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4.NF How Many Tenths and Hundredths?

### Alignments to Content Standards

Domain
NF: Number and Operations---Fractions
Cluster
Understand decimal notation for fractions, and compare decimal fractions.
Standard
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. For example, express $3/10$ as $30/100$, and add $3/10 + 4/100 = 34/100$.
Domain
NF: Number and Operations---Fractions
Cluster
Understand decimal notation for fractions, and compare decimal fractions.
Standard
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite $0.62$ as $62/100$; describe a length as $0.62$ meters; locate $0.62$ on a number line diagram.

### Tags

This task is not yet tagged.

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

1. 1 tenth + 4 hundredths = ______________ hundredths
2. 4 hundredth + 1 tenths = ______________ 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 tenths + 3 hundredths + __________ hundreths
8. 80 hundredths = __________ tenths

### 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.

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