7 + 9 - 8 x 2 = ? A. 9 C. 0 B. 16 D. 3
I decided to include an order of operations question in these examples because not only is it an important critical thinking skill to master in math, but it's also fun to dazzle Facebook friends by correctly answering random posts that read '1 out of 10 people will not know the answer to this problem.' First, it's good to know an acronym/sentence to remember the correct order of operations. I learned it by this sentence: 'Please Excuse My Dear Aunt Sally.' We know from this sentence that we must compute order of operations this way every time: 1st - Parentheses/Exponents; 2nd - Multiplication/Division, and last - Addition/Subtraction. In the above problem we must first multiply 8 and 2 to arrive at 16. Then we must add 7 and 9 together, which is also 16. We'll have this to solve now: 16 - 16, which is 0. The correct selection is C. We'll be those 1 out of 10 people who knows the answer! Awesome!
10 x 11 = ? A. 100 C. 101 B. 11 D. 110
My reasoning behind this particular multiplication problem is to offer students a shortcut to multiply any 2 digit number by 11. The shortcut is always as follows, no matter what the 2 digit number is: First, we must add the 2 numbers together as separate integers to arrive at a sum. In the above question, we would add 1 and 0 together to get a sum of 1. Then, we'd separate the original 2 digits of the number being multiplied by 11 with a blank in between like so: 1_0. Finally, we'll place the sum we arrived at (1) when adding the integers. The correct answer is D, 110.
Liam hit 7 home runs in the first part of the baseball season. If he averages 2 home runs for every week he plays baseball, which equation describes the number of total home runs, h, he can hit after w, more weeks? A. h = 2w + 7 C. 2h + w = 9 B. w = 7h + 2 D. h = 7w + 2
In this problem, we must first know what we need to solve for to be able to isolate the variable if possible. Since this question is trying to solve for home runs hit, then we know that h is by itself on one side of the equal sign. We know this because of the phrase 'which equation describes the number of total home runs, h, he can hit.' Now we have to know what goes on the other side of the equal sign to complete the equation. His average is 2 home runs for every week played. To figure out how many home runs he'll have after a certain number of weeks we must multiply weeks (w) by 2, which is expressed as 2w. Finally, we must add the number of home runs he has already hit (7) because we're arriving at a total number of home runs after a certain amount of baseball after so many weeks. This known number of home runs will be expressed in the equation as +7. When it's all said and done, the final equation is h = 2w +7. Option A represents the correct answer.