Problem 58 - Basic College Mathematics

Question

Calculate. $$ 2.56 \div(4-3.84)+6.3 \times 0.2 $$

Step-by-Step Solution

Answer

17.26

Step 1 - Simplify inside the parentheses

Calculate the expression inside the parentheses first: \(4 - 3.84\).

Step 2 - Perform the subtraction

Subtract 3.84 from 4: \(4 - 3.84 = 0.16\).

Step 3 - Perform the division

Divide 2.56 by the result from Step 2: \(2.56 \div 0.16 = 16\).

Step 4 - Perform the multiplication

Multiply 6.3 by 0.2: \(6.3 \times 0.2 = 1.26\).

Step 5 - Add the results

Add the results from Step 3 and Step 4: \(16 + 1.26 = 17.26\).

Key Concepts

Division

Division is one of the basic arithmetic operations. It involves splitting a number into equal parts. For example, in the exercise, we need to divide 2.56 by 0.16. Here, 2.56 is the dividend, and 0.16 is the divisor. To solve it, we ask how many times 0.16 fits into 2.56. The answer is 16. When performing division, make sure the divisor is not zero, as division by zero is undefined.

Remember the notation: \( \frac{a}{b} = c \), where \( a \) is the dividend, \( b \) is the divisor, and \( c \) is the quotient.

Subtraction

Subtraction means taking away a number from another number. It's another basic arithmetic operation. In the given problem, the subtraction operation simplifies the expression inside the parentheses: \(4 - 3.84\). Subtracting involves aligning the decimal points and subtracting each digit starting from the right.

This gives us \(4 - 3.84 = 0.16\). So, the equation inside the parentheses results in 0.16. Always remember to perform subtraction from left to right and pay attention to borrowing if needed.

Multiplication

Multiplication is like repeated addition. It tells us how many times one number is added to itself. In this exercise, we need to multiply 6.3 by 0.2. When multiplying decimals, you can ignore the decimal points, multiply the numbers as if they are whole, and then place the decimal point in the result.

For instance, \(6.3 \times 0.2\) can be thought of as \(63 \times 2 = 126\). Since we moved the decimal one place to the left in 6.3 and one place to the left in 0.2, we need to move it two places to the left in the result: \(1.26\). Thus, \(6.3 \times 0.2 = 1.26\). Multiplying 6.3 by 0.2 gives us 1.26.