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Answer :
To solve the division problem [tex]\(83.5 \div 6.25\)[/tex], we start with a couple of key steps to simplify the process by eliminating the decimals. Here's a detailed step-by-step explanation:
1. Remove Decimals: To make the division easier, multiply both the dividend (83.5) and the divisor (6.25) by 100. This step achieves two objectives:
- It converts the decimal numbers into whole numbers, which are often easier to divide.
- It simplifies the division process using larger numbers that are directly proportional to the original values.
So, we have:
- [tex]\(83.5 \times 100 = 8350\)[/tex]
- [tex]\(6.25 \times 100 = 625\)[/tex]
2. New Division Problem: Now, you can rewrite the division problem with whole numbers:
[tex]\[
\text{New division problem: } 8350 \div 625
\][/tex]
3. Perform the Division: Proceed by dividing 8350 by 625. This simplifies nicely, leading to:
[tex]\[
8350 \div 625 = 13.36
\][/tex]
So, the quotient of [tex]\(83.5 \div 6.25\)[/tex] is 13.36.
By following these steps, you can see how decimals are handled by scaling up, performing integer division, and maintaining the same quotient as the original problem with decimals.
1. Remove Decimals: To make the division easier, multiply both the dividend (83.5) and the divisor (6.25) by 100. This step achieves two objectives:
- It converts the decimal numbers into whole numbers, which are often easier to divide.
- It simplifies the division process using larger numbers that are directly proportional to the original values.
So, we have:
- [tex]\(83.5 \times 100 = 8350\)[/tex]
- [tex]\(6.25 \times 100 = 625\)[/tex]
2. New Division Problem: Now, you can rewrite the division problem with whole numbers:
[tex]\[
\text{New division problem: } 8350 \div 625
\][/tex]
3. Perform the Division: Proceed by dividing 8350 by 625. This simplifies nicely, leading to:
[tex]\[
8350 \div 625 = 13.36
\][/tex]
So, the quotient of [tex]\(83.5 \div 6.25\)[/tex] is 13.36.
By following these steps, you can see how decimals are handled by scaling up, performing integer division, and maintaining the same quotient as the original problem with decimals.
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