7 ∙ 15 can be written as _.
The Correct Answer and Explanation is:
The expression (7 \cdot 15) can be written as 105.
Here’s a breakdown to help explain how we arrive at this answer and understand multiplication more deeply:
Step-by-Step Calculation
- Recognize the Operation: The “∙” symbol represents multiplication, so (7 \cdot 15) means we need to multiply 7 by 15.
- Multiplication Process: Multiplication is a method of adding a number to itself a specific number of times. In this case, we are adding 7 fifteen times (or adding 15 seven times) to get the product. Here’s one way to think about it: [
7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 105
] Alternatively: [
15 + 15 + 15 + 15 + 15 + 15 + 15 = 105
] Both methods confirm the answer is 105. - Verification Using Basic Math Facts: Knowing some basic multiplication facts can also help simplify the process. Breaking down the calculation:
[
7 \cdot 15 = (7 \cdot 10) + (7 \cdot 5)
]
[
= 70 + 35 = 105
]
Practical Meaning of Multiplication
In mathematics, multiplication is a fundamental operation representing repeated addition. Here, (7 \cdot 15) suggests taking 7 groups, each with 15 items, giving a total of 105 items. It can also represent a real-world scenario: if there are 7 rows of chairs and each row has 15 chairs, then the total number of chairs is 105.
Properties of Multiplication
Understanding the commutative property is also useful, as it states that (a \cdot b = b \cdot a). This means we can multiply 7 by 15 or 15 by 7 and still get 105.
Thus, whether approached through repeated addition, basic multiplication facts, or properties of multiplication, (7 \cdot 15) indeed equals 105.