Question
How can decomposing the number 23
into 20+3
make multiplying easier?
into 20+3
make multiplying easier?
Answers
Answered by
GPT-4o mini
Decomposing the number 23 into 20 + 3 can make multiplication easier through the distributive property of multiplication over addition. This property allows us to break down a multiplication problem into simpler and more manageable parts.
For example, if you want to multiply 23 by a number, say 5, you can decompose it as follows:
\[
23 \times 5 = (20 + 3) \times 5
\]
Using the distributive property, this can be expressed as:
\[
= (20 \times 5) + (3 \times 5)
\]
Now we calculate each part:
\[
20 \times 5 = 100
\]
\[
3 \times 5 = 15
\]
Now, adding these two results together gives:
\[
100 + 15 = 115
\]
So instead of multiplying 23 directly by 5, we simplified the problem by breaking it down into two easier multiplications: 20 times 5 and 3 times 5. This method can be especially helpful when multiplying numbers that may be harder to handle if kept together. It can help with mental math and also allows for easier computation on paper.
For example, if you want to multiply 23 by a number, say 5, you can decompose it as follows:
\[
23 \times 5 = (20 + 3) \times 5
\]
Using the distributive property, this can be expressed as:
\[
= (20 \times 5) + (3 \times 5)
\]
Now we calculate each part:
\[
20 \times 5 = 100
\]
\[
3 \times 5 = 15
\]
Now, adding these two results together gives:
\[
100 + 15 = 115
\]
So instead of multiplying 23 directly by 5, we simplified the problem by breaking it down into two easier multiplications: 20 times 5 and 3 times 5. This method can be especially helpful when multiplying numbers that may be harder to handle if kept together. It can help with mental math and also allows for easier computation on paper.