Regroup a tenth when subtracting hundredths

start. How do you subtract 0.27 from 0.6?

Answer: Write 0.60 as five tenths and ten hundredths. Remove two tenths and seven hundredths to leave three tenths and three hundredths: 0.33.

Teacher response: Listen for this idea: Subtract the smaller digit from the larger digit in each column. Follow up: The subtraction removes 0.27 from 0.60; it does not independently choose a direction for each column. When there are too few hundredths to remove, exchange a tenth.

example. How do you subtract 0.27 from 0.6?

1. Estimate the result: 0.6 minus a little less than 0.3 should be a little more than 0.3.
2. Name 0.60 as six tenths. Exchange one tenth for ten hundredths: five tenths and ten hundredths still total 0.60.
3. Remove seven hundredths from the ten hundredths, then two tenths from the five tenths.
4. Record 0.33 and check by addition: 0.33 + 0.27 = 0.60. The check confirms the original amount is recovered.

Worked example: Write 0.60 as five tenths and ten hundredths. Remove two tenths and seven hundredths to leave three tenths and three hundredths: 0.33.

p1. Calculate 0.8 − 0.36.

Answer: 0.44

Teacher response: Rename 0.80 as 7 tenths and 10 hundredths, then subtract.

p2. Calculate 1.00 − 0.45.

Answer: 0.55

Teacher response: One whole is 100 hundredths; 100 − 45 = 55 hundredths.

p3. Calculate 0.73 − 0.18.

Answer: 0.55

Teacher response: Exchange one tenth; 13 hundredths minus 8 hundredths leaves 5.

e1. Calculate 1.2 − 0.47.

Answer: 0.73

Teacher response: Use 1.20, regroup across the needed places and check 0.73 + 0.47 = 1.20.

transfer. Explain why changing 0.60 into 0.510 is not a correct way to record five tenths and ten hundredths.

Answer: 0.510 means five tenths, one hundredth and zero thousandths. Five tenths plus ten hundredths is 0.60; the temporary count 10 must stay in the hundredths column.

next. If exchanges change the total, model the original amount with tenths and hundredths. If secure, subtract from one whole and explain both exchanges.