Cross Products and Proportions

The video tutorial explains how to solve proportions using two methods: clearing fractions by multiplying both sides by the least common denominator (LCD) and using cross products. The first method involves simplifying the equation by eliminating fractions, while the second method uses the property of cross products in proportions. Both methods lead to the same solution, demonstrating their validity. The tutorial emphasizes the importance of simplifying answers and provides a step-by-step guide to solving the equations.

What are the two methods discussed for solving proportions?

• Graphing and substitution

• Clearing fractions and cross products

• Using logarithms and exponents

• Factoring and completing the square

What is the first step in clearing fractions from a proportion?

• Add the fractions

• Divide both sides by the greatest common factor

• Multiply both sides by the least common denominator

• Subtract the fractions

How do you simplify the equation after multiplying by the LCD?

• Multiply the denominators

• Subtract the numerators

• Add the numerators

• Cancel common factors between numerators and denominators

What is the simplified form of 36/10?

• 4.5

• 18/5

• 3.5

• 7/2

When converting a fraction to a decimal, what should you ensure?

• The decimal is repeating

• The decimal is rounded

• The decimal is irrational

• The decimal is terminating

What is a cross product in the context of proportions?

• The sum of the numerators

• The product of the means

• The difference of the denominators

• The product of the extremes

In the cross products method, what must be true for the equation to hold?

• The denominators must be equal

• The numerators must be equal

• The fractions must be improper

• The cross products must be equal

What is the result of 2x times 7 in the cross products method?

• 28x

• 21x

• 9x

• 14x

What equation do you get after distributing in the cross products method?

• 10x = 2x + 18

• 10x = 4x + 36

• 14x = 2x + 18

• 14x = 4x + 36

What is the final solution for x using both methods?

• x = 18/5 or 3.6

• x = 36/10 or 3.6

• x = 18/10 or 1.8

• x = 36/5 or 7.2