1. Lesson 107: Numbers, Numerals, and Value Number Word Problems

2. We remember that a numeral is a single symbol or a meaningful arrangement of symbols that we use to represent a particular number. We say that the value of each of the following numerals is three, because each numeral represents the number /27 2 – 1 2

3. Thus, we see that number and value mean the same thing
Thus, we see that number and value mean the same thing. Also, we see that it would be redundant to speak of the value of a number, because that is the same thing as saying the number of a number. But we can speak of the value of a numeral, because this is the number represented by the numeral. Since paying excessive attention to the difference between a number and a numeral is often counterproductive, we sometimes use the word number when we should use the word numeral.

4. The value of a digit in a decimal numeral depends on the position of the digit with respect to the decimal point. The digit 6 in the numeral has a value of 6 times 1, or 6, because it is in the units place, which is the first place to the left of the decimal point. The digit 9 has a value of 9 times 10, or 90, because it is in the tens place, which is two places to the left of the decimal point. The digit 4 has a value of 400 because it is in the hundreds place, which is three places to the left of the decimal point. We can use the fact that the value of a digit depends on its position to solve some rather interesting word problems.

5. To solve these problems, we will use U to represent the units digit; T to represent the tens digit, and H to represent the hundreds digit. Also, we will say that
The value of the units digit is 1U
The value of the tens digit is 10T
The value of the hundreds digit is 100H

6. Example: The sum of the digits in a two digit counting number is 11
Example: The sum of the digits in a two digit counting number is 11. If the digits are reversed, the new number is 27 greater than the original number. What was the original number?

7. Answer: U + T = 11 10T + U 10U + T 10T + U + 27 = 10U + T 47

8. Example: The sum of the digits of a two digit counting number was 9
Example: The sum of the digits of a two digit counting number was 9. when the digits were reversed, the new number was 45 less than the original number. What was the original number?

9. Answer: T + U = 9 10T + U 10U + T 10U + T + 45 = 10T + U 72

10. Example: The sum of the digits in a two digit counting number was 15
Example: The sum of the digits in a two digit counting number was 15. if the digit were reversed, the new number was 9 greater than the original number. What was the original number?

11. Answer: 78

12. HW: Lesson 107 #1-30