Question

Four points are graphed on the number line.

Part A: Choose the two points whose values have the greatest sum. Approximate this sum. Explain your reasoning.

Part B : Choose the two points whose values have the greatest difference. Approximate this difference. Explain your reasoning.

Part C: Choose the two points whose values have the greatest product. Approximate this product. Explain your reasoning.

Part D: Choose the two points whose values have the greatest quotient. Approximate this quotient. Explain your reasoning.

Answer 1

Step 1: Given points are $R=-2.75,S=-1.25,T=0.4,U=2.1$

Step 2: Part A:

$$\begin{gathered} R+S=-2.75+(-1.25)=-4.0 \\ R+T=-2.75+0.4=-2.35 \\ R+U=-2.75+2.1=-0.65 \\ S+T=-1.25+0.4=-0.85 \\ S+U=-1.25+2.1=0.85 \\ T+U=0.4+2.1=2.5 \end{gathered}$$

The points T and U have the greatest sum.

Step 3: Part B:

$$\begin{gathered} R-S=-2.75-(-1.25)=-1.5 \\ R-T=-2.75-0.4=-3.15 \\ R-U=-2.75-2.1=-4.85 \\ S-T=-1.25-0.4=-1.65 \\ S-U=-1.25-2.1=-3.35 \\ T-U=0.4-2.1=-1.7 \end{gathered}$$.

The points R and S have the greatest difference.

Step 4: Part C:

$$\begin{gathered} R·S=-2.75·(-1.25)=3.4375 \\ R·T=-2.75·0.4=-1.1 \\ R·U=-2.75·2.1=-5.775 \\ S·T=-1.25·0.4=-0.5 \\ S·U=-1.25·2.1=-2.625 \\ T·U=0.4·2.1=0.84 \end{gathered}$$

The points R and S have the greatest product.

Step 5: Part D:

$$\begin{gathered} \frac{R}{S}=\frac{-2.75}{(-1.25)}=2.2 \\ \frac{R}{T}=\frac{-2.75}{0.4}=-6.875 \\ \frac{R}{U}=\frac{-2.75}{2.1}=-1.309 \\ \frac{S}{T}=\frac{-1.25}{0.4}=-3.125 \\ \frac{S}{U}=\frac{-1.25}{2.1}=-0.595 \\ \frac{T}{U}=\frac{0.4}{2.1}=0.190 \\ \frac{U}{T}=\frac{2.1}{0.4}=5.25 \end{gathered}$$

The points U and T have the greatest quotient.

Final Answer: The points T and U have the greatest sum.

The points R and S have the greatest difference.

The points R and S have the greatest product.

The points U and T have the greatest quotient.