Evaluate 3+(-1/2)
The question asks to perform an arithmetic operation where two numbers need to be added together: the integer 3 and the negative fraction -1/2. Essentially, the problem is requesting to find the sum of a positive whole number and a negative fractional number.
$3 + \left(\right. - \frac{1}{2} \left.\right)$
Answer
Solution:
Step 1:
Eliminate the parentheses to simplify the expression: $3 - \frac{1}{2}$
Step 2:
Convert the integer to a fraction with the same denominator as $\frac{1}{2}$ by multiplying by $\frac{2}{2}$: $3 \times \frac{2}{2} - \frac{1}{2}$
Step 3:
Merge the integer with the fraction: $\frac{3 \times 2}{2} - \frac{1}{2}$
Step 4:
Write both terms over the shared denominator: $\frac{3 \times 2 - 1}{2}$
Step 5:
Perform the arithmetic operations in the numerator.
Step 5.1:
First, multiply $3$ by $2$: $\frac{6 - 1}{2}$
Step 5.2:
Next, subtract $1$ from $6$: $\frac{5}{2}$
Step 6:
Present the final answer in various formats.
Exact Form: $\frac{5}{2}$
Decimal Form: $2.5$
Mixed Number Form: $2 \frac{1}{2}$
Knowledge Notes:
The problem involves the basic arithmetic operation of addition with a negative fraction. To solve it, we need to understand several key concepts:
Parentheses in Arithmetic: Parentheses indicate which operations should be performed first. In this case, removing the parentheses does not change the operation because there are no operations inside the parentheses to perform first.
Common Denominator: When adding or subtracting fractions, it's necessary to have a common denominator. In this problem, we convert the whole number to a fraction with the same denominator as the fraction we are subtracting.
Fraction Multiplication: To convert a whole number to a fraction with a specific denominator, we multiply the whole number by a fraction that is equivalent to 1 (such as $\frac{2}{2}$) so that the value of the number does not change.
Combining Fractions: With a common denominator, fractions can be combined by adding or subtracting their numerators.
Simplifying Fractions: After combining fractions, the resulting fraction can often be simplified or expressed in different forms, such as a mixed number or decimal.
Equivalent Forms of Numbers: Numbers can be represented in various forms. Fractions can be converted to decimals or mixed numbers, depending on the context or preference for the representation of the number.
In this problem, we used these concepts to combine a whole number and a fraction, simplify the resulting fraction, and express the answer in different forms.
