Interactive study guide — Reveal Math Unit 3 · Standard 6.RP
Write ratios in three forms, identify part-to-part vs. part-to-whole relationships, and calculate unit rates.
A ratio compares two quantities. It can be written three ways: a : b, a to b, or a/b.
A part-to-part ratio compares one part of a group to another part (e.g., red marbles to blue marbles). A part-to-whole ratio compares one part to the total (e.g., red marbles to all marbles).
A unit rate is a rate with a denominator of 1. Divide to find it.
A class has 12 boys and 18 girls. What is the ratio of boys to girls in simplest form?
You drive 150 miles in 3 hours. What is the unit rate?
A bag has 5 red and 8 blue marbles. What is the part-to-whole ratio of red marbles to total marbles?
Generate equivalent ratios using multiplication and division, and verify with cross products.
Equivalent ratios are ratios that express the same relationship. Multiply or divide both terms by the same number to find them.
A ratio table organizes equivalent ratios in rows or columns. A double number line shows two quantities lined up at equivalent values.
Cross products can verify equivalence: if a/b = c/d, then a × d = b × c.
Which ratio is equivalent to 3 : 5?
In a ratio table, if the first row is 4 and 10, what pair comes next when you multiply by 2?
Are 6 : 9 and 10 : 15 equivalent? Use cross products.
Plot equivalent ratios on a coordinate plane, interpret the slope as a unit rate, and connect graphs to tables and equations.
Each equivalent ratio can be plotted as an ordered pair (x, y) on the coordinate plane. All equivalent ratios form a straight line through the origin.
The slope (steepness) of the line equals the unit rate. In the equation y = kx, k is the constant of proportionality (unit rate).
A graph of equivalent ratios always passes through which point?
The equation y = 3x represents a proportional relationship. What is the unit rate?
The point (6, 9) is on a proportional line through the origin. What is the constant of proportionality?
Compare rates to find better buys, understand percents as ratios per 100, and convert between fractions, decimals, and percents.
To find the better buy, calculate the unit rate for each option and compare.
A percent means "per 100." It is a ratio that compares a number to 100.
Converting: Fraction → Decimal → Percent
Divide numerator by denominator to get a decimal, then multiply by
100 to get a percent.
Pack A: 6 pencils for $3. Pack B: 10 pencils for $4. Which is the better buy?
What is 40% written as a fraction in simplest form?
Convert 3/8 to a percent.
Convert units within and between measurement systems using ratio reasoning and conversion factors.
A conversion factor is a ratio equal to 1 that relates two units (e.g., 12 inches / 1 foot).
Multiply by the conversion factor so the unwanted unit cancels out. For multi-step conversions, chain conversion factors.
How many feet are in 36 inches?
Convert 5 kilometers to meters. (1 km = 1,000 m)
How many inches are in 2 yards? (1 yard = 3 feet, 1 foot = 12 inches)
Tap a card to reveal the definition.