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 1/5 + 9 1/2 = 177/10 = 17 7/10 = 17.7
Spelled result in words is one hundred seventy-seven tenths (or seventeen and seven tenths).How do we solve fractions step by step?
- Conversion a mixed number 8 1/5 to a improper fraction: 8 1/5 = 8 1/5 = 8 · 5 + 1/5 = 40 + 1/5 = 41/5
To find a new numerator:
a) Multiply the whole number 8 by the denominator 5. Whole number 8 equally 8 * 5/5 = 40/5
b) Add the answer from the previous step 40 to the numerator 1. New numerator is 40 + 1 = 41
c) Write a previous answer (new numerator 41) over the denominator 5.
Eight and one fifth is forty-one fifths. - Conversion a mixed number 9 1/2 to a improper fraction: 9 1/2 = 9 1/2 = 9 · 2 + 1/2 = 18 + 1/2 = 19/2
To find a new numerator:
a) Multiply the whole number 9 by the denominator 2. Whole number 9 equally 9 * 2/2 = 18/2
b) Add the answer from the previous step 18 to the numerator 1. New numerator is 18 + 1 = 19
c) Write a previous answer (new numerator 19) over the denominator 2.
Nine and one half is nineteen halfs. - Add: 41/5 + 19/2 = 41 · 2/5 · 2 + 19 · 5/2 · 5 = 82/10 + 95/10 = 82 + 95/10 = 177/10
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(5, 2) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 2 = 10. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - forty-one fifths plus nineteen halfs is one hundred seventy-seven 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
Op | 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) |
Fractions in word problems:
- Closer to one
Here are two sums: A=1/2 + 1/3 and B=1/5 + 1/3. Which of the two sums is closer in value to 1? You must show your working and state clearly whether the answer is A or B. - Anesa
Anesa ate 3/4 of her pizza, and Eman ate 1/4 of her pizza. Who ate the greater part of the pizza? - 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.
more math problems »