Answer :
Let's go through each part of the question step by step:
- Firstly, we need to know the product of 12 and 8, which is:
[tex]12 \times 8 = 96[/tex]
We will compare this to the results of each given calculation:
a) 3 x 4 x 8
We can perform the multiplication as follows:
[tex](3 \times 4) \times 8 = 12 \times 8 = 96[/tex]
This calculation gives 96, which is equal to the product of 12 and 8.
b) 12 x 4 x 2
Performing this multiplication step-by-step:
[tex](12 \times 4) \times 2 = 48 \times 2 = 96[/tex]
This calculation also results in 96, which is equal to the product of 12 and 8.
c) 2 + 10 x 8
According to the order of operations (PEMDAS/BODMAS), we should do multiplication before addition:
[tex]2 + (10 \times 8) = 2 + 80 = 82[/tex]
This calculation results in 82, which is not equal to the product of 12 and 8.
Next, let's use the distributive law to solve the given calculations:
a) 39 x 7
Using the distributive law [tex](a + b) \times c = a \times c + b \times c[/tex]:
[tex]39 \times 7 = (40 - 1) \times 7[/tex]
[tex]= 40 \times 7 - 1 \times 7[/tex]
[tex]= 280 - 7 = 273[/tex]
b) 38 x 8
Similarly, apply the distributive law:
[tex]38 \times 8 = (40 - 2) \times 8[/tex]
[tex]= 40 \times 8 - 2 \times 8[/tex]
[tex]= 320 - 16 = 304[/tex]
c) 29 x 7
Finally, apply the distributive law:
[tex]29 \times 7 = (30 - 1) \times 7[/tex]
[tex]= 30 \times 7 - 1 \times 7[/tex]
[tex]= 210 - 7 = 203[/tex]
In summary, part (a) and (b) under the first question give results equal to the product of 12 and 8, while part (c) does not. For the second question, applying the distributive law gives us answers for each multiplication operation.
