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How to Evaluate the Expression $6.25 \\div 0.5 - 2(2.1)^2$
Mathematics
Grade 7
Question Content
Evaluate the following: $6.25 \\div 0.5 - 2(2.1)^2$
Correct Answer
7.39
Detailed Solution Steps
1
Step 1: Follow the order of operations (PEMDAS/BODMAS). First calculate the exponent: $(2.1)^2 = 2.1 \\times 2.1 = 4.41$
2
Step 2: Perform the multiplication: $2 \\times 4.41 = 8.82$
3
Step 3: Carry out the division: $6.25 \\div 0.5 = 12.5$
4
Step 4: Subtract the result of the multiplication from the result of the division: $12.5 - 8.82 = 7.39$
Knowledge Points Involved
1
Order of Operations (PEMDAS/BODMAS)
A set of rules that dictates the sequence to solve mathematical expressions: Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). It ensures consistent results when evaluating complex expressions.
2
Decimal Exponentiation
The process of multiplying a decimal number by itself a specified number of times. For a number $a^n$, it means multiplying $a$ by itself $n$ times. For example, $(2.1)^2 = 2.1 \\times 2.1 = 4.41$.
3
Decimal Division
The operation of dividing one decimal number by another. To divide by a decimal like 0.5, you can convert it to a whole number by multiplying both the dividend and divisor by 10 (or a power of 10), e.g., $6.25 \\div 0.5 = (6.25 \\times 10) \\div (0.5 \\times 10) = 62.5 \\div 5 = 12.5$.
4
Decimal Multiplication
The operation of multiplying two decimal numbers. Multiply the numbers as if they were whole numbers, then count the total number of decimal places in the factors and place the decimal point in the product accordingly. For example, $2 \\times 4.41 = 8.82$.
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