Show how you would mentally calculate the following. State what method/methods and/or properties you are using: 8 * 25 * 7 * 4
Please help immediately!!! :(
Try using the associative and distributive properties make the problem easier to solve. For example, 4*12*3*2 I would use the distributive property to break apart the twelve (It isn't really necessary rn 4 me b/c 12 is a teensy number, but for bigger numbers like 25, it is) so my problem now reads [(4*10)+(4*2)]*3*2 So I can then multiply and add my bracketed numbers so that my problem reads 48*3*2 I am now going to use the associative property so my problem reads 48(3*2) I multiply 3*2 to get 6 so my problem is 48*6. Once more I'm gonna use the distributive property so I can solve the 48*6 more easily-- (6*40)+(6*8) To get my final answer of 288. I really hoped this helped! Sorry for any potential mistakes- you might wanna look up a video by Kahn Acadamy or another reliable source just in case cause it's 4:35 am where I am and I haven't gotten a wink of sleep all night 😩
Oh my, I think they wanted you to notice the 4*25 which is 100
and 8*7 = 56
so 8 * 25 * 7 * 4 = 5600
To mentally calculate the expression 8 * 25 * 7 * 4, we can break it down into smaller computations and simplify as we go along. Here's an example step-by-step solution using basic arithmetic properties and mental math:
Step 1: Multiply 8 by 25
- Method: Multiplying two-digit numbers ending in 5
- We can mentally calculate 8 * 25 by multiplying 8 by 10 (80) and half the result (40).
- Calculation: 8 * 25 = 80 + 40 = 120
Step 2: Multiply the result from Step 1 (120) by 7
- Method: Mental multiplication by larger numbers
- We can multiply 120 by 7 by breaking it down into smaller calculations.
- Calculation: 120 * 7 = (100 * 7) + (20 * 7) = 700 + 140 = 840
Step 3: Multiply the result from Step 2 (840) by 4
- Method: Mental multiplication by powers of 2
- Multiplying by 4 can be done by doubling and doubling again.
- Calculation: 840 * 4 = (840 * 2) + (840 * 2) = 1680 + 1680 = 3360
So, the solution to 8 * 25 * 7 * 4 is 3360.
By breaking down the expression and simplifying at each step, you can mentally calculate the multiplication without needing to use a calculator or pen and paper.
Remember, practice is key to improving mental math skills!