Fill In The Blanks: Making Math Sentences True

Hey guys! Let's dive into some math problems where we need to fill in the blanks to make the sentences true. This is a great way to sharpen our problem-solving skills and get comfortable with different math operations. We'll break down each problem step by step, so you can see exactly how to find the missing pieces. Let's get started!

Understanding the Basics

Before we jump into the problems, let's quickly review some fundamental math concepts. It's super important to have a solid grasp of these basics, as they'll help us tackle these fill-in-the-blank questions with confidence.

• Multiplication: Remember, multiplication is just a shortcut for repeated addition. For example, 3 * 4 means adding 3 four times (3 + 3 + 3 + 3), which equals 12.
• Division: Division is the opposite of multiplication. It's like splitting a total into equal groups. So, 10 / 2 means splitting 10 into 2 equal groups, which gives us 5 in each group.
• Addition: Addition is combining two or more numbers to find their total.
• Subtraction: Subtraction is finding the difference between two numbers.
• Order of Operations: If a problem has multiple operations, we need to follow the order of operations (often remembered by the acronym PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This ensures we solve the problem in the correct sequence.

Why This Matters

Knowing these basics inside and out is like having the right tools for a job. When we understand how these operations work, we can approach these fill-in-the-blank problems systematically and accurately. This isn't just about getting the right answer; it's about building a strong foundation in math that will help you in more advanced topics later on.

Problem Breakdown and Solutions

Let's take each equation one by one and figure out those missing numbers. Remember, the goal is to make both sides of the equation equal. This means the expression on the left side needs to have the same value as the expression on the right side. We'll use our knowledge of math operations to solve these. Think of it like balancing a scale – we need to make sure both sides weigh the same!

a) 0.4 * 0.2 * 0.3 = 0.4 *

Okay, let's tackle this one. The equation is 0.4 * 0.2 * 0.3 = 0.4 * blank. Our mission is to find the missing number that makes this equation true. The key here is to focus on what's happening on both sides of the equals sign. On the left side, we have three numbers being multiplied together. On the right side, we have 0.4 being multiplied by something we don't know yet. To find that mystery number, we need to do a bit of math magic!

Let's first calculate the left side of the equation. We've got 0.4 multiplied by 0.2, which gives us 0.08. Then, we multiply that result (0.08) by 0.3, and we get 0.024. So, the left side of the equation equals 0.024. Now, we know that 0.4 multiplied by our missing number must also equal 0.024. This is where we switch gears and use division. To find the missing number, we'll divide 0.024 by 0.4. When we do that, we get 0.06. So, the missing number is 0.06. We can double-check our answer by multiplying 0.4 by 0.06, and guess what? It equals 0.024. Success!

Therefore, the answer is:

Answer: 0.06

b) 0.75 / 5 = 15 *

Next up, we have 0.75 / 5 = 15 * blank. This problem mixes division and multiplication, so we need to be a little strategic. Just like in the previous problem, our goal is to find the missing number that makes both sides of the equation equal. Let's start by simplifying the left side. We have 0.75 divided by 5. If you do the division, you'll find that 0.75 divided by 5 equals 0.15. Great! Now we know that 15 multiplied by our missing number must also equal 0.15.

To find that missing number, we're going to use division again, but this time, we're dividing 0.15 by 15. When we do that division, we get 0.01. That's our missing number! To be absolutely sure, let's check our work. We'll multiply 15 by 0.01, and what do you know? It equals 0.15, just like we wanted. This confirms that our answer is correct. So, the missing number in this equation is 0.01.

Therefore, the answer is:

Answer: 0.01

c) 1.3 + 1.5 = _ + 2.0

Alright, let's move on to 1.3 + 1.5 = blank + 2.0. This one involves addition, which makes things a little simpler. The challenge here is to figure out what number, when added to 2.0, gives us the same result as 1.3 + 1.5. As always, we'll start by simplifying one side of the equation. Let's add 1.3 and 1.5 together. When we do that, we get 2.8. So, now we know that our missing number, plus 2.0, must also equal 2.8. Think of it like balancing a see-saw – both sides need to be at the same height.

To find the missing number, we'll use subtraction. We're going to subtract 2.0 from 2.8. When we do that, we get 0.8. So, our missing number is 0.8. To double-check, we can add 0.8 and 2.0 together, and guess what? It equals 2.8, which is exactly what we wanted. That confirms our answer is correct. We've successfully found the missing piece in this addition puzzle!

