Free ASVAB Practice Tests

To divide fractions, invert the second fraction and then multiply:

\( \frac{4}{6} \) ÷ \( \frac{4}{8} \) = \( \frac{4}{6} \) x \( \frac{8}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{6} \) x \( \frac{8}{4} \) = \( \frac{4 x 8}{6 x 4} \) = \( \frac{32}{24} \) = 1\(\frac{1}{3}\)

To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

3c + 2z = 9c - 9z + 8
3c = 9c - 9z + 8 - 2z
3c - 9c = -9z + 8 - 2z
-6c = -11z + 8
c = \( \frac{-11z + 8}{-6} \)
c = \( \frac{-11z}{-6} \) + \( \frac{8}{-6} \)
c = 1\(\frac{5}{6}\)z - 1\(\frac{1}{3}\)

A concave (or converging) mirror bulges inward and focuses reflected light on the mirror's focal point where the mirror's angles of incidence converge. In contrast, a convex (or diverging) mirror bulges outward and diffuses the light waves that strike it. A common use of a concave mirror is in a reflecting telescope, a common use of a convex mirror is in the side view mirror of a car.

The Joule (J) is the standard unit of energy and has the unit \({kg \times m^2} \over s^2\).

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

The thermostat controls coolant (and, through it, engine) temperature by regulating the flow of coolant through the radiator. A bypass tube allows coolant to bypass the radiator and flow back into the water pump when its temperature is low enough that the thermostat is closed.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 50mph \times 1h \)
50 miles

To balance this lever the torques on each side of the fulcrum must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

Solving for R_a, our missing value, and plugging in our variables yields:

R_a = \( \frac{R_bd_b}{d_a} \) = \( \frac{25 lbs. \times 3 ft.}{6 ft.} \) = \( \frac{75 ft⋅lb}{6 ft.} \) = 12.5 lbs.

The atomic mass of an element listed in the Periodic Table represents the average mass of a single atom of that element and is measured in atomic mass units (amu). This number is an average as some elements have isotopes with atoms that vary in their number of neturons and, therefore, differ in weight.