Solve Math Equations: Step-by-Step Solutions

by Andrew McMorgan 45 views

Hey Plastik Magazine readers! Today, we're diving into some fun math equations. Don't worry, we'll break it down step-by-step so it's super easy to follow. Let's get started!

Equation 1: 35−(9imes4−2−16)extbackslashdiv2=35-(9 imes 4-2-16) extbackslash div 2=

Let's tackle the first equation: 35−(9imes4−2−16)extbackslashdiv2=35-(9 imes 4-2-16) extbackslash div 2=. To solve this, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Trust me guys, it's not as intimidating as it sounds!

Step 1: Parentheses

First, we focus on the expression inside the parentheses: (9imes4−2−16)(9 imes 4-2-16). Within the parentheses, we again follow the order of operations. Multiplication comes first. Think of it as a little puzzle within the bigger puzzle.

  • 9imes4=369 imes 4 = 36

Now, our expression inside the parentheses looks like this: (36−2−16)(36-2-16). Next up are the subtraction operations. We perform them from left to right. It's like reading a sentence – you go from the beginning to the end!

  • 36−2=3436 - 2 = 34
  • 34−16=1834 - 16 = 18

So, the expression inside the parentheses simplifies to 1818. We've conquered the first step! See? Math can be fun when you break it down. The original equation now looks much simpler: 35−(18)extbackslashdiv2=35 - (18) extbackslash div 2=.

Step 2: Division

Now that we've simplified the parentheses, the next operation according to PEMDAS is division. We have 18extbackslashdiv218 extbackslash div 2. This is a straightforward division problem.

  • 18extbackslashdiv2=918 extbackslash div 2 = 9

Our equation now transforms to: 35−9=35 - 9 =. We're getting closer to the final answer!

Step 3: Subtraction

Finally, we perform the subtraction. This is the last step, and it’s a breeze.

  • 35−9=2635 - 9 = 26

Therefore, the solution to the first equation, 35−(9imes4−2−16)extbackslashdiv2=35-(9 imes 4-2-16) extbackslash div 2=, is 2626. Ta-da! You guys nailed it! Remember, the key is to take it one step at a time and follow the order of operations.

Equation 2: (15+29)extbackslashdiv4−3imes(22−19)=(15+29) extbackslash div 4-3 imes(22-19)=

Alright, let's move on to the second equation: (15+29)extbackslashdiv4−3imes(22−19)=(15+29) extbackslash div 4-3 imes(22-19)=. We're going to use the same PEMDAS strategy here. Remember, parentheses first, then exponents, multiplication and division (from left to right), and finally, addition and subtraction (from left to right). Let’s dive in!

Step 1: Parentheses

We have two sets of parentheses in this equation: (15+29)(15+29) and (22−19)(22-19). Let's simplify each of these.

  • (15+29)=44(15+29) = 44
  • (22−19)=3(22-19) = 3

Now, substitute these values back into the original equation. It becomes: 44extbackslashdiv4−3imes3=44 extbackslash div 4 - 3 imes 3 =. See how much cleaner it looks already? You've got this!

Step 2: Division and Multiplication

Next up are division and multiplication. According to PEMDAS, we perform these operations from left to right. So, let's start with the division.

  • 44extbackslashdiv4=1144 extbackslash div 4 = 11

Now, we have: 11−3imes3=11 - 3 imes 3 =. Let's do the multiplication.

  • 3imes3=93 imes 3 = 9

Our equation now looks like: 11−9=11 - 9 =. We’re in the home stretch!

Step 3: Subtraction

Finally, we perform the subtraction.

  • 11−9=211 - 9 = 2

Therefore, the solution to the second equation, (15+29)extbackslashdiv4−3imes(22−19)=(15+29) extbackslash div 4-3 imes(22-19)=, is 22. You guys are crushing it! Just a little bit more to go.

Equation 3: 13imes(6+9−5)extbackslashdiv(14−9)=13 imes(6+9-5) extbackslash div(14-9)=

Okay, let's jump into the third and final equation: 13imes(6+9−5)extbackslashdiv(14−9)=13 imes(6+9-5) extbackslash div(14-9)=. Just like before, we're sticking with PEMDAS to make sure we get the right answer. We've got this down now, right?

Step 1: Parentheses

This equation has two sets of parentheses as well: (6+9−5)(6+9-5) and (14−9)(14-9). Let’s simplify them one at a time.

First, let’s tackle (6+9−5)(6+9-5). Inside this set, we have addition and subtraction. We perform these from left to right.

  • 6+9=156 + 9 = 15
  • 15−5=1015 - 5 = 10

So, (6+9−5)(6+9-5) simplifies to 1010. Now, let's simplify the second set of parentheses: (14−9)(14-9).

  • 14−9=514 - 9 = 5

Great! Now our original equation looks like this: 13imes10extbackslashdiv5=13 imes 10 extbackslash div 5 =. Much simpler, isn't it? We're making fantastic progress!

Step 2: Multiplication and Division

According to PEMDAS, we perform multiplication and division from left to right. So, let's start with the multiplication.

  • 13imes10=13013 imes 10 = 130

Now our equation is: 130extbackslashdiv5=130 extbackslash div 5 =. On to the division!

  • 130extbackslashdiv5=26130 extbackslash div 5 = 26

And just like that, we've reached the end!

Therefore, the solution to the third equation, 13imes(6+9−5)extbackslashdiv(14−9)=13 imes(6+9-5) extbackslash div(14-9)=, is 2626. Awesome job, you guys! You tackled all three equations like pros.

Conclusion

So, to recap, the solutions are:

  1. 35−(9imes4−2−16)extbackslashdiv2=∗∗26∗∗35-(9 imes 4-2-16) extbackslash div 2= **26**
  2. (15+29)extbackslashdiv4−3imes(22−19)=∗∗2∗∗(15+29) extbackslash div 4-3 imes(22-19)= **2**
  3. $13 imes(6+9-5) extbackslash div(14-9)= 26

Remember, the key to solving math equations is to follow the order of operations (PEMDAS) and break down the problem into smaller, manageable steps. Keep practicing, and you'll become math wizards in no time! You guys are amazing!