Answer :
We need to check if the two fractions in each proportion are equal.
1. For the first proportion,
[tex]$$\frac{24}{30} \quad \text{and} \quad \frac{20}{25},$$[/tex]
when simplified both give
[tex]$$\frac{24}{30} = 0.8 \quad \text{and} \quad \frac{20}{25} = 0.8.$$[/tex]
Since they are equal, the first proportion is true.
2. For the second proportion,
[tex]$$\frac{10}{25} \quad \text{and} \quad \frac{40}{100},$$[/tex]
simplifying gives
[tex]$$\frac{10}{25} = 0.4 \quad \text{and} \quad \frac{40}{100} = 0.4.$$[/tex]
These fractions are equal, so the second proportion is true.
3. For the third proportion,
[tex]$$\frac{25}{45} \quad \text{and} \quad \frac{75}{135},$$[/tex]
simplifying shows
[tex]$$\frac{25}{45} \approx 0.5556 \quad \text{and} \quad \frac{75}{135} \approx 0.5556.$$[/tex]
Since they are equal, the third proportion is true.
4. For the fourth proportion,
[tex]$$\frac{18}{48} \quad \text{and} \quad \frac{20}{50},$$[/tex]
we calculate
[tex]$$\frac{18}{48} = 0.375 \quad \text{and} \quad \frac{20}{50} = 0.4.$$[/tex]
Since [tex]$0.375 \neq 0.4$[/tex], the fourth proportion is false.
Thus, the false proportion is:
[tex]$$\frac{18}{48}=\frac{20}{50}.$$[/tex]
1. For the first proportion,
[tex]$$\frac{24}{30} \quad \text{and} \quad \frac{20}{25},$$[/tex]
when simplified both give
[tex]$$\frac{24}{30} = 0.8 \quad \text{and} \quad \frac{20}{25} = 0.8.$$[/tex]
Since they are equal, the first proportion is true.
2. For the second proportion,
[tex]$$\frac{10}{25} \quad \text{and} \quad \frac{40}{100},$$[/tex]
simplifying gives
[tex]$$\frac{10}{25} = 0.4 \quad \text{and} \quad \frac{40}{100} = 0.4.$$[/tex]
These fractions are equal, so the second proportion is true.
3. For the third proportion,
[tex]$$\frac{25}{45} \quad \text{and} \quad \frac{75}{135},$$[/tex]
simplifying shows
[tex]$$\frac{25}{45} \approx 0.5556 \quad \text{and} \quad \frac{75}{135} \approx 0.5556.$$[/tex]
Since they are equal, the third proportion is true.
4. For the fourth proportion,
[tex]$$\frac{18}{48} \quad \text{and} \quad \frac{20}{50},$$[/tex]
we calculate
[tex]$$\frac{18}{48} = 0.375 \quad \text{and} \quad \frac{20}{50} = 0.4.$$[/tex]
Since [tex]$0.375 \neq 0.4$[/tex], the fourth proportion is false.
Thus, the false proportion is:
[tex]$$\frac{18}{48}=\frac{20}{50}.$$[/tex]
