Page 179 - ABCTE Study Guide_Neat

Review

There are a number of rules for working with exponents and powers. Most importantly:

• To multiply powers with the same base, add their exponents.
• To divide powers with the same base, subtract their exponents.
• To raise a power to a power, multiply the exponents.
• Any number raised to the zero power is one.

The opposite operation of raising a number to a power is taking its root.

• Finding fractional powers of a number is the same as finding the root of a number:
raising a number to the 1/2 power is the same as finding its square root.
• Numbers in scientific notation are composed of a decimal number between 1 and 10
and a power of 10.
• Numbers between 0 and 1 have negative exponents.
• Numbers greater than 1 have positive exponents.

Proportional Reasoning

Lesson Objective

Now let's turn our attention to ratios and proportions. We'll also discuss the idea of scale, and see how this
applies to a geometric figure.

Previously Covered

• In the previous section, we refreshed your memory on bases, powers, exponents, roots,
and their attendant operations.
• We also covered the basics of scientific notation.

Ratios and Proportions

A ratio is a quotient used to compare two numbers.

A ratio can be represented:

• As a fraction ( )
• With a colon (4 : 5 )
• With the word to (4 to 5)

Although a ratio may look like a fraction, it can have a larger first number (top) than second number
(bottom).

A proportion is two or more ratios that are equivalent to each other. In a proportion, the cross products
are equal. Cross products are the result of multiplying on the diagonal across the equal sign.