B2.11 · Divide decimals to thousandths by whole numbers up to ten

Ontario Grade 6 Mathematics

Number

Sharing decimal amounts into equal groups

What you will learn

• Divide decimals written to the thousandths place by whole numbers up to ten.
• Use place value to explain what happens when a digit cannot be divided evenly.
• Check a decimal division answer by multiplying the quotient by the divisor.

Start with equal sharing

• Division shares a total into equal groups.
• Keep the decimal places in order: tenths, hundredths, thousandths.
• The answer is called the quotient.

Use place value to share

• Regroup a remainder into ten units of the next smaller place.
• Place the quotient's decimal point above the dividend's decimal point.
• Use a zero to hold a place when that place has no amount to share.

Check the quotient

• Multiply the quotient by the divisor to check the dividend.
• The divisor is the number you divide by.

Try a careful practice routine

• Work from the whole-number place toward the thousandths.
• Show or say what each regrouped remainder represents.
• Use multiplication to check.

Worked example

Share tenths equally

1. Share the whole units
   There are 4 whole units for 6 groups, so each group gets 0 whole units. The 4 whole units left over can be regrouped as 40 tenths.
   $$4 = 40\text{ tenths}$$
2. Share the tenths
   Add the 8 tenths in the original amount to the 40 regrouped tenths. There are 48 tenths altogether. Sharing 48 tenths among 6 groups gives 8 tenths per group.
   $$48\text{ tenths} \div 6 = 8\text{ tenths}$$
3. Write and check the quotient
   Eight tenths is written as 0.8. Multiply 0.8 by 6 to check that the total is 4.8.
   $$0.8 \times 6 = 4.8$$

Worked example

Regroup through hundredths

1. Share units and tenths
   The 3 units cannot give one whole unit to each of 4 groups. Regroup 3 units as 30 tenths, then add the 2 tenths already there. Sharing 32 tenths gives 8 tenths per group.
   $$30 + 2 = 32\text{ tenths};\quad 32 \div 4 = 8$$
2. Share hundredths
   There are 7 hundredths. Sharing them among 4 groups gives 1 hundredth each, with 3 hundredths left. Regroup those 3 hundredths as 30 thousandths, then add the 6 thousandths already in the number.
   $$30 + 6 = 36\text{ thousandths}$$
3. Share thousandths and check
   Share 36 thousandths among 4 groups. Each group gets 9 thousandths. The quotient is 0.819. Multiplication checks the result.
   $$36 \div 4 = 9;\quad 0.819 \times 4 = 3.276$$

Worked example

Hold a zero in the quotient

1. Share units and tenths
   Share 7 units among 5 groups. Each group gets 1 unit, with 2 units left. Regroup the 2 units as 20 tenths. Sharing 20 tenths among 5 groups gives 4 tenths each.
   $$7 \div 5 = 1\text{ remainder }2;\quad 20\text{ tenths} \div 5 = 4\text{ tenths}$$
2. Keep the hundredths place
   There are 3 hundredths to share among 5 groups. Each group gets 0 hundredths, with 3 hundredths left. Write 0 in the hundredths place so the thousandths digit stays in the correct place. Regroup the remainder as 30 thousandths and add the 5 thousandths already present.
   $$30 + 5 = 35\text{ thousandths}$$
3. Share thousandths and check
   Each group gets 7 thousandths because 35 divided by 5 is 7. The zero in the hundredths place makes the quotient 1.407, not 1.47. Check by multiplying.
   $$35 \div 5 = 7;\quad 1.407 \times 5 = 7.035$$

Common mistakes and how to avoid them

Lesson summary

• Divide from the largest place value toward the thousandths.
• Regroup leftovers as ten units of the next smaller place.
• Write zeroes when needed to hold places in the quotient.
• Check by multiplying the quotient by the divisor.

Check your understanding

Key terms

Decimal point

The mark that separates whole units from parts of a unit.

Dividend

The amount being divided.

Divisor

The number of equal groups, or the number you divide by.

Quotient

The answer to a division question.

Regroup

Trade an amount for an equal amount in smaller place-value units.

Continue through Grade 6 Math

View the complete Grade 6 Math Ontario Grade 6 Mathematics curriculum and lessons

• B2.10 · Divide whole numbers by proper fractions
• B2.12 · Solve problems with ratios, percents, and rates
• B1.1 · Read and represent whole numbers to one million
• B1.2 · Represent integers on horizontal and vertical number lines
• B1.3 · Compare and order integers, decimals, and fractions
• B1.4 · Read, represent, compare, and order decimals to thousandths

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation B2.11. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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