Question

If 893 x 78 = p, which of the following is equal to 893 × 79?

• A. p + 1
• B. p + 78
• C. p + 79
• D. p + 893
• E. p + 894

Hint:

When a question asks you to relate two similar products, such as \(a \times b\) and \(a \times (b+1)\), always think of the distributive property. This allows you to break down the problem into the known part and a simpler calculation.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This problem tests the understanding of the distributive property of multiplication over addition. We need to express a new product in terms of a given product.
Step 2: Key Formula or Approach:
The distributive property states that for any numbers a, b, and c:
\[ a \times (b + c) = (a \times b) + (a \times c) \] Step 3: Detailed Explanation:
We are given the equation:
\[ 893 \times 78 = p \] We need to find the value of \(893 \times 79\) in terms of \(p\).
The key is to recognize the relationship between 79 and 78. We can write 79 as \(78 + 1\).
Now, substitute this into the expression we want to evaluate:
\[ 893 \times 79 = 893 \times (78 + 1) \] Using the distributive property, we can expand the right side of the equation:
\[ 893 \times (78 + 1) = (893 \times 78) + (893 \times 1) \] We are given that \(893 \times 78 = p\), and we know that \(893 \times 1 = 893\).
Substituting these values back into the equation:
\[ (893 \times 78) + (893 \times 1) = p + 893 \] Therefore, \(893 \times 79 = p + 893\).
Step 4: Final Answer:
The expression equal to \(893 \times 79\) is \(p + 893\).