Chapter 38, Problem 7A

To determine

(a)

The number of units counted going form $-11$ to $-2$.

Answer to Problem 7A

The main scale setting is $\text{4}\text{.725}\text{in}-\text{4}\text{.750}\text{in}$.

Explanation of Solution

Given information:

The first number is $-11$ and second number is $-2$.

The figure below shows the number scale.

Figure-(1)

Write the expression for the number of units from first number to second number for negative (left) side of the scale.

  $N=N_2-N_1$ ..... (I)

Here, the first number is $N_2$ and second number is $N_1$.

Calculation:

Substitute $-11$ for $N_2$ and $-2$ for $N_1$ in Equation (I).

  $\begin{array}{c}N=-2-\left(-11\right)\\ =-2+11\\ =+9\end{array}$

Conclusion:

Therefore, the number of units counted going form $-11$ to $-2$ is $+9$.

To determine

(b)

The number of units counted going form $-8$ to $-3$.

Answer to Problem 7A

The number of units counted going form $-8$ to $-3$ is $+5$.

Explanation of Solution

Calculation:

Substitute $-3$ for $N_2$ and $-8$ for $N_1$ in Equation (I).

  $\begin{array}{c}N=-3-\left(-8\right)\\ =-3+8\\ =+5\end{array}$

Conclusion:

Therefore, the number of units counted going form $-8$ to $-3$ is $+5$.

To determine

(c)

The number of units counted going form $-6$ to $0$.

Answer to Problem 7A

The number of units counted going form $-6$ to $0$ is $6$.

Explanation of Solution

Calculation:

Substitute $-6$ for $N_1$ and $0$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=0-\left(-6\right)\\ =+6\end{array}$

Conclusion:

Therefore, the number of units counted going form $-6$ to $0$ is $+6$.

To determine

(d)

The number of units counted going form $-2$ to $-8$.

Answer to Problem 7A

The number of units counted going form $-6$ to $0$ is $-6$.

Explanation of Solution

Calculation:

Substitute $-2$ for $N_1$ and $-8$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=-8-\left(-2\right)\\ =-8+2\\ =-6\end{array}$

Conclusion:

Therefore, the number of units counted going form $-6$ to $0$ is $-6$.

To determine

(e)

The number of units counted going form $+2$ to $-8$.

Answer to Problem 7A

The number of units counted going form $+2$ to $-8$ is $+10$.

Explanation of Solution

Calculation:

Substitute $+2$ for $N_1$ and $-8$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=+2-\left(-8\right)\\ =+2+8\\ =+10\end{array}$

Conclusion:

Therefore, the number of units counted going form $+2$ to $-8$ is $+10$.

To determine

(f)

The number of units counted going form $+3$ to $+10$.

Answer to Problem 7A

The number of units counted going form $+3$ to $+10$ is $+7$.

Explanation of Solution

Calculation:

Substitute $+3$ for $N_1$ and $+10$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=+10-\left(+3\right)\\ =+10-3\\ =+7\end{array}$

Conclusion:

Therefore, the number of units counted going form $+3$ to $+10$ is $+7$.

To determine

(g)

The number of units counted going form $+10$ to $-10$.

Answer to Problem 7A

The number of units counted going form $+10$ to $-10$ is $-20$.

Explanation of Solution

Calculation:

Substitute $+10$ for $N_1$ and $-10$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=-10-\left(+10\right)\\ =-10-10\\ =-20\end{array}$

Conclusion:

Therefore, the number of units counted going form $+10$ to $-10$ is $-20$.

To determine

(h)

The number of units counted going form $+10$ to $0$.

Answer to Problem 7A

The number of units counted going form $+10$ to $0$ is $-20$.

Explanation of Solution

Calculation:

Substitute $+10$ for $N_1$ and $-10$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=-10-\left(+10\right)\\ =-10-10\\ =-20\end{array}$

Conclusion:

Therefore, the number of units counted going form $+10$ to $-10$ is $-20$.

To determine

(i)

The number of units counted going form $+4$ to $+7$.

Answer to Problem 7A

The number of units counted going form $+4$ to $+7$ is $+3$.

Explanation of Solution

Calculation:

Substitute $+4$ for $N_1$ and $+7$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=+7-\left(+4\right)\\ =+7-4\\ =+3\end{array}$

Conclusion:

Therefore, the number of units counted going form $+4$ to $+7$ is $+3$.

To determine

(j)

The number of units counted going form $+9$ to $+1$.

Answer to Problem 7A

The number of units counted going form $+9$ to $+1$ is $-8$.

