Rational Numbers
Lessons in this chapter
About Rational Numbers
Rational Numbers completes the number line for 6th grade: every fraction and decimal, positive and negative, now has a place on it.
Identify Rational Numbers gives the definition: any number that can be written as a fraction of two integers. That takes in whole numbers, fractions, terminating decimals and repeating decimals, which is almost every number kids have met.
Plot Rational Numbers on Number Line is the lesson that makes them concrete. Placing −3 and a half, 0.75 and two thirds on the same line requires converting between forms, which is why the fraction and decimal chapters come first.
Find Opposites and Absolute Values of Rational Numbers extends 6th grade's integer work to fractions and decimals, with no change to the meaning: the opposite is the mirror across zero and the absolute value is the distance.
Compare and Order Rational Numbers is the hardest lesson because the numbers arrive in mixed forms. Comparing −2 and three quarters with −2.8 means converting to a common form first, and then remembering that with negatives the larger absolute value is the smaller number.
Each of the four lessons in Rational Numbers opens as a 6th grade math worksheet in the page. Plot Rational Numbers on Number Line and Compare and Order Rational Numbers in particular give math problems worked one at a time and marked as you go, since both are easier to judge from attempts than from an explanation. Free to try, with no login needed for your first 3.
Frequently asked questions
Identify Rational Numbers widens the number line again, from integers to anything that can be written as one whole number over another, which brings fractions and decimals and their negatives into the same system. Plot Rational Numbers on Number Line gives that a picture, and the third lesson extends opposites and absolute value from integers to these new numbers. Compare and Order Rational Numbers closes it by asking children to order a mixed set, where a fraction and a decimal and a negative have to be compared against each other. The chapter sits in the Common Core domain The Number System (6.NS).
Any number that can be written as a fraction of two integers. Whole numbers, fractions, terminating decimals and repeating decimals all qualify.
Every terminating or repeating decimal is. A decimal that never ends and never repeats, like pi, is not, but those come later.
Convert to one form first. Three quarters is 0.75, so you are comparing −2.8 with −2.75, and −2.8 is further left, so it is smaller.
Because a larger distance from zero on the negative side means further left. −8 has a bigger absolute value than −3 and is the smaller number.
Same ideas, wider set. Opposites and absolute value work identically; only the numbers they apply to have expanded to include fractions and decimals.