Self-Test C-1.2: Transpose Equations and Formulas

Complete Self-Test C-1.2 and check your answers.

1. Add the following sets of numbers:

a. [latex]+3, +7[/latex] =                        e. [latex]–19, –1[/latex] =                    

b. [latex]+6, +9[/latex] =                        f. [latex]–37, –36[/latex] =                    

c. [latex]+1, –9[/latex] =                        g. [latex]+12, –13[/latex] =                    

d. [latex]–8, –4[/latex] =                        h. [latex]+39, –27[/latex] =                    

2. Complete the following subtraction problems:

a. [latex](+12)\space–(–3)[/latex] =                        c. [latex](–3)\space–(+6)[/latex] =                    

b. [latex](+90)\space–(+10)[/latex] =                        d. [latex](–3)\space–(+12)[/latex] =                    

3. Complete the following multiplication problems:

a. [latex](+18) \times (+2)[/latex] =                        d. [latex](–11) \times (+7)[/latex] =                    

b. [latex](–9) \times (+12)[/latex] =                        e. [latex](–7) \times (–32)[/latex] =                    

c. [latex](–8) \times (–4)[/latex] =                    

4. Complete the following division problems:

a. [latex](+14) \div (–2)[/latex] =                        c. [latex](–85) \div (+12)[/latex] =                    

b. [latex](–9) \div (–7)[/latex] =                        d. [latex](+41) \div (–2)[/latex] =                    

5. Solve each problem, using f = 8, g = 9 and h = 10.

a. [latex]h + f = a \quad a =[/latex]                               f. [latex]\frac{((f + h)g)}{2} = a \quad a =[/latex]                     

b. [latex]f^2 + 3g = y \quad y =[/latex]                               g. [latex]\frac{gf}{h} = d \quad d =[/latex]                     

c. [latex]h - 9 = b \quad b =[/latex]                               h. [latex]3(h-f) = n \quad n =[/latex]                     

d. [latex]\sqrt{g + \frac{h}{3}} = m \quad m =[/latex]                               i. [latex]2f + 3g + 4h = x \quad x =[/latex]                    

e. [latex]hfg = c \quad c =[/latex]                               j. [latex]\frac{(fg)^2}{h} = P \quad P =[/latex]                    

6. Solve the following for a and check by substituting the answer into the original equation:

a. [latex]a + 4 = 10 \quad a =[/latex]                     

b. [latex]a \space – 13 = 15 \quad a =[/latex]                     

c. [latex]2a + 12 \space – 7 = 14 \quad a =[/latex]                     

7. Solve the following for b and check:

a. [latex]14 + 12b = 99 \space – 2b \quad b =[/latex]                        c. [latex]\frac{b}{2} + 5 = 2b \quad b =[/latex]                     

b. [latex]\frac{b}{15} = 3 \quad b =[/latex]                        d. [latex]4b \space – 3 = 2b + 7 \quad b =[/latex]                     

8. Solve the following proportions for a and check:

a. [latex]\frac{a}{27} = \frac{9}{81} \quad a =[/latex]                        c. [latex]\frac{1}{a} = \frac{7}{35} \quad a =[/latex]                     

b. [latex]\frac{3}{a} = \frac{8}{36} \quad a =[/latex]                     

9. A fan turning at 1,500 RPM is moving 2,500 CFM of air. If the CFM is to be increased to 3,000, what must the new fan speed be?

RPM =                                                                                                                   

Answer Key: Self-Test C-1.2 is on the other page.