Explanation of Solution

Calculation:

Substitute $+9$ for $N_1$ and $+1$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=+1-\left(+9\right)\\ =+1-9\\ =-8\end{array}$

Conclusion:

Therefore, the number of units counted going form $+9$ to $+1$ is $-8$.

To determine

(k)

The number of units counted going form $+11$ to $0$.

Answer to Problem 7A

The number of units counted going form $+11$ to $0$ is $-11$.

Explanation of Solution

Calculation:

Substitute $+11$ for $N_1$ and $0$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=0-\left(+11\right)\\ =0-11\\ =-11\end{array}$

Conclusion:

Therefore, the number of units counted going form $+11$ to $0$ is $-11$.

To determine

(l)

The number of units counted going form $0$ to $-6$.

Answer to Problem 7A

The number of units counted going form $0$ to $-6$ is $+6$.

Explanation of Solution

Calculation:

Substitute $0$ for $N_1$ and $-6$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=0-\left(-6\right)\\ =0+6\\ =+6\end{array}$

Conclusion:

Therefore, the number of units counted going form $0$ to $-6$ is $+6$.

To determine

(m)

The number of units counted going form $-7.5$ to $+10$.

Answer to Problem 7A

The number of units counted going form $-7.5$ to $+10$ is $+17.5$.

Explanation of Solution

Calculation:

Substitute $-7.5$ for $N_1$ and $+10$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=+10-\left(-7.5\right)\\ =+10+7.5\\ =+17.5\end{array}$

Conclusion:

Therefore, the number of units counted going form $-7.5$ to $+10$ is $+17.5$.

To determine

(n)

The number of units counted going form $+10$ to $-7.5$.

Answer to Problem 7A

The number of units counted going form $+10$ to $-7.5$ is $-17.5$.

Explanation of Solution

Calculation:

Substitute $-7.5$ for $N_2$ and $+10$ for $N_1$ in Equation (I).

  $\begin{array}{c}N=-7.5-\left(+10\right)\\ =-7.5-10\\ =-17.5\end{array}$

Conclusion:

Therefore, the number of units counted going form $+10$ to $-7.5$ is $-17.5$.

To determine

(o)

The number of units counted going form $+10.8$ to $-4.3$.

Answer to Problem 7A

The number of units counted going form $+10.8$ to $-4.3$ is $+6.5$.

Explanation of Solution

Calculation:

Substitute $+10.8$ for $N_1$ and $-4.3$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=-4.3-\left(-10.8\right)\\ =-4.3+10.8\\ =+6.5\end{array}$

Conclusion:

Therefore, the number of units counted going form $+10.8$ to $-4.3$ is $+6.5$.

To determine

(o)

The number of units counted going form $-2.3$ to $-0.8$.

Answer to Problem 7A

The number of units counted going form $-2.3$ to $-0.8$ is $+3.5$.

Explanation of Solution

Calculation:

Substitute $-2.3$ for $N_1$ and $-0.8$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=-0.8-\left(-4.3\right)\\ =-0.8+4.3\\ =+3.5\end{array}$

Conclusion:

Therefore, the number of units counted going form $-2.3$ to $-0.8$ is $+3.5$.

To determine

(q)

The number of units counted going form $+7\frac{1}{2}$ to $2\frac{1}{4}$.

Answer to Problem 7A

The number of units counted going form $+7\frac{1}{2}$ to $2\frac{1}{4}$ is $-5\frac{1}{4}$.

Explanation of Solution

Calculation:

Substitute $+7\frac{1}{2}$ for $N_1$ and $2\frac{1}{4}$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=2\frac{1}{4}-\left(+7\frac{1}{2}\right)\\ =\frac{9}{4}-\frac{15}{2}\\ =\frac{18-60}{8}\\ =-5\frac{1}{4}\end{array}$

Conclusion:

Therefore, the number of units counted going form $+7\frac{1}{2}$ to $2\frac{1}{4}$ is $-5\frac{1}{4}$.

To determine

(r)

The number of units counted going form $+5\frac{3}{4}$ to $-5\frac{3}{4}$.

Answer to Problem 7A

The number of units counted going form $+5\frac{3}{4}$ to $-5\frac{3}{4}$ is $-5\frac{3}{4}$.

Explanation of Solution

Calculation:

Substitute $+5\frac{3}{4}$ for $N_1$ and $-5\frac{3}{4}$ for $N_2$ in Equation (I).

  $\begin{array}{c}N=-5\frac{3}{4}-\left(+5\frac{3}{4}\right)\\ =2\left(-\frac{23}{4}\right)\\ =-\frac{46}{4}\\ =-5\frac{3}{4}\end{array}$

Conclusion:

Therefore, the number of units counted going form $+5\frac{3}{4}$ to $-5\frac{3}{4}$ is $-5\frac{3}{4}$.