Fraction Classroom
Decimal explanations

Grade 5 · Read, model and practise

Add decimals by matching their units

Align ones with ones and tenths with tenths, then regroup a complete set of ten hundredths.

Try the practice questions

Start with this question

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

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

Make the idea visible

The first two rows are addends; the final row is the sum. Columns count the same unit.OnesTenthsHundredths070026096
The first two rows are addends; the final row is the sum. Columns count 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.

A useful error to discuss

A learner might say: Line up the final digits and add 7 + 26 to get 0.33.

Ask what each digit counts. The 7 counts tenths and the 6 counts hundredths. Match the decimal points so like units share a column.

Practise, then check

Try the first three questions with the model. Try the final check without help. A correct value is a starting point: explain how your units or drawing support it.

Practice 1

Answer & reasoning

0.75 · 40 hundredths + 35 hundredths = 75 hundredths.

Practice 2

Answer & reasoning

1.28 · The 2 counts tenths; the 8 counts hundredths.

Practice 3

Answer & reasoning

0.95 · 15 hundredths regroup as 1 tenth and 5 hundredths.

Independent check

Answer & reasoning

1.06 · 106 hundredths is one whole and six hundredths.

Explain a new situation

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

Discuss the explanation

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

Materials for your group

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Choose the next step

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

Open a related complete lesson →

Original Fraction Classroom examples and explanations. Curriculum reference: CCSS 5.NBT.B.7. Grade alignment describes the intended topic; it is not an endorsement or evidence of classroom results.

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