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Chapter 1: Problem 26

Use divisibility rules to determine whether the given mumber is divisible by 5 . $$319,424$$

Short Answer

Expert verified
Answer: No, 319,424 is not divisible by 5.

Step by step solution

01

Identify the last digit of the number

To apply the divisibility rule for 5, we need to look at the last digit of the number. In this case, the given number is 319,424, and its last digit is 4.
02

Apply the divisibility rule for 5

The divisibility rule for 5 states that if the last digit is 0 or 5, the number is divisible by 5. The last digit of 319,424 is 4, which is not 0 nor 5.
03

Determine if the number is divisible by 5

Since the last digit of 319,424 is 4, and the divisibility rule for 5 requires the last digit to be 0 or 5, we can conclude that 319,424 is not divisible by 5.

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Key Concepts

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

Divisibility by 5
Understanding divisibility rules is crucial in mathematics, especially when learning about factors and multiples. The rule for divisibility by 5 is quite simple and is based on just the last digit of the number. This rule states that a number is divisible by 5 if its last digit is either 0 or 5. This means you don't need to perform long division to determine divisibility by 5. Simply check the last digit.

For example:
  • If a number ends in 0, like 50, 120, or 430, it is divisible by 5.
  • If a number ends in 5, like 15, 275, or 995, it is also divisible by 5.
This rule is beneficial because it provides a quick way to check divisibility, which can save time when analyzing large sets of numbers.
Last Digit
The last digit of a number holds significant importance in many divisibility rules, not just for 5. In the context of our exercise, the last digit is used to determine divisibility by 5 directly. This means you only need to focus on the final digit of the number.

In the number 319,424, as per the solution, the last digit is 4. Because 4 does not meet the requirement of ending in 0 or 5, 319,424 is not divisible by 5. Recognizing the importance of the last digit helps simplify various arithmetic tasks, as it allows for quick evaluations of certain divisibility rules.
Prealgebra
Prealgebra is an essential foundation in mathematics. It includes basic arithmetic like addition, subtraction, multiplication, and division, as well as the introduction to rules of divisibility. These rules help simplify mathematical calculations and reasoning, forming a basis for more advanced math topics later on.

Learning prealgebra concepts, such as divisibility rules, allows students to tackle problems with increased confidence and efficiency. These foundational skills are used throughout their math journey, making it easier to understand complex algebraic concepts in future courses.

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Most popular questions from this chapter

Round each number so that there is only one nonzero digit. $$8723$$

Simplify. Show your steps. $$5^{2} \cdot 3 \div 15+4-3^{2}$$

Graph the number on a number line. $$4$$

Round \(5,652,992,481\) to the specified place. ten thousands

Write the number in standard form. 8 thousands \(+7\) hundreds \(+9\) tens \(+2\) ones
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