This calculator adds two fractions. When fractions have different denominators, firstly convert all fractions to common denominator. Find Least Common Denominator (LCD) or simple multiply all denominators to find common denominator. When all denominators are same, simply add the numerators and place the result over the common denominator. Then simplify the result to the lowest terms or a mixed number.
The result:
1/2 + 2/9 = 13/18 ≅ 0.7222222
Spelled result in words is thirteen eighteenths.
How do we solve fractions step by step?
- Add: 1/2 + 2/9 = 1 ·
9/2 · 9 + 2 · 2/9 · 2 = 9/18 + 4/18 = 9 + 4/18 = 13/18
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 9) = 18. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 9 = 18. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one half plus two ninths is thirteen eighteenths.
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 signs 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
| + | 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) |
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 /) has the same priority and then must evaluate from left to right.
The below workout with step by step calculation shows how to find what is 2/9 minus 1/6 in simplest form by using the following methods:
1. LCM method,
2. Cross multiplication method.
Problem and Workout - LCM Method:
What is 2/9 minus 1/6 as a fraction?
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 2/9
Fraction
B: 1/6What to be found?
2/9-1/6 = ?
Find what's the difference between 2/9 and 1/6.
step 2 Compare the denominators of fractions 2/9 and 1/6 to identify whether it is a like or unlike fraction subtraction. Since the denominators of given fractions 2/9 and 1/6 are not equal, it is said to be unlike fractions subtraction.
step 3For unlike fractions subtraction, find the LCM (least common multiple) of both denominators of fractions 2/9 and 1/6:
The LCM of 9 and 6 is 18.
step 4 Write the fractions 2/9 and 1/6 in the subtraction expression form and multiply LCM with all the numerators and denominators of both fractions.
=2/9-1/6
=(2 x 18)/(9 x
18)-(1 x 18)/(6 x 18)
step 5 Simplify the expression to have common denominator:
=4/18-3/18
step 6 Take the common values out and rewrite the above expression like the below:
=1/18 x (4/1-3/1)
=1/18 x (4 - 3)
step 7Simplify the above expression further:
=1/18 x 1
=1/18
2/9-1/6=1/18
Hence,
2/9 minus 1/6 equals to 1/18 in fraction.
Problem and Workout - Cross Multiplication Method
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 2/9
Fraction B: 1/6What to be found?
2/9-1/6 = ?
Find what's the difference between 2/9 and 1/6.
step 2 Find the product of numerator of Fraction A and denominator of Fraction B (2 x 6), find the
product of numerator of Fraction B and denominator of Fraction A (1 x 9), and find the product of both denominators of Fraction A and Fraction B (9 x 6) and rewrite the equation as like the below:
= (2 x 6) - (1 x 9)/(9 x 6)
step 3 Simplify and rewrite the fraction:
= (12 - 9)/54
= 3/54
= 1/18
2/9-1/6 =
1/18
Hence,
2/9 minus 1/6 = 1/18