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Solve, using properties/ methods that si...

Solve, using properties/ methods that simplify the calculations:
`422xx35`

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The correct Answer is:
To solve the multiplication of 422 and 35 using properties that simplify calculations, we can use the distributive property. Here’s a step-by-step solution: ### Step 1: Split the Numbers We can split the numbers into more manageable parts: - Split 422 into 400 and 22. - Split 35 into 30 and 5. So, we can rewrite the multiplication as: \[ 422 \times 35 = (400 + 22) \times (30 + 5) \] ### Step 2: Apply the Distributive Property Now, we will apply the distributive property to multiply each part: \[ (400 + 22) \times (30 + 5) = 400 \times 30 + 400 \times 5 + 22 \times 30 + 22 \times 5 \] ### Step 3: Calculate Each Multiplication Now, we will calculate each of these products: 1. \( 400 \times 30 = 12000 \) 2. \( 400 \times 5 = 2000 \) 3. \( 22 \times 30 = 660 \) 4. \( 22 \times 5 = 110 \) ### Step 4: Add All the Products Together Now we will add all the results from the multiplications: \[ 12000 + 2000 + 660 + 110 \] Calculating this step-by-step: - First, add \( 12000 + 2000 = 14000 \) - Next, add \( 14000 + 660 = 14660 \) - Finally, add \( 14660 + 110 = 14770 \) ### Final Answer Thus, the final answer for \( 422 \times 35 \) is: \[ \boxed{14770} \]
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