Help Solving Math Problems Step-by-Step

Hey guys! Need some help tackling these math problems. Let's break them down step by step and make sure we understand the process. Math can be super fun when we approach it the right way!

Problem 1: 25% × 0.5 : 3/4

Let's dive into the first problem: 25% × 0.5 : 3/4. To solve this, we need to remember the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). First, let's convert everything into a more manageable format. We can express 25% as a decimal, which is 0.25. So the problem becomes 0.25 × 0.5 : 3/4. Now, let's perform the multiplication first: 0.25 × 0.5 = 0.125. Next, we need to deal with the division. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3. So, the problem now looks like this: 0.125 : 3/4 = 0.125 × 4/3. To solve this, we multiply 0.125 by 4, which equals 0.5. Then, we divide 0.5 by 3. The result is approximately 0.1667 (repeating). So, the answer to the first problem, 25% × 0.5 : 3/4, is approximately 0.1667. Understanding the conversion of percentages to decimals and the concept of reciprocals is crucial in solving these kinds of problems. Remember, practice makes perfect! The more you work through these problems, the more comfortable you'll become with the steps involved. Also, visualizing these numbers can sometimes help. Think of 25% as one-quarter, 0.5 as one-half, and 3/4 as three-quarters. This can give you a clearer sense of the magnitude of the numbers you're working with. And don't be afraid to break the problem down into smaller, more manageable parts. This can make the whole process seem less daunting. Keep practicing, and you'll master these calculations in no time!

Problem 2: 25% × 0.75 : 1 1/2

Okay, let's move on to the second problem: 25% × 0.75 : 1 1/2. Again, let's start by converting everything into a format that's easier to work with. We know 25% is 0.25. The decimal 0.75 is already in a convenient form. And 1 1/2 can be expressed as an improper fraction, which is 3/2. So, the problem now reads 0.25 × 0.75 : 3/2. First, we multiply 0.25 × 0.75. To do this, we can think of 0.25 as 1/4 and 0.75 as 3/4. Multiplying these fractions gives us (1/4) × (3/4) = 3/16. In decimal form, 3/16 is 0.1875. So, the problem now looks like this: 0.1875 : 3/2. Remember, dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/2 is 2/3. Thus, the problem becomes 0.1875 × 2/3. To solve this, we can multiply 0.1875 by 2, which gives us 0.375. Then, we divide 0.375 by 3. The result is 0.125. Therefore, the answer to the second problem, 25% × 0.75 : 1 1/2, is 0.125. When dealing with percentages and fractions, it's often helpful to convert them into decimals to simplify the calculations. However, sometimes working with fractions directly can be more efficient, especially when the numbers align nicely, as in this case with 1/4 and 3/4. The key is to choose the method that feels most comfortable and efficient for you. And remember, double-checking your work is always a good idea, especially in math! It's easy to make a small mistake, but catching it early can save you a lot of frustration. Keep up the great work, and you'll become a math whiz in no time!

Problem 3: 1 1/2 × 0.75 : 1 1/2

Let's tackle the third problem: 1 1/2 × 0.75 : 1 1/2. We'll start by converting the mixed number to an improper fraction and keeping the decimal as is for now. So, 1 1/2 becomes 3/2. The problem now looks like this: 3/2 × 0.75 : 3/2. Next, let's convert the decimal 0.75 into a fraction. We know that 0.75 is equivalent to 3/4. So, the problem becomes 3/2 × 3/4 : 3/2. Now, let's perform the multiplication first: 3/2 × 3/4. To multiply fractions, we multiply the numerators (top numbers) and the denominators (bottom numbers). So, (3 × 3) / (2 × 4) = 9/8. The problem now looks like this: 9/8 : 3/2. Remember, dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/2 is 2/3. So, the problem becomes 9/8 × 2/3. Now, we multiply the fractions: (9 × 2) / (8 × 3) = 18/24. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6. So, 18/24 simplifies to 3/4. Therefore, the answer to the third problem, 1 1/2 × 0.75 : 1 1/2, is 3/4 or 0.75. This problem highlights the importance of being comfortable working with both fractions and decimals. Knowing how to convert between the two can make calculations much easier. Additionally, simplifying fractions whenever possible can prevent you from working with larger, more cumbersome numbers. And as always, understanding the order of operations is crucial to getting the correct answer. By breaking the problem down into smaller steps and carefully performing each operation, you can successfully solve even complex-looking equations. Keep practicing, and you'll build confidence in your math skills!

