Problem 2 - Fundamentals of Mathematics

Question

Find the first five multiples of the following numbers. 5

Step-by-Step Solution

Answer

The first five multiples of 5 are 5, 10, 15, 20, and 25.

Step 1: Understanding the Concept of Multiples

A multiple of a number is the product of that number and an integer. For example, multiples of 5 can be found by multiplying 5 by 1, 2, 3, and so on.

Step 2: Calculate the First Multiple

The first multiple of 5 is obtained by multiplying 5 by 1: \(5 \times 1 = 5\).

Step 3: Calculate the Second Multiple

The second multiple of 5 is obtained by multiplying 5 by 2: \(5 \times 2 = 10\).

Step 4: Calculate the Third Multiple

The third multiple of 5 is obtained by multiplying 5 by 3: \(5 \times 3 = 15\).

Step 5: Calculate the Fourth Multiple

The fourth multiple of 5 is obtained by multiplying 5 by 4: \(5 \times 4 = 20\).

Step 6: Calculate the Fifth Multiple

The fifth multiple of 5 is obtained by multiplying 5 by 5: \(5 \times 5 = 25\).

Key Concepts

product of a number

When we talk about the "product of a number," we are referring to the result you get when you multiply that number by another number. The multiply operation is a fundamental arithmetic operation that tells us that we are adding the number to itself a certain number of times. For example:- If you multiply 5 by 3, you are essentially adding 5 three times: \(5 + 5 + 5 = 15\). This is the same as saying \(5 \times 3 = 15\). - We can express multiplication formally as \(a \times b = c\), where \(a\) and \(b\) are numbers, and \(c\) is the product.The notion of a product is essential not just in finding multiples, but in many areas of math, such as algebra and even geometry, where you calculate the area of a rectangle by multiplying its length by its width.

integers in mathematics

Integers in mathematics are the set of numbers that include whole numbers and their negative counterparts. That means integers include:

• Positive numbers (like 1, 2, 3, ...)
• Negative numbers (like -1, -2, -3, ...)
• Zero (0)

Understanding integers is important when discussing multiples because multiples involve multiplying by whole numbers, which are integers. For example, when we find multiples of 5, we multiply 5 by integers such as 1, 2, 3, etc. All these results, like 5, 10, and 15, are still part of the integer set because they are whole numbers without fractions or decimals.

basic arithmetic operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. Multiplication, one of the main arithmetic operations, is particularly important when calculating multiples, as it involves finding the product of a number with integers.- **Addition** adds values together to get a sum, like \(2 + 3 = 5\).- **Subtraction** is the opposite of addition, locating the difference between numbers, as in \(5 - 2 = 3\).- **Multiplication** is repeated addition—adding the same number several times—like \(4 \times 2 = 8\), which is the same as \(4 + 4\).- **Division** breaks a number into several equal parts, such as \(6 \div 2 = 3\).In the context of finding multiples, multiplication is key. When you compute multiples of 5, for example, you are continuously multiplying 5 by successive integers, like \(5 \times 1 = 5\), \(5 \times 2 = 10\), and so on, representing how multiplication operates efficiently instead of repeatedly adding 5 multiple times by hand.