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Chapter 1: Problem 44

Which of the following numbers is not divisible by 5? $$7871, 9595, 3745, 4480$$

Short Answer

Expert verified
7871 is not divisible by 5.

Step by step solution

01

Understanding Divisibility by 5

A number is divisible by 5 if it ends with either 0 or 5. This is the basic rule we will apply to determine divisibility.
02

Checking Each Number

Look at the last digit of each number: 1. 7871 ends with 1. 2. 9595 ends with 5. 3. 3745 ends with 5. 4. 4480 ends with 0.
03

Identifying the Number Not Divisible by 5

Using the divisibility rule, we see that 7871 does not end in 0 or 5, so it 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 the concept of divisibility by 5 is like learning a magic trick for sorting numbers quickly. A number is divisible by 5 if it ends in either 0 or 5. This rule is simple and clear. When you check a number, zero in on the last digit.
  • If it ends in 0, like 4480, it dances smoothly into a divisible by 5 category.
  • If it ends in 5, such as 9595 or 3745, it's equally ready to be effortlessly divided by 5.
  • However, if the last digit is anything else, like in 7871, it just doesn't fit into the divisibility by 5 category.
Remembering this small rule can save you tons of time and make math seem less like a daunting mountain!
Prealgebra
Prealgebra is a friendly introduction to more advanced mathematics. It builds a solid foundation by mainly focusing on basic number operations and properties. Think of it as the gateway to understanding algebra and beyond. In prealgebra, you'll often deal with concepts like:
  • Basic operations like addition, subtraction, multiplication, and division.
  • Understanding number patterns, including odd and even numbers.
  • Grasping core concepts such as factors and multiples.
These principles prepare you for future math challenges. Applying the divisibility rules, for instance, can make learning these basic concepts not only easier but also fun. It's a logical way to engage with numbers without needing advanced calculations.
Number Properties
Number properties are like the rules of the road for navigating through the world of mathematics. They help ensure that when we play with numbers in operations, we understand what happens behind the scenes. Knowing these properties provides insight into understanding various math problems and equations more effectively. Key properties include:
  • Commutative Property: This allows switching the order in operations like addition and multiplication, such as in 3 + 5 = 5 + 3.
  • Associative Property: This focuses on grouping. For example, (2 + 3) + 4 is the same as 2 + (3 + 4).
  • Distributive Property: A helpful tool in simplifying expressions, like in 2(3 + 4) = 2*3 + 2*4.
Grasping these properties equips you with a skillset that's useful for both simple calculations and more complex algebraic expressions. Applying these nurtures a deeper understanding and appreciation for math as a whole.

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Most popular questions from this chapter

Simplify the given expression. $$ \frac{16+2}{13-11} $$

Use the distributive property to evaluate the given expression. $$ 6 \cdot(7-2) $$

Simplify the given expression. $$ 45 \div 3 \cdot 5 $$

This exercise introduces the Sieve of Eratosthenes, an ancient algorithm for finding the primes less than a certain number \(n\), first created by the Greek mathematician Eratosthenes. Consider the grid of integers from 2 through 100 . $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ \hline 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 \\ \hline 22 & 23 & 24 & 25 & 26 & 27 & 28 & 29 & 30 & 31 \\ \hline 32 & 33 & 34 & 35 & 36 & 37 & 38 & 39 & 40 & 41 \\ \hline 42 & 43 & 44 & 45 & 46 & 47 & 48 & 49 & 50 & 51 \\ \hline 52 & 53 & 54 & 55 & 56 & 57 & 58 & 59 & 60 & 61 \\ \hline 62 & 63 & 64 & 65 & 66 & 67 & 68 & 69 & 70 & 71 \\ \hline 72 & 73 & 74 & 75 & 76 & 77 & 78 & 79 & 80 & 81 \\ \hline 82 & 83 & 84 & 85 & 86 & 87 & 88 & 89 & 90 & 91 \\ \hline 92 & 93 & 94 & 95 & 96 & 97 & 98 & 99 & 100 & \\ \hline \end{array} $$ To find the primes less than 100 , proceed as follows. i) Strike out all multiples of \(2(4,6,8\), etc. \()\) ii) The list's next number that has not been struck out is a prime number. iii) Strike out from the list all multiples of the number you identified in step (ii). iv) Repeat steps (ii) and (iii) until you can no longer strike any more multiples. v) All unstruck numbers in the list are primes.

Simplify the given expression. $$ 11 \cdot[12-4]-10 $$
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