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Fraction Classroom · 2.2.0 · Student pages

Why can dividing a decimal give a larger number?

Count how many small measured groups fit in an amount, and name the unit of the quotient.

Anonymous group code: __________   Date: __________

Four equal jumps of 0.2 reach 0.8. Each interval represents one piece.00.20.40.60.80.8
Four equal jumps of 0.2 reach 0.8. Each interval represents one piece.

Discuss the opening question

start. How many 0.2-metre pieces fit in 0.8 metres of ribbon?

Work through the explanation

example. How many 0.2-metre pieces fit in 0.8 metres of ribbon?

  1. Name both units: the total is 0.8 metres, and each piece is 0.2 metres. Assume exact cuts with no loss for this mathematics task.
  2. Rename both lengths in tenths of a metre. Ask how many groups of two tenths fit in eight tenths.
  3. Count four groups and record a quotient of 4 pieces. Do not label it 4 metres.
  4. Check with multiplication: four pieces × 0.2 metres per piece = 0.8 metres. The product recovers the original length.

Worked example: Four pieces. Eight tenths contains four groups of two tenths, so 0.8 ÷ 0.2 = 4.

Practise, then check independently

Use p1–p3 for practice. Try e1 without help. Show how your place-value units or model support the result.

p1. How many 0.3-metre pieces fit in 0.9 metres? Enter the piece count.

p2. How many 0.25-litre servings fit in 1 litre? Enter the serving count.

p3. Calculate 0.6 ÷ 0.1.

e1. How many 0.2-metre pieces fit in 1.4 metres? Enter the piece count.

Explain a new situation

transfer. Compare the questions 0.8 ÷ 4 and 0.8 ÷ 0.2. What does each answer measure?