5-3 Proportion Word Problems

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. It can be written in the form \( \frac{a}{b} = \frac{c}{d} \).

Front

How do you set up a proportion for similar figures?

Back

To set up a proportion for similar figures, use the corresponding sides of the figures. For example, if two triangles are similar, you can write \( \frac{side1}{side2} = \frac{side1'}{side2'} \).

Front

What is the cross-multiplication method in solving proportions?

Back

The cross-multiplication method involves multiplying the numerator of one ratio by the denominator of the other ratio. If \( \frac{a}{b} = \frac{c}{d} \), then \( a \cdot d = b \cdot c \).

Front

How do you find the missing value in a proportion?

Back

To find the missing value in a proportion, set up the proportion and use cross-multiplication to solve for the unknown variable.

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions show that two ratios are equal. For example, if the ratio of apples to oranges is 2:3, the proportion can be \( \frac{2}{3} = \frac{4}{6} \).

Front

How can proportions be used in real-life situations?

Back

Proportions can be used in various real-life situations such as cooking (scaling recipes), finance (currency exchange), and construction (measuring dimensions).

Front

What is the formula for finding the height of an enlarged painting using proportions?

Back

If a painting is enlarged, the proportion can be set up as \( \frac{original\ width}{original\ height} = \frac{new\ width}{new\ height} \).

Front

How do you solve a proportion involving currency exchange rates?

Back

Set up the proportion using the exchange rate, then cross-multiply to find the unknown amount. For example, if \( \frac{1\ dollar}{6\ Pounds} = \frac{x\ dollars}{132\ Pounds} \).

Front

What is the importance of rounding in solving word problems?

Back

Rounding is important in word problems to provide a practical answer that is easy to understand and apply, especially in time and money calculations.

Front

How do you determine the number of items you can buy with a certain amount of money using proportions?

Back

Set up a proportion comparing the cost of a known quantity to the desired quantity. For example, if 20 apples cost $12, then \( \frac{20\ apples}{12\ dollars} = \frac{x\ apples}{3\ dollars} \).