Step-by-Step Cross Multiplication Tutorial

Welcome to understanding cross multiplication with Spark.E!Cross multiplication helps us work with equivalent fractions. Let's start with a simple example: two-thirds equals four-sixths.When we cross multiply, we multiply diagonally across the equals sign.Two times six equals twelve, and three times four also equals twelve. When the cross products are equal, the fractions are equivalent.In general form, we write proportions as a over b equals c over d.The cross multiplication principle states that a times d equals b times c.This relationship is always true for equivalent fractions.We can understand why cross multiplication works by looking at equal areas.If two rectangles have equal areas, their length times width must be equal.This is exactly what cross multiplication shows us - the products must be equal.Cross multiplication helps us solve real-world problems, like scaling recipes.If we need to scale a recipe from two-thirds to a fraction over nine, cross multiplication helps us find the unknown value.To perform cross multiplication, we start with a proportion written as two equal fractions.We multiply diagonally across the equals sign. First, multiply a times d.Then multiply b times c.These cross products must be equal to each other.This gives us the equation a d equals b c.Let's see how this works with actual numbers. Consider the proportion three-fourths equals nine-twelfths.Multiply three times twelve on one side.And four times nine on the other side.Both cross products equal thirty-six, confirming these fractions are equivalent.Remember these key points about cross multiplication.After cross multiplication, we'll have an equation with one variable to solve.To solve for x, we need to isolate it by dividing both sides by the coefficient of x, which is 3.When we divide both sides by 3, we get x equals 4.It's crucial to verify our answer by plugging it back into the original proportion.Substituting x equals 4, we get three-fourths equals twelve-fourths.Converting to decimals, we can see that both sides equal zero point seven five, confirming our answer is correct.Now, let's try another example. Solve for x in the equation five x equals twenty.Following the same process, we divide both sides by five.This gives us x equals four.