If you have 18 tens and 20 ones, what is the total number they represent?

Introduction / Context:
This question checks your understanding of place value in the base ten number system. Tens and ones are fundamental concepts in early arithmetic and appear frequently in reasoning questions that test basic number sense. Converting a description such as 18 tens and 20 ones into a single number requires careful handling of place values and simple addition.

Given Data / Assumptions:
- There are 18 tens.- There are 20 ones.- We work in the standard base ten system, where 1 ten equals 10 ones.- We need the total value when tens and ones are combined.

Concept / Approach:
In the decimal system, each ten represents a value of 10. So 18 tens represent 18 multiplied by 10. Ones represent single units. Therefore, the total number is the sum of the value of all tens and all ones. The key is to convert the tens into their equivalent number of ones or directly into their numeric value, and then add the ones. This reinforces the idea that the digit in the tens place has a value ten times the digit itself.

Step-by-Step Solution:
- Calculate the value of 18 tens.- Each ten is equal to 10, so 18 tens is 18 * 10.- 18 * 10 = 180.- Next, calculate the value of 20 ones.- Each one is simply 1, so 20 ones is 20.- Add the value of the tens and ones: 180 + 20.- 180 + 20 = 200.- Therefore, 18 tens and 20 ones together represent the number 200.

Verification / Alternative check:
Consider grouping the 20 ones into tens. Since 10 ones make 1 ten, 20 ones are equal to 2 tens. So in total there are 18 tens plus 2 tens, that is 20 tens. Now 20 tens are equal to 20 * 10 = 200. This alternate viewpoint also leads to the same answer and confirms that the reasoning is correct.

Why Other Options Are Wrong:
- Option 1820: This looks like a concatenation of 18 and 20, but that is not how place value works.- Option 180: This represents only 18 tens and ignores the value of the 20 ones.- Option 160: This would imply that the ones somehow reduced the total rather than increasing it.- Option 220: This overcounts the contribution of tens and ones and does not match either decomposition method.

Common Pitfalls:
A common mistake is to treat the expression 18 tens 20 ones as the four digit number 1820 without converting tens and ones to their actual values. Another issue is failing to regroup the ones into tens when that makes the calculation clearer. Always remember that place value is multiplicative: the tens digit has a value equal to digit times 10, and the ones digit has value equal to digit times 1.

Final Answer:
The total number represented by 18 tens and 20 ones is 200.