A rectangle has a height to width ratio of \(3 : 4.5\). Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.

One rectangle measures 2 units by 7 units. A second rectangle measures 11 units by 37 units. Are these two figures scaled versions of each other? If so, find the scale factor. If not, briefly explain why.

In Russia people make matryoshka dolls, which are hollow, wooden dolls that fit inside each other.

1. What is the scale factor between the largest and smallest figures?
2. Find the width of the third figure.

Ants have 6 legs. Elena and Andre write equations showing the proportional relationship between the number of ants, \(a\), and the number of ant legs, \(l\).

• Elena writes \(a = 6 \boldcdot l\).
• Andre writes \(l = \frac{1}{6} \boldcdot a\).

Do you agree with either of the equations? Explain your reasoning.

Lin has a scale model of a modern train. The model is created at a scale of 1 to 48.

1. The height of the model train is 102 millimeters. What is the actual height of the train in meters? Explain your reasoning.

2. On the scale model, the distance between the wheels on the left and the wheels on the right is \(1\frac14\) inches. The state of Wyoming has old railroad tracks that are 4.5 feet apart. Can the modern train travel on those tracks? Explain your reasoning.

On the grid, draw a scaled copy of quadrilateral ABCD with a scale factor \(\frac{2}{3}\).

Solve each equation mentally.

1. \(\frac{5}{2} \boldcdot x=1\)
2. \(x \boldcdot \frac{7}{3}=1\)
3. \(1\div \frac{11}{2}=x\)