Evaluate (9*(3+3))÷6
The question is asking to perform a mathematical calculation following the order of operations, otherwise known as PEMDAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). The expression provided has parentheses, multiplication, and division. The task is to first add the numbers inside the parentheses, then multiply the result by the number outside the parentheses, and finally divide the product by the number mentioned at the end of the expression.
$9 \cdot \left(\right. 3 + 3 \left.\right) \div 6$
Answer
Solution:
Step:1
Express the division as a ratio: $\frac{9 \cdot (3 + 3)}{6}$.
Step:2
Identify and eliminate common factors between numerator and denominator.
Step:2.1
Extract the factor of $3$ from the numerator: $\frac{3 \cdot (3 \cdot (3 + 3))}{6}$.
Step:2.2
Proceed to reduce the fraction by canceling out common factors.
Step:2.2.1
Factor out $3$ from the denominator: $\frac{3 \cdot (3 \cdot (3 + 3))}{3 \cdot 2}$.
Step:2.2.2
Eliminate the common factor of $3$: $\frac{\cancel{3} \cdot (3 \cdot (3 + 3))}{\cancel{3} \cdot 2}$.
Step:2.2.3
Reformulate the fraction: $\frac{3 \cdot (3 + 3)}{2}$.
Step:3
Combine the sum within the parentheses: $\frac{3 \cdot 6}{2}$.
Step:4
Finalize by simplifying the fraction.
Step:4.1
Calculate the product of $3$ and $6$: $\frac{18}{2}$.
Step:4.2
Divide $18$ by $2$ to get the result: $9$.
Knowledge Notes:
The problem at hand involves basic arithmetic operations and an understanding of how to simplify expressions. Here are the relevant knowledge points:
Order of Operations: In mathematics, the order of operations dictates that calculations within parentheses are performed first, followed by multiplication and division from left to right. This problem requires us to apply this rule.
Division as a Fraction: Division can be represented as a fraction, where the dividend (the number being divided) is the numerator and the divisor (the number by which the dividend is divided) is the denominator.
Simplifying Fractions: To simplify a fraction, one can cancel out any common factors that appear in both the numerator and the denominator. This is based on the property that $\frac{a \cdot c}{b \cdot c} = \frac{a}{b}$, provided $c \neq 0$.
Multiplication and Division: When simplifying expressions, multiplication is the process of combining groups of equal size, and division is the process of splitting into equal parts. In this problem, we multiply and divide integers.
Common Factors: A common factor is a number that divides exactly into two or more other numbers. In this problem, we identify $3$ as a common factor of both the numerator and the denominator, allowing us to simplify the fraction.
By understanding and applying these concepts, the given expression can be evaluated step by step to arrive at the final result.
