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How to Evaluate the Arithmetic Expression 6.25 ÷ 0.5 - 2(2.1)²
Mathematics
Grade 7 (Junior High School)
Question Content
Evaluate the following expression: 6.25 ÷ 0.5 - 2(2.1)²
Correct Answer
7.39
Detailed Solution Steps
1
Step 1: Follow the order of operations (PEMDAS/BODMAS) and first calculate the exponent: (2.1)² = 2.1 × 2.1 = 4.41
2
Step 2: Perform the multiplication operation: 2 × 4.41 = 8.82
3
Step 3: Carry out the division operation: 6.25 ÷ 0.5 = 12.5
4
Step 4: Finally, do the subtraction operation: 12.5 - 8.82 = 7.39
Knowledge Points Involved
1
Order of Operations (PEMDAS/BODMAS)
PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) is a set of rules that dictates the sequence to solve mathematical expressions. It ensures consistent results by prioritizing operations from highest to lowest priority. This rule applies to all arithmetic expressions with multiple operations.
2
Exponentiation of Decimals
Exponentiation of a decimal means multiplying the decimal number by itself the number of times indicated by the exponent. For example, (a.b)² = (a.b) × (a.b). This is used to calculate squares, cubes, etc., of non-whole numbers in arithmetic expressions.
3
Decimal Multiplication and Division
Decimal multiplication involves multiplying decimals as whole numbers and then placing the decimal point based on the total number of decimal places in the factors. Decimal division can be simplified by converting the divisor to a whole number by multiplying both the divisor and dividend by a power of 10, then performing whole number division. These operations are foundational for solving arithmetic expressions with non-integer values.
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