Explore the foundational concepts of mathematics through engaging problem-solving and real-world applications in 7th grade.
A ratio is a way to compare two amounts, showing how many times one value contains or is contained by the other. Ratios can be written in three ways: 3 to 2, 3:2, or \( \frac{3}{2} \).
When two ratios are equal, we call them a proportion. Proportional relationships are all around us, from recipes to maps and even shopping discounts!
To solve for an unknown in a proportion, you can use cross-multiplication. If \( \frac{a}{b} = \frac{c}{d} \), then \( a \times d = b \times c \).
You use ratios when you double a recipe, compare prices per ounce at the store, or read a map scale. Understanding how quantities relate helps you make better decisions every day.
\[\frac{a}{b} = \frac{c}{d}\]
If there are 8 apples for every 4 oranges, the ratio is 8:4 or 2:1.
A map uses a scale of 1 inch:10 miles. If two cities are 3 inches apart on the map, they are 30 miles apart in real life.
Ratios and proportions help you compare and solve problems involving relationships between numbers.