CoResolva Step By Step Solutions To Math Problems

Hey guys! Welcome to our deep dive into solving some math equations with CoResolva. We're going to break down each problem step-by-step, making sure you not only get the right answers but also understand the process behind them. So, grab your pencils, and let's get started!

A) 8752 – 25.56 = ?

Let's kick things off with subtraction. Subtraction is one of the foundational operations in mathematics, and mastering it is crucial for more complex calculations. In this case, we're subtracting a decimal number from a whole number. To accurately perform this calculation, it's essential to align the decimal points correctly. This ensures that we're subtracting the correct place values from each other. When dealing with whole numbers and decimals, think of the whole number as having an implied decimal point at the end (e.g., 8752 is the same as 8752.00). This will help you line up the numbers properly. Now, let’s dive into the solution.

First, write down the numbers vertically, aligning the decimal points:

  8752.00
-   25.56
-------

Notice how we've added .00 to 8752 to make the subtraction cleaner. Now, we'll perform the subtraction column by column, starting from the rightmost column. If a digit in the top number is smaller than the corresponding digit in the bottom number, we'll need to borrow from the digit to its left. This is a fundamental part of the subtraction process, and it’s important to understand when and how to borrow. In the hundredths column, we have 0 – 6. Since 0 is less than 6, we need to borrow from the tenths column. But the tenths column also has a 0, so we need to borrow from the ones column first. Borrowing 1 from the ones column turns the 2 into a 1, and the 0 in the tenths column becomes 10. Now we can borrow 1 from the 10, making it 9, and the 0 in the hundredths column becomes 10.

Now we can subtract: 10 – 6 = 4. Write down 4 in the hundredths place. Moving to the tenths column, we have 9 – 5 = 4. Write down 4 in the tenths place. In the ones column, we have 1 – 5. Again, we need to borrow. Borrow 1 from the tens column, making the 5 into a 4, and the 1 becomes 11. Now, 11 – 5 = 6. Write down 6 in the ones place. In the tens column, we have 4 – 2 = 2. Write down 2 in the tens place. In the hundreds and thousands columns, we simply bring down the digits since there are no corresponding digits to subtract. Thus, the result is 8726.44. So, 8752 – 25.56 = 8726.44.

Solution: 8752 – 25.56 = 8726.44

B) 7865 × 5.6 = ?

Next up, we have a multiplication problem involving a whole number and a decimal. Multiplication is essentially repeated addition, and it's vital in many areas of math and real-life applications. When multiplying with decimals, the key is to ignore the decimal point during the multiplication process and then place it correctly in the final answer. Let’s walk through this calculation step-by-step to ensure you grasp the technique.

First, we set up the multiplication as if there were no decimal points:

  7865
×   5.6
-------

Now, we multiply 7865 by 6 (ignoring the decimal for now). 6 × 5 = 30, write down 0 and carry over 3. 6 × 6 = 36, plus the carried-over 3, gives 39, write down 9 and carry over 3. 6 × 8 = 48, plus the carried-over 3, gives 51, write down 1 and carry over 5. 6 × 7 = 42, plus the carried-over 5, gives 47. So, the first partial product is 47190. Next, we multiply 7865 by 5. Since we’re multiplying by the tens digit, we add a 0 as a placeholder in the ones place of the second partial product. 5 × 5 = 25, write down 5 and carry over 2. 5 × 6 = 30, plus the carried-over 2, gives 32, write down 2 and carry over 3. 5 × 8 = 40, plus the carried-over 3, gives 43, write down 3 and carry over 4. 5 × 7 = 35, plus the carried-over 4, gives 39. So, the second partial product is 393250.

Now, we add the two partial products:

  47190
+ 393250
--------
 440440

Finally, we need to place the decimal point. In the original problem, 5.6 has one decimal place. Therefore, our answer should also have one decimal place. So, we count one place from the right in 440440 and place the decimal point. This gives us 44044.0. Thus, 7865 × 5.6 = 44044.

Solution: 7865 × 5.6 = 44044

C) 865.5 ÷ 40 = ?

Let's tackle division, where we're dividing a decimal number by a whole number. Division is the inverse operation of multiplication and helps us distribute a quantity into equal parts. When dividing decimals, it's essential to keep track of the decimal point's placement. In this case, we’re dividing 865.5 by 40. Let’s see how to solve this step-by-step.

