Representing Equivalent Ratios in Tables
Representing equivalent ratios in tables is a Grade 6 math skill in Big Ideas Math Advanced 1, Chapter 5: Ratios and Rates. Students create ratio tables by scaling a given ratio up or down, ensuring every row maintains the same multiplicative relationship. This skill connects to proportional reasoning and unit rate concepts.
Key Concepts
Two ratios, $a : b$ and $c : d$, are equivalent ratios if there is a positive number $p$ such that $$c = p \times a, \quad d = p \times b.$$ This means you can create equivalent ratios by multiplying both parts of the ratio by the same positive number. Ratio tables organize these equivalent ratios in rows or columns to show the relationship clearly.
Common Questions
How do you represent equivalent ratios in a table?
Start with a known ratio and multiply or divide both quantities by the same number to create additional rows. Each row in the table must have the same ratio (same unit rate). For example, 2:3 becomes 4:6, 6:9, 8:12.
How do you check if ratios in a table are equivalent?
Divide the two quantities in each row. If the quotient (unit rate) is the same for all rows, the ratios are equivalent. You can also cross multiply to verify: if a/b = c/d, then ad = bc.
What is the connection between equivalent ratios and proportions?
Equivalent ratios are the basis of proportionality. When two ratios are equivalent, they form a proportion. A table of equivalent ratios is a visual representation of a proportional relationship.
Where is this skill taught in Big Ideas Math Advanced 1?
Representing equivalent ratios in tables is covered in Chapter 5: Ratios and Rates of Big Ideas Math Advanced 1, the Grade 6 math textbook.