Answer :
Certainly! Let's solve the problem step-by-step using the column method of multiplication and see how the distributive law is applied.
a) Work out the number that should replace each letter.
We are given a multiplication problem involving the number 143 and the number 852, which is broken down using the column method. We need to find the numbers that replace each letter in the solution.
1. First component:
We need to find what 143 should be multiplied with to get 286, which is denoted by the triangle symbol.
This means:
[tex]\(143 \times A = 286\)[/tex]
Solving for [tex]\(A\)[/tex], we find:
[tex]\(A = 2\)[/tex]
2. Second component:
We see [tex]\(143 \times B = 7150\)[/tex].
Solving for [tex]\(B\)[/tex], we get:
[tex]\(B = 50\)[/tex]
3. Third component:
We see [tex]\(143 \times \square = 114400\)[/tex].
Solving for the square, we have:
The square = 800
Therefore, the numbers that replace each letter are [tex]\(A = 2\)[/tex], [tex]\(B = 50\)[/tex], and the square = 800.
b) Explain how the column method of multiplication uses the distributive law.
The column method for multiplication leverages the distributive law to break down the multiplication into more manageable parts. Here's how it works:
When you multiply 143 by 852, you can break down 852 into parts that make calculation easier:
[tex]\[
852 = 2 + 50 + 800
\][/tex]
Using the distributive law, the multiplication can be distributed as follows:
[tex]\[
143 \times 852 = 143 \times (2 + 50 + 800)
\][/tex]
This expression can be expanded and solved separately:
[tex]\[
143 \times 852 = (143 \times 2) + (143 \times 50) + (143 \times 800)
\][/tex]
- [tex]\(143 \times 2 = 286\)[/tex]
- [tex]\(143 \times 50 = 7150\)[/tex]
- [tex]\(143 \times 800 = 114400\)[/tex]
Finally, by adding these components together, we get the total:
[tex]\[
286 + 7150 + 114400 = 121836
\][/tex]
This result matches the complete multiplication of 143 by 852. Thus, the column method effectively uses the distributive law to simplify and solve the multiplication step-by-step.
a) Work out the number that should replace each letter.
We are given a multiplication problem involving the number 143 and the number 852, which is broken down using the column method. We need to find the numbers that replace each letter in the solution.
1. First component:
We need to find what 143 should be multiplied with to get 286, which is denoted by the triangle symbol.
This means:
[tex]\(143 \times A = 286\)[/tex]
Solving for [tex]\(A\)[/tex], we find:
[tex]\(A = 2\)[/tex]
2. Second component:
We see [tex]\(143 \times B = 7150\)[/tex].
Solving for [tex]\(B\)[/tex], we get:
[tex]\(B = 50\)[/tex]
3. Third component:
We see [tex]\(143 \times \square = 114400\)[/tex].
Solving for the square, we have:
The square = 800
Therefore, the numbers that replace each letter are [tex]\(A = 2\)[/tex], [tex]\(B = 50\)[/tex], and the square = 800.
b) Explain how the column method of multiplication uses the distributive law.
The column method for multiplication leverages the distributive law to break down the multiplication into more manageable parts. Here's how it works:
When you multiply 143 by 852, you can break down 852 into parts that make calculation easier:
[tex]\[
852 = 2 + 50 + 800
\][/tex]
Using the distributive law, the multiplication can be distributed as follows:
[tex]\[
143 \times 852 = 143 \times (2 + 50 + 800)
\][/tex]
This expression can be expanded and solved separately:
[tex]\[
143 \times 852 = (143 \times 2) + (143 \times 50) + (143 \times 800)
\][/tex]
- [tex]\(143 \times 2 = 286\)[/tex]
- [tex]\(143 \times 50 = 7150\)[/tex]
- [tex]\(143 \times 800 = 114400\)[/tex]
Finally, by adding these components together, we get the total:
[tex]\[
286 + 7150 + 114400 = 121836
\][/tex]
This result matches the complete multiplication of 143 by 852. Thus, the column method effectively uses the distributive law to simplify and solve the multiplication step-by-step.
