Ratios
Ratios express the relationship between two quantities in Grade 8 math (Yoshiwara Core Math). A ratio can be written as a fraction (3/4), with a colon (3:4), or in words (3 to 4). Ratios compare parts to parts or parts to a whole. If a bag has 6 red and 4 blue marbles, the ratio of red to blue is 6:4 = 3:2 (simplified). Equivalent ratios scale both terms by the same factor. Ratios are foundational for proportions, rates, percents, and scale drawings throughout Grade 8 mathematics.
Key Concepts
Property A ratio shows the relative sizes of two values by dividing one value into the other. The ratio of $a$ to $b$ is sometimes denoted by $a : b$, and it is computed as the quotient $\frac{a}{b}$.
Examples A classroom has 24 students and 2 teachers. The ratio of students to teachers is $\frac{24}{2}$, which simplifies to $\frac{12}{1}$ or 12 to 1. A recipe calls for 3 cups of flour and 2 cups of sugar. The ratio of flour to sugar is 3 to 2, or $\frac{3}{2}$. In a parking lot, there are 50 cars and 15 trucks. The ratio of cars to trucks is $\frac{50}{15}$, which simplifies to $\frac{10}{3}$. For every 10 cars, there are 3 trucks.
Explanation A ratio is a way to compare two quantities by division. Think of it as a recipe: 'for every $a$ of this, you have $b$ of that'. Simplifying the ratio makes this relationship easier to understand at a glance.
Common Questions
What is a ratio in math?
A ratio compares two quantities, written as a fraction, with a colon, or in words. For example, 3 to 4, 3:4, or 3/4.
What is the difference between part-to-part and part-to-whole ratios?
Part-to-part compares two subgroups (boys to girls). Part-to-whole compares one part to the total.
How do you find equivalent ratios?
Multiply or divide both terms by the same nonzero number. 3:4 = 6:8 = 9:12.
How do you simplify a ratio?
Divide both terms by their GCF. 6:4 ÷ 2 = 3:2.
How are ratios related to fractions?
A ratio a:b = fraction a/b. Operations on ratios follow the same rules as fractions.