Divide whole numbers with a decimal quotient and round the result

What you will learn

• Divide whole numbers with a decimal quotient and round the result

Models used: number sentences, stories, tables.

Before you start

• Multiply and divide two-place decimals by one-digit numbers

Keep sharing into smaller decimal units

Three litres are shared equally among four containers. How many litres go in each?

1. The complete bar is the whole. Each labelled section is one part of it.

   Three litres cannot give each of four containers a whole litre. We need smaller units.

   3 ÷ 4

   The requested accuracy sets the size of the rounding interval. Its midpoint decides the nearer endpoint.

   3

   ?container 1?container 2?container 3?container 4

2. The complete bar is the whole. Each labelled section is one part of it.

   Rename three litres as 300 hundredths of a litre. Now share the 300 hundredths equally into four groups.

   300 ÷ 4 = 75 hundredths

   300

   7575 hundredths7575 hundredths7575 hundredths7575 hundredths

3. Read the place heading before the digit. A counter in a different column has a different value.

   Each container receives 75 hundredths of a litre. Write this as 0.75 litre.

   3 ÷ 4 = 0.75

   Ones0

   Tenths7

   Hundredths5

   0.75 = 7 tenths + 5 hundredths

4. Start at the marked number. A jump to the right adds; a jump to the left takes away. Read the size of each jump.

   If an answer to one decimal place is needed, round 0.75 to 0.8. Keep the exact quotient separate from its rounded value.

   Exact: 0.75 · To 1 decimal place: 0.8

Worked example: A new example, together

Calculate 55 ÷ 6, rounded to 1 decimal places.

1. Round only at the final step. Read each value with the heading above its column.

   Locate the requested place first, then its two neighbours and midpoint.

   Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

   Round only at the final step

   Unrounded value	Requested decimal places
   9.1667	1

2. Round only at the final step. Read each value with the heading above its column.

   Keep digits through the requested 1 decimal places.

   Round only at the final step

   Unrounded value	Requested decimal places
   9.1667	1

   Calculate 55 ÷ 6, rounded to 1 decimal places.

   9.2

3. Round only at the final step. Read each value with the heading above its column.

   Keep digits through the requested 1 decimal places.

   Round only at the final step

   Unrounded value	Requested decimal places
   9.1667	1

4. Round only at the final step. Read each value with the heading above its column.

   Inspect the next digit: 5 or more rounds the retained value up.

   Round only at the final step

   Unrounded value	Requested decimal places
   9.1667	1

5. Round only at the final step. Read each value with the heading above its column.

   The rounded answer is 9.2.

   Round only at the final step

   Unrounded value	Requested decimal places
   9.1667	1

6. Round only at the final step. Read each value with the heading above its column.

   Check the result against the question we started with.

   Check neighbouring rounded values and the halfway point.

   We found 9.2. Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

   Round only at the final step

   Unrounded value	Requested decimal places
   9.1667	1

Common mistakes to discuss

• Rounding one digit at a time. Round once, from the digit in the next smaller place. 2.449 to one decimal place is 2.4; rounding the 9, then the 4, would wrongly give 2.5.

Check your understanding

• Divide whole numbers with a decimal quotient and round the result
• justify decimal rounding at the requested accuracy
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.