Find the number that makes each equation true. Explain or show your reasoning.

1. \(\dfrac{\boxed{\phantom{\frac{0}{000}}}}{12} = \dfrac{2}{3}\)
2. \(\dfrac{5}{6} = \dfrac{\boxed{\phantom{\frac{0}{000}}}}{12}\)

1. The road around a lake is 15 kilometers long. What is the distance in meters?
2. The length of an alligator is 4 meters. What is the length in centimeters?

The value of the 6 in 618,204 is how many times the value of the 6 in 563? Explain or show your reasoning.

Find the value of each sum.

1. \(\frac{3}{8} + \frac{9}{8}\)
2. \(3\frac{1}{5} + \frac{3}{5}\)
3. \(2\frac{4}{10} + 1\frac{7}{10}\)

Lin spends 5 minutes reading a story. Noah spends 3 times as long as Lin. How long does Noah spend reading the story? Explain or show your reasoning.

1. Write a multiplication expression for the shaded area, and find the value of the expression. Explain or show your reasoning.

   

2. Find the value of \(\frac{5}{7} \times \frac{10}{3}\).

The line plot shows the lengths of some toothpicks, in inches.

Dot plot titled Toothpick Measurements from 0 to 3 by 1’s. Hash marks by eighths. Horizontal axis, toothpick lengths, in inches. Beginning at 1 and 6 eighths, the number of X’s above each eighth increment is 5, 3, 4, 2, 0, 1.

1. How many measurements are there?
2. What is the difference in length between the longest toothpick and the shortest toothpick?

1. Write a multiplication equation relating the values of 0.5 and 0.05.
2. Write a division equation relating the values of 0.5 and 0.05.

Write each number, using exponential form.

1. \(10 \times 10 \times 10\)
2. \(100 \times 100\)
3. 100,000
4. 1,000,000,000

1. How many centimeters are in each measurement?

   0.12 m

   3.5 m

   19 m

2. How many millimeters are in each measurement?

   3 m

   37 m

   1,915 m

3. How does a whole number of meters change when it is represented in millimeters? Explain or show your reasoning.

1. How many meters are in each measurement?

   16 millimeters

   1,375 millimeters

   57 millimeters

2. How does a whole number of millimeters change when you represent the measurement in meters? Explain or show your reasoning.

A track is 366 meters around. An athlete runs 15 laps. What is the distance in kilometers? Explain or show your reasoning.

Clare drinks 8 glasses of water each day. There are 235 milliliters in each glass. How many liters of water does Clare drink each day? Explain or show your reasoning.

A track is 400 yards around. How many full laps does Tyler run if he runs at least 2 miles?

1. Write each number, using exponential form. 

   1. 1,000,000,000 (the approximate combined population of North America and South America, in 2023)
   2. 100,000,000,000 (the estimated number of stars in the Milky Way)

   3. 100,000,000,000,000 (the denomination of a bill in Zimbabwean (zim-BAHB-way-yen) dollars, from 2008)

      

   4. 10,000,000,000,000,000,000 (the estimated number of grains of sand on Earth)
   5. 1,000,000,000,000,000,000,000,000 (the estimated number of stars in the universe)
   6. 10,000,000,000,000,000,000,000,000,000,000,000,000,000 (the estimated number of living cells that ever existed on Earth)
   7. 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
      000,000,000,000,000,000,000,000,000,000 (the estimated number of atoms in the universe!)
2. How is exponential form helpful for writing these numbers?

You have a piggy bank with 1 kilogram of coins inside. Which coins do you want to have in the piggy bank? Explain or show your reasoning.