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Chapter 5: Problem 91

Evaluate. $$ 38 \div 10 $$

Short Answer

Expert verified
3.8 or 3 remainder 8

Step by step solution

01

Understand Division

The division operation breaks a number into equal parts. In this case, we need to divide 38 by 10 to find out how many times 10 fits into 38.
02

Perform the Division

Divide 38 by 10. When dividing, start with the whole number part. 38 divided by 10 gives 3 as the whole number part because 10 fits into 38 three times.
03

Find the Remainder

Next, calculate the remainder. Since 10 fits into 38 three times completely, we multiply 10 by 3 which equals 30. Subtract 30 from 38 to find the remainder: 38 - 30 = 8.
04

Express the Result

Combine the whole number part and the remainder to express the result. The division 38 divided by 10 is 3 remainder 8, which can also be expressed as: 3 with a remainder of 8 or 3.8 when using decimal notation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Division operation
Let's explore the idea of division first. Division helps us split a number into equal smaller parts. When you see a problem like \(38 \div 10\), it means we want to see how many times 10 fits into 38 without going over.
Think of it like having 38 candies and wanting to make as many packs of 10 candies as possible. You repeatedly group the candies into packs of 10 until you can't group anymore.

For our example:
  • Start by seeing how many times 10 fits into 38.
  • 10 fits into 38 a total of 3 times as 10 * 3 = 30.
  • So, the whole number result of the division is 3.
Finding remainder
Next, let's find out what happens to the leftover part after forming complete groups.
After grouping the 38 candies into 3 full packs of 10, we have used 30 candies (since 10 * 3 = 30). Now, we subtract the used candies from the total to find the remainder.
For our case:
  • 38 - 30 = 8.
So, the remainder is 8, indicating we have 8 candies left after making full packs.
Similarly, in mathematical terms, when you divide 38 by 10, you are left with a remainder of 8.
Expressing results in decimal notation
Now, it's time to express our result in a more universal format 鈥� decimal notation.
Decimal notation helps in understanding the result of division in a simpler form.
Remember we got 3 as the whole number part and 8 as the remainder in our previous steps. We can also express it as a decimal:
Here's how:
  • First, take the whole number result, which is 3.
  • Next, understand that the remainder 8 is actually a part of the next 10.
  • So, represent it as 8 out of 10, which is \(\frac{8}{10}\) or 0.8 in decimal form.
Combining these, we get 3 + 0.8 = 3.8.

So, \(38 \div 10\) can be expressed as 3.8 in decimal notation.

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