How Many Tenths and Hundredths?

Task

Finish the equations to make true statements. Write one number in each space.

1. 1 tenth + 4 hundredths = ______________ hundredths
2. 4 hundredths + 1 tenth = ______________ hundredths
3. 5 tenths + 2 hundredths = ______________ hundredths
4. 5 hundredths + 2 tenths = ______________ hundredths
5. 14 hundredths = __________ hundredths + 4 hundredths
6. 14 hundredths = __________ tenths + 4 hundredths
7. 14 hundredths = 1 tenth + 3 hundredths + __________ hundredths
8. 80 hundredths = __________ tenths

IM Commentary

Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation.

In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things.

Part (h) addresses the notion of equivalence between hundredths and tenths.

Solution

1. 14
2. 14
3. 52
4. 25
5. 10
6. 1
7. 1
8. 8