Divide larger numbers by 2-digit numbers: word problems

Learning Objectives Analyze word problems to identify similar figures and their corresponding parts. Set up correct proportions to represent the relationships between similar figures. Calculate the scale factor of similar figures by accurately dividing larger numbers by 2-digit numbers. Determine unknown side lengths or perimeters of similar figures using a calculated scale factor. Solve multi-step word problems involving geometric similarity that require precise long division. Interpret the quotient from a division calculation as a scale factor in a real-world context. How do city planners use a small map to manage a huge city, or how does an artist scale a sketch to a giant mural? 🗺️ It's all about similarity, and the key is precise division! This tutorial connects a...

TermDefinitionExample Similar PolygonsPolygons that have the same shape but may have different sizes. For two polygons to be similar, their corresponding angles must be congruent, and the ratio of their corresponding side lengths must be constant.A rectangle with sides 10 cm and 20 cm is similar to a larger rectangle with sides 50 cm and 100 cm. The ratio of corresponding sides is 50/10 = 5 and 100/20 = 5. Scale Factor (k)The constant ratio between the corresponding side lengths of two similar figures. It is calculated by dividing the length of a side on the new figure (the image) by the length of the corresponding side on the original figure (the pre-image).A model car has a length of 18 cm. The actual car is 450 cm long. The scale factor from the model to the actual car is 450 ÷ 18 = 25...

Scale Factor Formula k = \frac{\text{length of image side}}{\text{length of corresponding pre-image side}} Use this formula to find the scale factor (k). In our word problems, this will typically involve dividing a larger number (the dividend) by a 2-digit number (the divisor). Proportionality of Sides \text{If Polygon } ABCDE \sim \text{Polygon } VWXYZ, \text{ then } \frac{AB}{VW} = \frac{BC}{WX} = \frac{CD}{XY} = k This rule establishes that the ratios of all pairs of corresponding sides in similar polygons are equal. You can set up a proportion using the calculated scale factor to find any unknown side length. Proportionality of Perimeters \frac{\text{Perimeter of Image}}{\text{Perimeter of Pre-image}} = k The ratio of the perimeters of two similar figures is equa...