Ratios, proportions, and algebraic thinking for sixth grade students.
A proportion is when two ratios are equal. It helps us find missing values and solve problems where things change at the same rate.
If \(\frac{a}{b} = \frac{c}{d}\), then these ratios form a proportion.
To find a missing number, use cross-multiplication: \[ \frac{a}{b} = \frac{c}{d} \implies a \times d = b \times c \]
Proportions help you scale recipes, convert measurements, or determine distances on a map.
If 3 pencils cost $6, how much do 5 pencils cost? Set up the proportion: 3/6 = 5/x.
On a map, 1 inch represents 8 miles. If two cities are 3.5 inches apart, they are 28 miles apart.
Proportions show when two ratios are equal and help solve for unknowns.