Question

answer the questions below about line 1 and line 2 shown below. 4·2 lin 2·4 lin answer attempt 1 out of 2 the expression was rewritten using the 4·2 means □ + □ + □ + □ which equals □. 2·4 means □ + □ which equals □.

Explanation:

Step1: Analyze \(4 \cdot 2\)

Multiplication \(a \cdot b\) can be thought of as adding \(a\) \(b\) times or \(b\) \(a\) times. For \(4 \cdot 2\), it means adding 2 four times. So we have \(2 + 2 + 2 + 2\).
To calculate the sum: \(2+2 = 4\), \(4 + 2 = 6\), \(6 + 2 = 8\). So \(4 \cdot 2=8\).

Step2: Analyze \(2 \cdot 4\)

For \(2 \cdot 4\), it means adding 4 two times. So we have \(4 + 4\).
To calculate the sum: \(4+4 = 8\). So \(2 \cdot 4 = 8\). Also, the rewrite from \(4 \cdot 2\) to \(2 \cdot 4\) uses the commutative property of multiplication (though the first part of the question about the property is a bit cut off, but for the fill - ins here):
For \(4 \cdot 2\) means \(2+2+2+2\) which equals \(8\).
For \(2 \cdot 4\) means \(4 + 4\) which equals \(8\).

Answer:

For \(4\cdot2\) means \(\boldsymbol{2}+\boldsymbol{2}+\boldsymbol{2}+\boldsymbol{2}\) which equals \(\boldsymbol{8}\).
For \(2\cdot4\) means \(\boldsymbol{4}+\boldsymbol{4}\) which equals \(\boldsymbol{8}\).