Compute the exact products mentally using substitution and the fact that multiplication distributes over addition. Show your use of the distributive property by filling in the blanks with the correct numbers.
Part 1 out of 2
a. [tex]44 \times 56[/tex]
[tex]\begin{aligned}
44 \times 56 & = \text { (select) } \\
& = \square \\
& = \square
\end{aligned}[/tex]
Answer (2)
Rewrite 44 as (40 + 4) and 56 as (50 + 6).
Apply the distributive property: ( 40 + 4 ) × ( 50 + 6 ) = 40 × 50 + 40 × 6 + 4 × 50 + 4 × 6 .
Calculate each term: 40 × 50 = 2000 , 40 × 6 = 240 , 4 × 50 = 200 , 4 × 6 = 24 .
Add the terms: 2000 + 240 + 200 + 24 = 2464 . Thus, 44 × 56 = 2464 .
Explanation
Rewrite the numbers We are asked to compute the product 44 × 56 using substitution and the distributive property. We can rewrite 44 as (40 + 4) and 56 as (50 + 6).
Apply the distributive property Now, we apply the distributive property: ( 40 + 4 ) × ( 50 + 6 ) = 40 × 50 + 40 × 6 + 4 × 50 + 4 × 6
Calculate each term Next, we calculate each term: 40 × 50 = 2000 40 × 6 = 240 4 × 50 = 200 4 × 6 = 24
Add the terms Finally, we add the terms: 2000 + 240 + 200 + 24 = 2464 Therefore, 44 × 56 = 2464 .
Examples
Understanding the distributive property is crucial in many areas, such as calculating areas and volumes. For instance, imagine you're designing a rectangular garden. If you decide to increase the length by 5 feet and the width by 2 feet, the distributive property helps you calculate the new area by breaking down the multiplication into smaller, manageable parts. This principle extends to more complex scenarios, like optimizing resource allocation in business or understanding polynomial multiplication in algebra.
We can calculate 44 times 56 by rewriting the numbers and using the distributive property. After expanding and calculating, we find that 44 times 56 equals 2464. This process helps simplify large multiplications into smaller, manageable parts.
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