Multiplication Property of Equality for Proportions
Multiplication property of equality for proportions is a Grade 6 math skill in Big Ideas Math Advanced 1, Chapter 14: Ratios and Proportions. Students apply the multiplication property of equality to cross-multiply proportions, converting the equation a/b = c/d into ad = bc to find missing values in proportional relationships.
Key Concepts
Multiplication Property of Equality: Multiplying both sides of an equation by the same non zero number maintains the equality. If $a=b$ and $c \neq 0$, then $ac = bc$. This property is essential for solving proportions by isolating the variable.
Common Questions
How do you use the multiplication property of equality to solve proportions?
In a proportion a/b = c/d, multiply both sides by both denominators to get ad = bc. This cross-multiplication technique eliminates the fractions and allows you to solve for the unknown variable directly.
What is cross multiplication?
Cross multiplication is the process of multiplying the numerator of each fraction by the denominator of the other: in a/b = c/d, you get a x d = b x c. It is a quick way to check if two ratios are equal or to solve for an unknown.
Why does cross multiplication work?
It works because of the multiplication property of equality — you can multiply both sides of an equation by the same value. Multiplying both sides of a/b = c/d by (b x d) gives ad = bc.
Where is this skill taught in Big Ideas Math Advanced 1?
Multiplication property of equality for proportions is covered in Chapter 14: Ratios and Proportions of Big Ideas Math Advanced 1, the Grade 6 math textbook.