1)The star diagram
*** ****
*** ****
may be used to demonstrate the truth of
a) 3x4=4x3
b) 2+(3x4)=2x(3+4)
c) 2x(3+4)=(2x3)+(2x4)
d) 2x(3x4)=2x3x4
2)The star diagram
*** **** *****
may be used to demonstrate the truth of
a) 3x4=4x3
b) 3x4x5
c) 3x(4+5)=3x4 + 3x5
d) (3+4)+5=3+(4+5)
you have 2 rows, each with 3+4 stars
So, what do you think?
Hint: distributive property
In #2, there is no multiplication, just 3+4+5 stars
So, what do you think?
Hint: associative property
I'm not sure about #1 but is #2 d?
Is #1 c?
you are correct on both of them. Good work.
To determine which options can be demonstrated using the star diagram, let's understand how the diagram is constructed.
In the star diagram, each row represents one number (or factor), and each column represents another number (or factor). The number of stars in each cell of the diagram represents the product of the corresponding row and column numbers.
Now let's analyze the options:
1) The star diagram *** **** can represent both 3x4 and 4x3 because multiplying 3 by 4 and 4 by 3 yields the same result, 12. So, option a) 3x4=4x3 is demonstrated by this star diagram.
2) The star diagram *** **** ***** can demonstrate the addition of two products. Each star represents the product of two numbers. In this case, the star diagram can demonstrate both option c) 3x(4+5)=3x4 + 3x5 and option d) (3+4)+5=3+(4+5) because the star diagram displays the products needed for both equations.
Therefore, the correct answers are:
1) a) 3x4=4x3
2) c) 3x(4+5)=3x4 + 3x5