Simplify 1/4*6
The given question, "Simplify 1/4*6," is a basic arithmetic problem that asks to perform multiplication between a fraction (1/4) and a whole number (6). The request is to find the product of these two numbers, which involves multiplying the numerator of the fraction by the whole number and keeping the denominator the same if applicable, thus simplifying the expression to its lowest terms or to a whole number if possible.
$\frac{1}{4} \cdot 6$
Answer
Solution:
Step 1: Identify and eliminate common factors.
- Step 1.1: Extract the factor of $2$ from the denominator $4$. $\frac{1}{2 \times 2} \cdot 6$
- Step 1.2: Extract the factor of $2$ from the numerator $6$. $\frac{1}{2 \times 2} \cdot (2 \times 3)$
- Step 1.3: Remove the common factor of $2$. $\frac{1}{\cancel{2} \times 2} \cdot (\cancel{2} \times 3)$
- Step 1.4: Simplify the expression. $\frac{1}{2} \cdot 3$
Step 2: Multiply the simplified fractions.
- Combine $\frac{1}{2}$ with $3$ to get $\frac{3}{2}$.
Step 3: Present the final result in various formats.
- Exact Form: $\frac{3}{2}$
- Decimal Form: $1.5$
- Mixed Number Form: $1 \frac{1}{2}$
Knowledge Notes:
Simplifying fractions involves finding and canceling out common factors between the numerator and the denominator.
A common factor is a number that divides exactly into two or more other numbers.
When simplifying expressions, it is helpful to break down composite numbers into their prime factors to easily identify common factors.
After canceling common factors, the remaining numbers can be multiplied to find the simplified form of the original expression.
The result of a simplified fraction can be expressed in different forms: as an exact fraction, a decimal, or a mixed number.
A mixed number consists of a whole number and a proper fraction, which is useful when expressing fractions greater than one in a more readable form.