First, set up the long division problem:

40 | 865.5

We start by dividing 86 by 40. 40 goes into 86 two times (2 × 40 = 80). Write 2 above the 6 in 865. Subtract 80 from 86, which gives 6. Bring down the next digit, 5, to make 65. Now, divide 65 by 40. 40 goes into 65 one time (1 × 40 = 40). Write 1 next to the 2 above. Subtract 40 from 65, which gives 25. Bring down the 5 after the decimal point, and also bring the decimal point up into the quotient (above the division line). We now have 255. Divide 255 by 40. 40 goes into 255 six times (6 × 40 = 240). Write 6 next to the 1 in the quotient. Subtract 240 from 255, which gives 15. Add a 0 to the dividend (after the 5) and bring it down, making it 150. Divide 150 by 40. 40 goes into 150 three times (3 × 40 = 120). Write 3 next to the 6 in the quotient. Subtract 120 from 150, which gives 30. Add another 0 to the dividend and bring it down, making it 300. Divide 300 by 40. 40 goes into 300 seven times (7 × 40 = 280). Write 7 next to the 3 in the quotient. Subtract 280 from 300, which gives 20. We could continue this process, but for most practical purposes, rounding to a few decimal places is sufficient. In this case, we have 21.637. Rounding to two decimal places, we get 21.64.

Solution: 865.5 ÷ 40 = 21.64 (rounded to two decimal places)

D) 2.15 × 59.8 = ?

Here we have another multiplication problem, this time involving two decimal numbers. The approach is similar to our previous multiplication problem: multiply as if there are no decimal points, and then place the decimal point in the final answer. This requires careful attention to detail to ensure accuracy. Let's break down this calculation to make it clear.

First, let's set up the multiplication:

   2.15
× 59.8
-------

Multiply 215 by 8 (ignoring the decimals for now). 8 × 5 = 40, write down 0 and carry over 4. 8 × 1 = 8, plus the carried-over 4, gives 12, write down 2 and carry over 1. 8 × 2 = 16, plus the carried-over 1, gives 17. So, the first partial product is 1720. Next, multiply 215 by 9. Since we’re multiplying by the tens digit, add a 0 as a placeholder. 9 × 5 = 45, write down 5 and carry over 4. 9 × 1 = 9, plus the carried-over 4, gives 13, write down 3 and carry over 1. 9 × 2 = 18, plus the carried-over 1, gives 19. So, the second partial product is 19350. Finally, multiply 215 by 5. Since we’re multiplying by the hundreds digit, add two 0s as placeholders. 5 × 5 = 25, write down 5 and carry over 2. 5 × 1 = 5, plus the carried-over 2, gives 7. 5 × 2 = 10. So, the third partial product is 107500.

Now, we add the partial products:

   1720
 19350
+107500
--------
128570

Next, we need to place the decimal point. In the original problem, 2.15 has two decimal places and 59.8 has one decimal place. So, in total, we have 2 + 1 = 3 decimal places. Therefore, our answer should have three decimal places. Count three places from the right in 128570 and place the decimal point. This gives us 128.570. Thus, 2.15 × 59.8 = 128.57.

Solution: 2.15 × 59.8 = 128.57

E) 605.2 ÷ 2.5 = ?

Let's dive into another division problem, but this time we're dividing a decimal by another decimal. Dividing by a decimal can seem tricky, but we'll simplify it by converting the divisor into a whole number. This makes the division process much easier to manage. So, how do we do that? Let’s break it down step by step.

First, write down the division problem:

2.  5 | 605.2

The key here is to eliminate the decimal in the divisor (2.5). To do this, we multiply both the divisor and the dividend by the same power of 10. In this case, we multiply both by 10 to move the decimal point one place to the right in the divisor. This gives us:

25 | 6052

Now we perform the long division with the whole number divisor. Divide 60 by 25. 25 goes into 60 two times (2 × 25 = 50). Write 2 above the 0 in 6052. Subtract 50 from 60, which gives 10. Bring down the next digit, 5, to make 105. Now, divide 105 by 25. 25 goes into 105 four times (4 × 25 = 100). Write 4 next to the 2 above. Subtract 100 from 105, which gives 5. Bring down the next digit, 2, to make 52. Divide 52 by 25. 25 goes into 52 two times (2 × 25 = 50). Write 2 next to the 4 above. Subtract 50 from 52, which gives 2. Since we have a remainder, we add a 0 to the dividend and bring it down, making it 20. However, 25 does not go into 20, so we add another 0 to the dividend and to the quotient after adding a decimal point, making it 200. 25 goes into 200 eight times (8 × 25 = 200). Write 8 next to the 2 in the quotient. Subtract 200 from 200, which gives 0. Thus, 605.2 ÷ 2.5 = 242.08.

Solution: 605.2 ÷ 2.5 = 242.08

F) 92.55 – 4548.3 = ?

In this problem, we're dealing with subtraction again, but this time, we're subtracting a larger number from a smaller one. This will result in a negative number. Understanding how to handle negative numbers is crucial in mathematics, as they often appear in various contexts. Let's walk through the steps to solve this problem accurately.

