Add decimals by matching their units

start. How can you explain 0.7 + 0.26 without treating 7 and 26 as the same unit?

Answer: Rename seven tenths as seventy hundredths. Seventy hundredths plus twenty-six hundredths is ninety-six hundredths, or 0.96.

Teacher response: Listen for this idea: Line up the final digits and add 7 + 26 to get 0.33. Follow up: Ask what each digit counts. The 7 counts tenths and the 6 counts hundredths. Match the decimal points so like units share a column.

example. How can you explain 0.7 + 0.26 without treating 7 and 26 as the same unit?

1. Estimate first: 0.7 plus about 0.3 should be close to 1. An answer near 0.3 cannot fit.
2. Write 0.70 above 0.26 in a place-value chart. The final zero names an empty hundredths place.
3. Combine units: seven tenths and two tenths make nine tenths; zero hundredths and six hundredths make six hundredths.
4. Read the result as nine tenths and six hundredths: 0.96. In other examples, exchange ten hundredths for one tenth before writing the result.

Worked example: Rename seven tenths as seventy hundredths. Seventy hundredths plus twenty-six hundredths is ninety-six hundredths, or 0.96.

p1. Calculate 0.4 + 0.35.

Answer: 0.75

Teacher response: 40 hundredths + 35 hundredths = 75 hundredths.

p2. Calculate 1.2 + 0.08.

Answer: 1.28

Teacher response: The 2 counts tenths; the 8 counts hundredths.

p3. Calculate 0.68 + 0.27.

Answer: 0.95

Teacher response: 15 hundredths regroup as 1 tenth and 5 hundredths.

e1. Calculate 0.9 + 0.16.

Answer: 1.06

Teacher response: 106 hundredths is one whole and six hundredths.

transfer. A learner says 0.5 + 0.42 = 0.47. Explain the error before giving the result.

Answer: The 5 was placed in the hundredths column. It represents 50 hundredths, so the sum is 92 hundredths, or 0.92.

next. If alignment is insecure, rename both addends in hundredths. If secure, use a sum that crosses one whole and ask for the exchange.