 3/5 of his salary on food and rent. This month he decided to buy his family presents. What fraction of his money does he spend on presents? - My whole
My whole number is 88 if you add 5 thousandths, 8 tenths, and 7 thousandths. What number will I be? - Sum of three fractions
What is the sum of 6/7, 1/2 & 3/4? - Evaluate 39
Evaluate the expression shown below and write your answer as a fraction in simplest form. (5)/(12) + (1)/(9) start fraction, 5, divided by, 12, end fraction, plus, one nine. - Maximo
Maximo had 4/6 of a pancake. Kayla gave him another 5/6 of a similar pancake. How many pancakes did Maximo have in the end? - Pizza 4
Marcus ate half pizza on Monday night. He then ate one-third of the remaining pizza on Tuesday. Which of the following expressions show how much pizza Marcus ate in total? - HW store
At the hardware store, 1/4 of the nails are size 2d, and 1/6 of the nails are size 4d. What fraction of the nails are either size 2d or 4d? - One evening
One evening, a restaurant served a total of 1/2 of a loaf of wheat bread and 7/8 of a loaf of white bread. How many loaves were served in all? - There 22
There is 5/8 of a pizza in one box and 9/12 of a pizza in another box. How much do you have altogether? - Adding two fractions
Find the missing fraction: 2/5 + 7/10 = - Randy
Randy solved the following problem: 7/8 + 9/16. He said: I can add 7 and 9 to get 16 and add 8 and 15 to get 23. The answer is 16/23. Is randy correct? Explain. - Katelyn
Katelyn ate ⅓ of an apple pie, and Chad ate ⅜ of the same pie. What fraction of the pie was eaten? - Samuel
Samuel has 1/3 of a bag of rice, and Isabella has a 1/2 bag of rice. What fraction of our bag of rice do they have altogether? - Integer add to fraction
Seven is added to the sum of 4/5 and 6/7 - Sum three fractions
Work out the sum of 1/4, 1/5, and 3/10.
more math problems »