Here is a base-ten diagram that represents 1.13. Use the diagram to find \(1.13 - 0.46\). Explain or show your reasoning.

Compute the following sums. If you get stuck, consider drawing base-ten diagrams.

1. \(0.027 + 0.004\)

2. \(0.203 + 0.01\)

3. \(1.2 + 0.145\)

A student said that we cannot subtract 1.97 from 20 because 1.97 has two decimal digits and 20 has none. Do you agree with that student? Explain or show your reasoning.

Decide which calculation shows the correct way to find \(0.3-0.006\), and explain your reasoning.

a. 3 tenths - 6 thousandths = 306 thousandths. 

b. 3 tenths - 6 thousandths = 97 thousandths 

problem c. 3 tenths - 6 thousandths = 24 thousandths.

problem d. 3 tenths - 6 thousandths = 294 thousandths. 

Complete the calculations so that each shows the correct difference.

Problem a. 14 and 6 tenths - 1 and 4 tenths = blank blank blank point 2.

Problem b. 38 and 60 hundredths - 6 and 75 hundredths = blank blank point blank 5.

Problem c. 241 and 76 hundredths -  2 and 18 hundredths = blank blank blank point blank 8.

The school store sells pencils for \$0.30 each, hats for \$14.50 each, and binders for \$3.20 each. Elena would like to buy 3 pencils, a hat, and 2 binders. She estimated that the cost will be less than \$20.

1. Do you agree with her estimate? Explain your reasoning.
2. Estimate the number of pencils she could buy with $5. Explain or show your reasoning.

A rectangular prism measures \(7\frac{1}{2}\) cm by 12 cm by \(15\frac{1}{2}\) cm.

1. Calculate the number of cubes with edge length \(\frac{1}{2}\) cm that fit in this prism.
2. What is the volume of the prism in \(\text{cm}^3\)? Show your reasoning. If you are stuck, think about how many cubes with \(\frac12\)-cm edge lengths fit into \(1\text{ cm}^3\).