First, set up the subtraction. Since we're subtracting a larger number from a smaller one, we can rewrite the problem as the negative of the difference between the two numbers. This means we’ll subtract the smaller number from the larger number and then add a negative sign to the result. Write down the numbers vertically, aligning the decimal points:

  4548.30
-   92.55
-------

Notice that we've added a 0 to 4548.3 to make the subtraction cleaner. Now, we'll perform the subtraction column by column, starting from the rightmost column. In the hundredths column, we have 0 – 5. Since 0 is less than 5, we need to borrow from the tenths column. Borrow 1 from the 3, making it 2, and the 0 becomes 10. Now, 10 – 5 = 5. Write down 5 in the hundredths place. Moving to the tenths column, we have 2 – 5. Again, we need to borrow. Borrow 1 from the ones column, making the 8 into a 7, and the 2 becomes 12. Now, 12 – 5 = 7. Write down 7 in the tenths place. In the ones column, we have 7 – 2 = 5. Write down 5 in the ones place. In the tens column, we have 4 – 9. We need to borrow from the hundreds column. Borrow 1 from the 5, making it 4, and the 4 becomes 14. Now, 14 – 9 = 5. Write down 5 in the tens place. In the hundreds column, we have 4, and in the thousands column, we also have 4. So, the difference is 4455.75. Since we were subtracting a larger number from a smaller one, our answer will be negative. Thus, 92.55 – 4548.3 = -4455.75.

Solution: 92.55 – 4548.3 = -4455.75

G) 748 ÷ 56 = ?

Let's move on to another division problem, this time dividing a whole number by another whole number. This is a fundamental skill in arithmetic and is used in various everyday situations. We'll use long division to solve this problem, which involves dividing 748 by 56. So, let's get started and break down the steps.

First, set up the long division:

56 | 748

We start by seeing how many times 56 goes into 74. 56 goes into 74 one time (1 × 56 = 56). Write 1 above the 4 in 748. Subtract 56 from 74, which gives 18. Bring down the next digit, 8, to make 188. Now, divide 188 by 56. 56 goes into 188 three times (3 × 56 = 168). Write 3 next to the 1 above. Subtract 168 from 188, which gives 20. Since there are no more digits to bring down, 20 is our remainder. We can express the result as a mixed number or as a decimal. To express it as a mixed number, we write the remainder over the divisor: 13 20/56. We can simplify the fraction 20/56 by dividing both the numerator and the denominator by their greatest common divisor, which is 4. So, 20 ÷ 4 = 5 and 56 ÷ 4 = 14. Thus, the mixed number is 13 5/14. To express the result as a decimal, we add a decimal point and a 0 to the dividend (748) and bring it down, making it 200. Divide 200 by 56. 56 goes into 200 three times (3 × 56 = 168). Write 3 after the decimal point in the quotient. Subtract 168 from 200, which gives 32. Add another 0 to the dividend and bring it down, making it 320. Divide 320 by 56. 56 goes into 320 five times (5 × 56 = 280). Write 5 next to the 3 in the quotient. Subtract 280 from 320, which gives 40. We could continue this process, but for most practical purposes, rounding to a few decimal places is sufficient. In this case, we have 13.35. So, 748 ÷ 56 ≈ 13.36 (rounded to two decimal places).

Solution: 748 ÷ 56 = 13.36 (rounded to two decimal places)

H) 49.8% de 1500 = ?

Finally, let's tackle a percentage problem. Percentages are used extensively in everyday life, from calculating discounts to understanding statistics. In this case, we're finding 49.8% of 1500. To do this, we first convert the percentage to a decimal and then multiply it by the number. Let’s break it down.

To convert a percentage to a decimal, we divide it by 100. So, 49.8% becomes 49.8 ÷ 100 = 0.498. Now, we multiply this decimal by 1500:

  0.498
× 1500
-------

First, multiply 0.498 by 0 (the ones place in 1500), which gives 0. Next, multiply 0.498 by 0 (the tens place in 1500), which also gives 0. Finally, multiply 0.498 by 15 (treating 1500 as 15 × 100):

    498
×  15
-------
   2490
+ 498
-------
  7470

So, 0.498 × 15 = 7.47. Since we multiplied by 15 instead of 1500, we need to multiply the result by 100: 7.47 × 100 = 747. Therefore, 49.8% of 1500 is 747.

Solution: 49.8% de 1500 = 747

Conclusion

And there you have it! We've solved a range of math problems using CoResolva, covering subtraction, multiplication, division, and percentages. Remember, the key to mastering math is practice and understanding the underlying concepts. Keep practicing, and you'll become a math whiz in no time! If you have any questions or want to explore more problems, feel free to ask. Happy calculating, guys!