Ratios, proportions, and algebraic thinking for sixth grade students.
A proportion is when two ratios are equal. It’s like saying two recipes make the same-tasting lemonade, even if the amounts are different.
You can set up a proportion using two ratios, like this:
\[ \frac{a}{b} = \frac{c}{d} \]
This means “a is to b as c is to d.”
If you know three values, you can solve for the fourth by “cross-multiplying”:
\[ a \times d = b \times c \]
Proportions help you scale things up or down, like doubling a recipe or creating a model.
Always check by plugging your answer back into the original proportion!
If 5 pencils cost $2.50, how much do 10 pencils cost? Set up the proportion \( \frac{5}{2.50} = \frac{10}{x} \).
If 2 maps have scales of 1:100 and 5:500, these proportions help you compare real distances.
Proportions show when two ratios are equal and help you solve for missing values.