Problem 4: 1 1/2 × 0.5 : 3/4 × 1/2

Alright, let's jump into the fourth problem: 1 1/2 × 0.5 : 3/4 × 1/2. As before, let's convert everything into fractions to make the calculations easier. 1 1/2 is the same as 3/2, and 0.5 is the same as 1/2. So the problem now looks like this: 3/2 × 1/2 : 3/4 × 1/2. Following the order of operations, we perform multiplication and division from left to right. First, let's multiply 3/2 × 1/2. This gives us (3 × 1) / (2 × 2) = 3/4. Now, the problem is 3/4 : 3/4 × 1/2. Next, we divide 3/4 : 3/4. Dividing a number by itself equals 1. So, we now have 1 × 1/2. Finally, we multiply 1 × 1/2, which equals 1/2. Therefore, the answer to the fourth problem, 1 1/2 × 0.5 : 3/4 × 1/2, is 1/2 or 0.5. This problem showcases how important it is to follow the order of operations. If we had performed the multiplication at the end before the division, we would have gotten a different (and incorrect) answer. It also demonstrates how simplifying as you go can make the problem easier to manage. By recognizing that 3/4 divided by 3/4 equals 1, we simplified the calculation significantly. Remember, math is like building a house – each step needs to be done in the right order to ensure a solid foundation. Keep practicing these principles, and you'll become a master builder of mathematical solutions!

Problem 5: 0.5 × 1/3 : 2% - 1/2 + 1/3

Last but not least, let's tackle the fifth problem: 0.5 × 1/3 : 2% - 1/2 + 1/3. This one has a mix of decimals, fractions, and percentages, so we need to be extra careful with our conversions and order of operations. First, let's convert everything into fractions. We know 0.5 is 1/2, and 2% is 2/100, which simplifies to 1/50. So the problem now looks like this: 1/2 × 1/3 : 1/50 - 1/2 + 1/3. Following the order of operations (PEMDAS/BODMAS), we start with multiplication and division from left to right. First, we multiply 1/2 × 1/3. This gives us (1 × 1) / (2 × 3) = 1/6. Now, the problem is 1/6 : 1/50 - 1/2 + 1/3. Next, we divide 1/6 by 1/50. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/50 is 50/1 or simply 50. So, 1/6 : 1/50 becomes 1/6 × 50, which equals 50/6. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, 50/6 simplifies to 25/3. The problem is now 25/3 - 1/2 + 1/3. Now, we perform addition and subtraction from left to right. To subtract 1/2 from 25/3, we need a common denominator. The least common multiple of 3 and 2 is 6. So, we convert 25/3 to 50/6 and 1/2 to 3/6. Now we have 50/6 - 3/6 + 1/3. 50/6 - 3/6 = 47/6. Now we add 1/3. Again, we need a common denominator, which is 6. So, 1/3 becomes 2/6. The problem is now 47/6 + 2/6. Adding these fractions gives us 49/6. Therefore, the answer to the fifth problem, 0.5 × 1/3 : 2% - 1/2 + 1/3, is 49/6. We can also express this as a mixed number: 8 1/6. This problem really tests our ability to work with different types of numbers and to follow the order of operations meticulously. It also highlights the importance of simplifying fractions whenever possible to make the calculations easier. Keep practicing these skills, and you'll be able to conquer any math problem that comes your way!

I hope these explanations help you understand how to solve these problems! Remember, math is all about practice and building a strong foundation of understanding. Keep up the great work, and you'll become a math pro in no time! If you have any more questions, don't hesitate to ask. Let's keep learning and growing together!