Problem 20 - Fundamentals of Mathematics

Question

Use a calculator to find each value. \(9,285+86(49)\)

Step-by-Step Solution

Answer

The value is 13,499.

Step 1: Understand the Expression

The expression given is \(9,285 + 86 \times 49\). We need to calculate this by first resolving the multiplication, then adding the result to 9,285.

Step 2: Perform Multiplication

Using the calculator, multiply 86 by 49. \(86 \times 49 = 4,214\).

Step 3: Add the Values Together

Now add the result from the multiplication to 9,285. Compute \(9,285 + 4,214 = 13,499\).

Key Concepts

Addition

Addition is one of the basic operations in mathematics, often symbolized by the plus sign "+". It involves combining two or more numbers to get a new total. For example, if you have apples in two baskets, one with 3 apples and another with 5 apples, you can find the total number of apples by using addition: 3 + 5 = 8. To ensure addition is straightforward, follow these tips:

• Align numbers correctly by their rightmost digit, especially when dealing with large numbers.
• Start adding from the rightmost digit and move leftwards, keeping track of any carry-over values.
• Use a calculator for long numbers to minimize human error, especially in adding thousands or millions.

In problems like the one in the exercise, where you need to add numbers resulting from operations, ensure the initial calculations (like multiplications) are correct before proceeding to the addition step.

Multiplication

Multiplication is another fundamental operation in math, represented by the symbol "\(\times\)" or sometimes just by juxtaposition (e.g., 86(49)). It involves calculating the total of one number added to itself repeatedly, as many times as there are units in the other number. For example, multiplying 4 by 3 (\(4 \times 3\)) means adding 4 three times: 4 + 4 + 4 = 12.The properties of multiplication include:

• Commutative Property: The order of numbers does not affect the result; \(a \times b = b \times a\).
• Associative Property: When multiplying several numbers, the way you group them doesn't affect the product; \((a \times b) \times c = a \times (b \times c)\).
• Identity Property: Any number multiplied by 1 stays the same; \(a \times 1 = a\).

In the example from the exercise, you multiply 86 by 49. Calculating this directly or using a calculator gives you 4,214, which you then use in the subsequent addition to find the solution.

Calculator Usage

Calculators can significantly ease arithmetic tasks, especially when dealing with large numbers or complex expressions. They are designed to perform basic operations, like addition and multiplication, swiftly and accurately.When using a calculator:

• Make sure you enter numbers correctly; incorrect input leads to incorrect results.
• Use parentheses to indicate the order of operations, if the calculator considers the order; though, in simple models, operations are performed sequentially.
• Double-check all entries before pressing the equals "=" button to ensure that your final solution is not based on an input error.

In exercises like the given one, the calculator helps to quickly solve operations such as \(86 \times 49\). Once you attain the result, add it to other numbers in the problem, here 9,285, to achieve an accurate solution. Always remember to review steps if the result seems off, as calculator errors often stem from user mistakes.