Let's analyze and correct the statements expressing the relationship between the numbers 100 and 25.
1. Division of the two numbers:
[tex]\[
\frac{100}{25} = 4
\][/tex]
This means that when you divide 100 by 25, the result is 4. So this relationship correctly corresponds to the fact that 100 divided by 25 equals 4.
2. 100 is four more than 25:
[tex]\[
25 + 4 = 29
\][/tex]
To see if 100 is four more than 25, we add 4 to 25. This gives us 29, which is not equal to 100. So, the statement that "100 is four more than 25" is incorrect.
3. 100 is one-quarter as large as 25:
[tex]\[
\frac{25}{100} = 0.25
\][/tex]
This means that if you take 25 and divide it by 100, you get 0.25. Here, the statement "100 is one-quarter as large as 25" should be reviewed. Actually, this means that "25 is one-quarter as large as 100". So, this statement is incorrectly phrased.
4. 100 is four times as large as 25:
[tex]\[
4 \times 25 = 100
\][/tex]
To verify that 100 is four times as large as 25, multiply 25 by 4. This gives 100. This statement is correct as 100 is indeed four times as large as 25.
5. 25 is four times as large as 100:
[tex]\[
4 \times 25 = 100, \quad \text{but} \quad 4 \times 100 = 400
\][/tex]
To test if 25 is four times as large as 100, we would have to multiply 25 by 4 and get a larger number than 100. However, since:
[tex]\[
4 \times 25 = 100 \quad \text{and} \quad 4 \times 100 = 400,
\][/tex]
the statement that "25 is four times as large as 100" is incorrect.
In conclusion, the correct relationships between the numbers 100 and 25 are:
- [tex]\( \frac{100}{25} = 4 \)[/tex]
- 100 is not four more than 25; 25+4=29, which is not equal to 100.
- 25 is one-quarter as large as 100 (not the other way around).
- 100 is indeed four times as large as 25.
- 25 is not four times as large as 100.
