Week 12: Rational expressions, statistics, and signed-number review

Field Book

44 to 47

Due

Test 10 due

Method

Paper first, every step

Fractions grow letters this week, and they follow the same law as always: matching denominators add their tops. The data toolkit opens too: mean, median, mode, and range, four ways to make one number speak for many.

What you have to be able to do

Add rational expressions with a common denominator
Find the mean, median, mode, and range of a data set
Stay sharp on signed-number arithmetic

The procedures

Rational expressions

A rational expression is a fraction with letters in it.
Same denominators: add or subtract the numerators, keep the denominator.
Collect like terms in the numerator when you finish.

The four statistics

Mean: add them all, divide by how many.
Median: order the list, take the middle value.
Mode is the most frequent value; range is largest minus smallest.

Signed-number review

Subtracting is still adding the opposite.
An even count of negative factors is positive; odd is negative.
Absolute value is distance, so it never goes negative.

Worked

WORKED

Add 2x7 + 4x7.
Same denominator: add the tops.
2x + 4x is 6x.
ANSWER: 6x7

WORKED

For the data 4, 9, 6, 9, 2: find the mean, median, mode, and range.
Ordered: 2, 4, 6, 9, 9. The sum is 30, and there are 5 values.
Mean 6, middle value 6, most frequent 9, spread 9 − 2.
ANSWER: mean 6, median 6, mode 9, range 7

Terms

Term	Meaning
rational expression	a fraction with letters in it
mean	add them all and divide by how many
median	the middle value of the ordered list
range	largest value minus smallest

Check yourself

1. Add: x3 + x3

2. Find the median of 3, 8, 5, 10, 7

3. Compute −5 − (−12)

reveal answers

2x3 · 7 · 7

This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.