Multiply two fractions using models: fill in the missing factor

Learning Objectives Identify the product of two fractions represented by an area model. Identify one factor of a multiplication problem when given the product and the other factor, all represented by an area model. Construct an area model to represent the multiplication of two fractions where one factor is missing. Determine the missing fractional factor by analyzing an incomplete area model. Explain the relationship between the area model and the algebraic representation of fraction multiplication with a missing factor. Solve real-world problems involving finding a missing fractional factor using area models. Ever tried to bake a cake but only had part of the ingredients? 🍰 Sometimes, you know the final amount and one part, but need to figure out the other missing part! I...

TermDefinitionExample FractionA number representing a part of a whole, expressed as a ratio of two integers, where the numerator is the number of parts and the denominator is the total number of equal parts in the whole.In the fraction $\frac{3}{4}$, 3 is the numerator (parts we have) and 4 is the denominator (total parts). Area ModelA visual tool that uses a square or rectangle divided into smaller parts to represent the multiplication of two fractions, where the area of the overlapping shaded region is the product.A $1 \times 1$ square divided into rows and columns, with shading to show fractions of each dimension and their product. FactorA number that is multiplied by another number to get a product. In fraction multiplication, both fractions being multiplied are factors.In $\frac{1}{2...

Fraction Multiplication Rule $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ To multiply two fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. This rule helps verify results from area models. Area Model Interpretation Area = Length $\times$ Width When using an area model, one factor represents the 'length' (e.g., horizontal shading), the other factor represents the 'width' (e.g., vertical shading), and the overlapping shaded region represents the 'area' or product. The total number of small squares in the unit square is the product of the denominators, and the number of double-shaded squares is the product of the numerators. Finding a Miss...