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Chapter 1: Problem 258

In the following exercises, multiply. $$(58)(4)$$

Short Answer

Expert verified
232

Step by step solution

01

Write down the multiplicands

Identify the numbers that need to be multiplied. In this case, the multiplicands are 58 and 4.
02

Use basic multiplication

Multiply the numbers directly. To multiply 58 by 4, you can use the standard multiplication algorithm.
03

Perform the multiplication

First, multiply the unit digit of 58 (which is 8) by 4: \( 8 \times 4 = 32 \). Write down 2 and carry over 3. Next, multiply the tens digit of 58 (which is 5) by 4, then add the carry over: \( 5 \times 4 = 20 \), plus the 3 carried over gives us 23. So, the result is 232.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

multiplicands
In multiplication, the numbers being multiplied are called **multiplicands**. In the exercise you are learning, these are the numbers 58 and 4. Understanding what a multiplicand is, is crucial in solving multiplication problems correctly. In our example, 58 and 4 are the numbers we identify for this operation. Breaking down the multiplicands into their individual digits (e.g., units place and tens place) helps us perform the multiplication more efficiently.
standard multiplication algorithm
The **standard multiplication algorithm** is a step-by-step method used to solve multiplication problems. This algorithm involves multiplying the digits of the multiplicands one by one and then combining the results. In our example of multiplying 58 by 4, you can perform the multiplication in parts:

1. Multiply the units digit of the first number (8 in 58) by the second number (4).
2. Then, multiply the tens digit of the first number (5 in 58) by the second number (4).

By following these steps, you ensure you cover both the place value and avoid mistakes.
carryover in multiplication
When you're multiplying numbers, sometimes the result of multiplying the unit digits is more than 9. This is where **carryover in multiplication** comes in. If the product of a multiplication step is a two-digit number, you record the unit digit and carry over the tens digit to the next higher place value. For example, in the multiplication of 58 with 4, multiplying the unit digit (8) by 4 results in 32. Here, you write down 2 and carry over 3. Next, you multiply the tens digit (5) by 4, add the carryover 3 (from 32), resulting in 23. The sum is then combined to give the final product, 232.
Using carryover correctly ensures accurate multiplication results.

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