Step-by-Step Solutions For Math Problems On Pages 119 And 123

Hey guys! 👋 Today, we're diving deep into some tricky math problems from your textbook. Specifically, we're going to break down exercises from pages 119 and 123. Trust me, math can be super fun once you get the hang of it, and I'm here to make sure you do! We'll tackle questions 3 and 6 from page 119, and then we'll conquer questions 2, 3, and 7 from page 123. So, grab your pencils, notebooks, and let's get started! 🚀

Page 119, Questions 3 & 6: Decoding the Math Mysteries

Let's start with page 119. Here, we'll tackle questions 3 and 6. It's super important to not just see the answer but to understand how we get there. Think of it like this: math problems are like puzzles, and we're the detectives! 🕵️‍♀️

Question 3: Unraveling the Problem

Okay, so let's assume question 3 on page 119 is something like this: "Solve the equation 2x + 5 = 11." Now, this might look intimidating at first, but trust me, it's totally doable. The key here is to isolate the variable. What does that mean? Well, we want to get 'x' all by itself on one side of the equation.

First things first, we need to get rid of that '+ 5'. How do we do that? We do the opposite operation! Since it's addition, we'll subtract 5 from both sides of the equation. Remember, whatever you do to one side, you gotta do to the other! This keeps the equation balanced. So, we get: 2x + 5 - 5 = 11 - 5, which simplifies to 2x = 6.

Great! We're one step closer. Now we have 2x = 6. What's happening between the 2 and the x? Multiplication! So, to undo multiplication, we do the opposite: division. We'll divide both sides by 2: (2x) / 2 = 6 / 2. This simplifies to x = 3. Boom! 💥 We solved it! The solution to the equation 2x + 5 = 11 is x = 3. Remember, always double-check your answer by plugging it back into the original equation. In this case, 2(3) + 5 = 6 + 5 = 11. It checks out! 🎉

Question 6: Tackling the Next Challenge

Let’s say question 6 on page 119 presents a different challenge, maybe a word problem like this: "A rectangular garden is 10 meters long and 5 meters wide. What is its area?" Word problems can seem scary, but they're just regular math problems disguised in words! 🎭

The first thing we need to do is understand the question. What are we being asked to find? In this case, it's the area of a rectangle. Okay, what's the formula for the area of a rectangle? It's length times width! So, Area = Length × Width.

Now, we identify the given information. We know the length is 10 meters and the width is 5 meters. Perfect! We have everything we need. Next, we plug the values into the formula: Area = 10 meters × 5 meters. And finally, we calculate the answer: Area = 50 square meters. Don't forget the units! Area is always measured in square units. So, the area of the rectangular garden is 50 square meters. 🌳

See? Word problems aren't so bad once you break them down into smaller steps. Remember to always read the problem carefully, identify what you're being asked to find, and use the correct formulas or methods to solve it.

Page 123, Questions 2, 3 & 7: Conquering More Math Problems

Alright, now let's move on to page 123 and tackle questions 2, 3, and 7. We'll keep using our detective skills to crack these problems! 🕵️‍♂️

Question 2: Deciphering the Equation

Imagine question 2 on page 123 is something like this: "Solve for y: 3y - 7 = 8." This looks similar to the equation we solved earlier, so we'll use the same strategy: isolate the variable.

First, we need to get rid of the '- 7'. To do that, we add 7 to both sides: 3y - 7 + 7 = 8 + 7. This simplifies to 3y = 15. Now we have 3y = 15. Again, the 3 and the y are being multiplied, so we'll divide both sides by 3: (3y) / 3 = 15 / 3. This gives us y = 5. Yay! 🎉 The solution to the equation 3y - 7 = 8 is y = 5. Always double-check: 3(5) - 7 = 15 - 7 = 8. It works!

Question 3: Cracking the Code

Let's say question 3 on page 123 involves fractions, like this: "What is 1/2 + 1/4?" Fractions can seem tricky, but they're just numbers too! The key to adding or subtracting fractions is to have a common denominator. What's a denominator? It's the bottom number in the fraction.

In this case, our denominators are 2 and 4. What's a common denominator for 2 and 4? Well, 4 is a multiple of 2, so we can use 4 as our common denominator. We need to rewrite 1/2 with a denominator of 4. To do that, we multiply both the numerator (top number) and the denominator by 2: (1 × 2) / (2 × 2) = 2/4. So, 1/2 is equivalent to 2/4.

Now we can add the fractions: 2/4 + 1/4. When we add fractions with the same denominator, we just add the numerators and keep the denominator the same: (2 + 1) / 4 = 3/4. So, 1/2 + 1/4 = 3/4. Remember, always simplify your answer if possible. In this case, 3/4 is already in its simplest form.

Question 7: Mastering the Challenge

Finally, let's tackle question 7 on page 123. Maybe it's a problem involving percentages, like this: "What is 20% of 50?" Percentages are just fractions in disguise! “Percent” means “out of one hundred,” so 20% is the same as 20/100.

To find 20% of 50, we can convert the percentage to a decimal and then multiply. To convert 20% to a decimal, we divide by 100: 20 / 100 = 0.20. Now we multiply: 0.20 × 50 = 10. So, 20% of 50 is 10. Another way to think about it is to recognize that 20% is the same as 1/5. So, we could also find 1/5 of 50 by dividing 50 by 5, which also gives us 10.

Remember, there are often multiple ways to solve a math problem. Find the method that makes the most sense to you and stick with it! 💪

Key Takeaways: Your Math Toolkit

Okay, guys, we've covered a lot! We tackled problems from pages 119 and 123, and we learned some super important strategies along the way. Let's recap some of the key takeaways:

• Isolate the variable: When solving equations, the goal is to get the variable all by itself on one side. Use inverse operations (addition/subtraction, multiplication/division) to do this.
• Understand word problems: Read carefully, identify what you're being asked to find, and break the problem down into smaller steps.
• Use formulas: Know your formulas! The area of a rectangle is length × width. The circumference of a circle is 2πr.
• Find common denominators: When adding or subtracting fractions, you need a common denominator.
• Convert percentages: Percentages can be converted to decimals or fractions to make calculations easier.
• Double-check your work: Always plug your answer back into the original equation or problem to make sure it's correct.

You've Got This! 💪

Math might seem challenging sometimes, but with practice and the right strategies, you can totally conquer it. Remember, it's okay to make mistakes! Mistakes are how we learn. Just keep practicing, keep asking questions, and keep believing in yourself. You've got this! 🎉 If you have more questions on these or other math topics, don't hesitate to ask. Let's keep learning and growing together! ✨