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Fill in the Blanks by Evaluating Groups in the Expression $8^2 \\cdot (2+6) \\div 4$
Mathematics
Grade 6
Question Content
First, evaluate the groups. Fill in the blanks: $8^{2} \\cdot (2 + 6) \\div 4 = \\square ? \\cdot \\square ? \\div 4$
Correct Answer
64, 8
Detailed Solution Steps
1
Step 1: Identify the grouped/parenthetical and exponential terms that need to be evaluated first, following the order of operations (PEMDAS/BODMAS).
2
Step 2: Calculate the exponential term $8^2$: $8 \\times 8 = 64$.
3
Step 3: Calculate the grouped addition term $(2 + 6)$: $2 + 6 = 8$.
4
Step 4: Substitute the evaluated values back into the original expression to fill the blanks: $8^{2} \\cdot (2 + 6) \\div 4 = 64 \\cdot 8 \\div 4$.
Knowledge Points Involved
1
Order of Operations (PEMDAS/BODMAS)
PEMDAS/BODMAS is a set of rules defining the sequence to evaluate mathematical expressions: Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication and Division (left to right), and finally Addition and Subtraction (left to right). It ensures consistent results when solving expressions with multiple operations.
2
Exponential Notation
Exponential notation like $a^b$ means multiplying the base $a$ by itself $b$ times. For $8^2$, the base is 8 and the exponent is 2, so it equals $8 \\times 8 = 64$. This is used to represent repeated multiplication concisely.
3
Parenthetical Expressions
Expressions enclosed in parentheses ( ) must be evaluated first in the order of operations. They group terms to indicate that the operation inside should be computed before interacting with other parts of the expression, such as $(2+6)$ which simplifies to 8.
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