Math Problems: Rounding, Division, Currency & Fractions

Let's break down these math problems step by step! We'll cover rounding, division, currency calculations, fractions, and more. If you're looking to sharpen your math skills, you've come to the right place. This guide aims to provide clear, concise explanations and solutions to help you understand these core mathematical concepts better. Whether you're a student, a parent helping with homework, or just someone who enjoys a good math challenge, we've got you covered. So, let's dive in and tackle these problems together, making math a little less daunting and a lot more fun. Remember, practice makes perfect, so feel free to revisit these explanations and try similar problems on your own.

1. Round 87 to the Nearest 10

When we're rounding, we're trying to find the closest multiple of 10. In this case, we're looking at 87. Think of the multiples of 10 around it: 80 and 90. Now, which one is 87 closer to? To figure this out, we look at the ones digit, which is 7. A helpful rule is that if the ones digit is 5 or more, we round up. If it's 4 or less, we round down. Since 7 is more than 5, we round up to the next multiple of 10. So, 87 rounded to the nearest 10 is 90. Rounding is a handy skill in everyday life. It helps us estimate totals, simplify numbers, and make quick calculations without needing exact figures. For instance, if you're estimating the cost of groceries, rounding each item's price to the nearest dollar can give you a rough total quickly. This concept extends beyond just rounding to the nearest 10; you can round to the nearest hundred, thousand, or any other place value, following the same principles. Remember, the goal of rounding is to simplify a number while keeping it reasonably close to its original value.

2. What is 200 Divided by 10?

Division is like splitting something into equal parts. When we divide 200 by 10, we're asking, "How many groups of 10 can we make from 200?" One way to think about it is to remove a zero from both numbers. So, 200 becomes 20, and 10 becomes 1. This simplifies the problem to 20 divided by 1, which is simply 20. Another way to visualize this is to think of 200 as 20 sets of 10. If you have 200 objects and you want to group them into sets of 10, you'll end up with 20 groups. This concept of division is fundamental in many areas of math and everyday life. Whether you're splitting a pizza among friends, calculating how many hours you need to work to earn a certain amount of money, or figuring out the average score on a test, division is a crucial tool. Understanding the relationship between division and multiplication is also key. Division is the inverse operation of multiplication, meaning that if 200 divided by 10 equals 20, then 20 multiplied by 10 equals 200.

3. Express the Sum of 26p, 28p, and 50p in Pounds (£)

This question involves adding amounts of money and then converting from pence (p) to pounds (£). First, we need to add the amounts together: 26p + 28p + 50p. Let's add 26p and 28p first, which gives us 54p. Now, add 54p to 50p, and we get 104p. But the question asks for the answer in pounds. Remember, there are 100 pence in one pound. So, to convert 104p to pounds, we divide by 100. 104 divided by 100 is £1.04. We can also think of this as 104p being one full pound (100p) and 4 pence left over. So, the total in pounds is £1.04. Understanding how to work with money is a practical skill that we use every day. It's important to be comfortable with adding and subtracting amounts, as well as converting between different units like pence and pounds (or cents and dollars in other currencies). This skill is essential for budgeting, shopping, and managing your finances. Practice makes perfect when it comes to handling money calculations, so keep working on similar problems to build your confidence.

4. Verify if 27p Equals 5p Plus Six 2ps

Here, we need to check if the two sides of the equation are equal. On one side, we have 27p. On the other side, we have "5p plus six 2ps." First, let's calculate the value of six 2ps. Six times 2 is 12, so six 2ps is 12p. Now, we add this to 5p: 5p + 12p = 17p. So, the right side of the equation is 17p. Now, we compare the two sides: 27p (left side) and 17p (right side). Clearly, 27p is not equal to 17p. Therefore, 27p does not equal 5p plus six 2ps. This type of problem tests your ability to follow instructions, perform basic arithmetic, and compare values. It’s a fundamental skill in mathematics to be able to break down a problem into smaller steps, solve each step, and then put the results together to get the final answer. In this case, we had to multiply, add, and then compare. These are all core mathematical operations that are used in a wide range of applications. Accuracy is also key in these types of problems, so it’s always a good idea to double-check your calculations.

5. How Many Tenths Are There in 1 1/2?

This question deals with fractions. First, we need to understand what "tenths" means. A tenth is one part of a whole that has been divided into 10 equal parts, or 1/10. Now, let's look at the number 1 1/2. This is a mixed number, which means it has a whole number part (1) and a fraction part (1/2). To find out how many tenths are in 1 1/2, we first need to convert it to an improper fraction. An improper fraction has a numerator (the top number) that is greater than or equal to the denominator (the bottom number). To convert 1 1/2 to an improper fraction, we multiply the whole number (1) by the denominator (2) and add the numerator (1). This gives us (1 * 2) + 1 = 3. So, 1 1/2 is equal to 3/2. Now, we want to express 3/2 in terms of tenths. To do this, we need to find an equivalent fraction with a denominator of 10. We can do this by multiplying both the numerator and the denominator of 3/2 by 5: (3 * 5) / (2 * 5) = 15/10. So, 1 1/2 is equal to 15/10. This means there are 15 tenths in 1 1/2. Understanding fractions is crucial for many areas of math, from basic arithmetic to more advanced topics like algebra and calculus. It’s important to be comfortable with converting between mixed numbers and improper fractions, finding equivalent fractions, and performing operations like addition, subtraction, multiplication, and division with fractions.

6. Subtract 36p from £1

This problem involves subtraction and working with different units of currency. We need to subtract 36p from £1. To do this easily, we first need to convert £1 into pence. We know that there are 100 pence in £1. So, £1 is equal to 100p. Now we can subtract 36p from 100p: 100p - 36p. To do this subtraction, we can think of it in a few ways. One way is to break 36p into 30p and 6p. First, subtract 30p from 100p: 100p - 30p = 70p. Then, subtract 6p from 70p: 70p - 6p = 64p. So, 100p - 36p = 64p. Therefore, subtracting 36p from £1 leaves us with 64p. This problem highlights the importance of being comfortable with subtraction and understanding how to convert between different units. Working with money often involves these types of calculations, whether you're figuring out change, budgeting your expenses, or calculating discounts. Practice with similar problems will help you build your confidence and accuracy when dealing with money-related math.

7. How Many 2p Coins Have the Same Value as Four 10p Coins?

This question involves multiplication and understanding the value of different coins. First, we need to calculate the total value of four 10p coins. To do this, we multiply the number of coins (4) by the value of each coin (10p): 4 * 10p = 40p. So, four 10p coins have a total value of 40p. Now, we need to find out how many 2p coins have the same value as 40p. To do this, we divide the total value (40p) by the value of each 2p coin (2p): 40p / 2p. 40 divided by 2 is 20. So, 20 2p coins have the same value as four 10p coins. This problem tests your understanding of multiplication and division, as well as your familiarity with the value of different coins. It’s a practical skill to be able to calculate the value of a collection of coins and to understand how many coins of one denomination are equivalent to a certain value in another denomination. These types of calculations come up in everyday situations, like when you're making purchases, counting change, or managing your money.