What are the partial products of 73 × 8
The Correct Answer and Explanation is :
To calculate (73 \times 8) using partial products, we break the number 73 into its expanded form (70 + 3). Then, multiply each part by 8 and add the results. Here’s the step-by-step process:
Step 1: Break 73 into expanded form
[
73 = 70 + 3
]
Step 2: Multiply each part by 8
[
70 \times 8 = 560
]
[
3 \times 8 = 24
]
Step 3: Add the partial products
[
560 + 24 = 584
]
Final Answer:
[
73 \times 8 = 584
]
Explanation (300 Words)
The partial products method is a foundational strategy in multiplication. It emphasizes breaking numbers into their place values (tens and ones), making calculations easier and more intuitive, especially for mental math or early math learners. In this case, the number 73 is split into (70) (tens place) and (3) (ones place). This decomposition simplifies the process because you’re multiplying smaller, more manageable numbers.
When we multiply the tens place ((70)) by (8), the result is (560). This is the first partial product. Similarly, multiplying the ones place ((3)) by (8) gives (24), which is the second partial product. Adding these partial products together ((560 + 24)) gives the total product, (584).
This method aligns closely with how multiplication is represented in expanded notation or in some grid or area methods. It helps reinforce the concept of place value and shows that multiplication is distributive. That is, multiplying (73) by (8) is the same as multiplying each part of (73) (the tens and the ones) by (8) separately, then combining the results.
The partial products strategy not only builds a strong understanding of how numbers work but also lays the groundwork for more advanced arithmetic and algebraic concepts, like the distributive property ((a(b + c) = ab + ac)). By practicing this approach, learners gain both procedural fluency and conceptual understanding, which are essential for tackling complex problems later on.