Therefore, the answer is:

Answer: 0.8

d) 4.5 - 1.2 = _ + 2.2

Next, we're tackling 4.5 - 1.2 = blank + 2.2. This equation mixes subtraction and addition, so we'll need to be careful with our steps. Just like before, our goal is to find the missing number that makes both sides of the equation equal. Let's start by simplifying the left side. We need to subtract 1.2 from 4.5. When we do that, we get 3.3. So, the left side of the equation equals 3.3. Now we know that our missing number, when added to 2.2, must also equal 3.3. It's like we're detectives, piecing together clues to solve a mystery!

To find that missing number, we're going to use subtraction again. We'll subtract 2.2 from 3.3. When we do that, we get 1.1. So, our missing number is 1.1. To double-check our answer, we can add 1.1 and 2.2 together. If we've done our math right, it should equal 3.3. Let's see... 1.1 plus 2.2 does indeed equal 3.3! We've cracked the code and found the missing number. This problem is a great example of how we can use our knowledge of different math operations to solve equations.

Therefore, the answer is:

Answer: 1.1

e) 6.5 + 1.5 - 1.0 = _ + 0.1 + 1.0

Now, let's dive into 6.5 + 1.5 - 1.0 = blank + 0.1 + 1.0. This problem looks a bit more complex because it involves both addition and subtraction on both sides of the equation. But don't worry, we'll break it down step by step, just like we've been doing. Our goal remains the same: find the missing number that makes both sides of the equation equal. Let's start by simplifying the left side. We'll first add 6.5 and 1.5 together, which gives us 8. Then, we'll subtract 1.0 from 8, which leaves us with 7. So, the left side of the equation simplifies to 7.

Now, let's simplify the right side as much as we can before we try to find the missing number. We have blank + 0.1 + 1.0. We can add 0.1 and 1.0 together, which gives us 1.1. So, now we know that our missing number, when added to 1.1, must equal 7. It's like we're trying to balance a seesaw, but with a few extra steps involved.

To find the missing number, we'll use subtraction. We're going to subtract 1.1 from 7. When we do that, we get 5.9. So, our missing number is 5.9. To double-check, we'll add 5.9, 0.1, and 1.0 together. If we've done our math correctly, it should equal 7. Let's see... 5.9 plus 0.1 is 6, and then adding 1.0 gives us 7. Success! We've found the missing piece in this equation puzzle. This problem shows us how important it is to take things one step at a time and stay organized when dealing with multiple operations.

Therefore, the answer is:

Answer: 5.9

f) 10 / 0.2 = _ * 0.5

Last but not least, we have 10 / 0.2 = blank * 0.5. This problem brings us back to division and multiplication. As always, our aim is to find the missing number that makes the equation true. Let's begin by simplifying the left side. We need to divide 10 by 0.2. If you remember how to divide by decimals, you can think of this as how many times 0.2 fits into 10. When we do the division, we find that 10 divided by 0.2 equals 50. Great! So, the left side of the equation simplifies to 50.

Now we know that our missing number, when multiplied by 0.5, must also equal 50. To find that missing number, we're going to use division again. We'll divide 50 by 0.5. This is like asking, "What number do we need to multiply by 0.5 to get 50?" When we do the division, we get 100. So, our missing number is 100. To verify our answer, let's multiply 100 by 0.5. If our math is correct, it should equal 50. And guess what? 100 multiplied by 0.5 does indeed equal 50. We've successfully solved the final puzzle in our set! This problem is a good reminder of how division and multiplication are related and how we can use them together to solve equations.

Therefore, the answer is:

Answer: 100

Final Thoughts

So, there you have it, guys! We've successfully filled in all the blanks and made those math sentences true. Remember, the key to solving these types of problems is to break them down step by step and use your knowledge of basic math operations. By simplifying one side of the equation at a time and then working to find the missing piece, you can tackle even the trickiest fill-in-the-blank math problems. Keep practicing, and you'll become a math whiz in no time!

If you enjoyed this, give it a thumbs up and be sure to share it with your friends and classmates. Let's make math fun and conquer those equations together! Until next time, keep learning and keep shining!