We are asked to calculate 30 times 8. This means we want to find the total when we have 30 groups, each containing 8 items, or 8 groups, each containing 30 items. Our goal is to determine the product of these two numbers.
To make this multiplication easier, we can break down 30 into simpler parts. Since 30 equals 3 times 10, we can rewrite our problem as 3 times 10, all multiplied by 8. This decomposition uses place value to simplify our calculation.
Now we can use the associative property of multiplication to rearrange our expression. This property tells us that we can group numbers in different ways without changing the result. So (3 times 10) times 8 becomes 3 times (10 times 8).
Now let's calculate step by step. First, we find 10 times 8, which equals 80. Then we multiply 3 by 80, which gives us 240. Therefore, 30 times 8 equals 240.
Another way to understand multiplication is by using arrays. We can represent 30 times 8 as an array of dots with 8 rows and 30 columns. To make it easier to count, we can group the columns into sections of 10. We have 8 rows, and each row has 30 dots grouped into three sections of 10. Counting all the dots confirms our answer of 240.
Let's apply this to a real-world situation. Imagine you're buying pencils for school. If you buy 30 packages of pencils, and each package contains 8 pencils, how many pencils do you have in total? Using our calculation, 30 times 8 equals 240, so you would have 240 pencils.
To summarize, we've calculated that 30 times 8 equals 240. We verified this using multiple methods: decomposition, array visualization, and a real-world application. All approaches led us to the same answer, confirming that 30 times 8 is indeed 240. This demonstrates how multiplication is a fundamental mathematical operation with many practical applications.