Cross Products Property
The cross products property is a Grade 6 math skill in Big Ideas Math Advanced 1, Chapter 14: Ratios and Proportions. The property states that if two ratios form a proportion (a/b = c/d), then their cross products are equal (ad = bc). Students use this to solve for missing values in proportions and to verify whether two ratios are proportional.
Key Concepts
A proportion is an equation stating that two ratios are equal: $\frac{a}{b} = \frac{c}{d}$.
Cross Products Property: If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$ where $b \neq 0$ and $d \neq 0$.
Common Questions
What is the cross products property?
If a/b = c/d, then a x d = b x c. The product of the means equals the product of the extremes. This is called cross multiplication and is a fast way to solve proportions.
How do you use cross products to solve a proportion?
Set the cross products equal and solve the resulting equation. For example, 3/4 = x/12: cross multiply to get 3 x 12 = 4 x x, so 36 = 4x, then x = 9.
How do cross products tell you if two ratios are equal?
If the cross products of two ratios are equal, the ratios form a proportion. For example, 2/3 and 4/6: cross products are 2 x 6 = 12 and 3 x 4 = 12. They are equal, so the ratios are proportional.
Where is the cross products property taught in Big Ideas Math Advanced 1?
The cross products property is covered in Chapter 14: Ratios and Proportions of Big Ideas Math Advanced 1, the Grade 6 math textbook.