Explore ratios and unit rates, fractions, and positive and negative numbers through everyday examples. Work through each idea, then try practice questions with clear explanations.
Lesson 1 · Ratios and unit rates
A ratio compares two quantities. A unit rate tells you how much of one quantity corresponds to one of another, such as dollars per notebook or miles per hour.
A classroom has 3 blue markers for every 5 red markers. The ratio of blue to red is 3:5.
If the number of each color doubles, there are 6 blue and 10 red markers. The comparison stays the same: 6:10 = 3:5.
Multiplying both parts of a ratio by the same nonzero number makes an equivalent ratio.
3:5 → 6:10 → 9:15Four identical notebooks cost $12. What is the price of one notebook?
“Per” is a useful clue that you're describing a rate for one unit.
Build your toolkit
These ideas connect to more advanced mathematics in Grades 7 and 8.
Multiply or divide both parts by the same nonzero value. Use tables to spot patterns and solve missing-value problems.
Both quantities were multiplied by 4.
Division can ask how many pieces of a certain size fit into a whole quantity.
There are six half-units in three wholes.
Use a number line to compare values above and below zero. Negative numbers are less than zero.
Numbers farther right on the line are greater.
Genius Practice
Choose a skill and answer three questions. Each answer includes an explanation so you can learn from the reasoning.
Question 1 of 3
Keep learning
Ask, “How do you know?” and “Can you check it another way?” Explaining a strategy helps students notice patterns and build confidence.