B2.8 · Divide three-digit whole numbers by decimal tenths

Ontario Grade 6 Mathematics

Number

Make the divisor a whole number, then divide

What you will learn

• Explain how tenths can help model division by a decimal number.
• Divide a three-digit whole number by a decimal number with one digit after the decimal point.
• Check a quotient using the original divisor.

Think in equal groups and tenths

• One whole equals ten tenths.
• Count the total and the group size in the same units.
• The quotient tells how many equal groups fit.

Change the question, then divide

• Multiply both numbers by $10$.
• The divisor becomes a whole number.
• Divide the changed numbers; the quotient is unchanged.

Check your answer and notice its size

• Check by multiplying the quotient by the original divisor.
• A divisor below $1$ can give a quotient greater than the dividend.
• The method also works when the divisor is greater than $1$.

Use the steps carefully

• Write the changed division question before calculating.
• Do not change only the divisor.
• Use multiplication to check the original question.

Worked example

Groups of six tenths

1. Count in tenths
   The divisor is six tenths. Count the $348$ wholes in tenths too. Multiplying both numbers by $10$ keeps the number of groups the same.
   $$348 \div 0.6 = 3{,}480 \div 6$$
2. Divide
   Find how many groups of $6$ fit into $3{,}480$. Since $6$ groups of $580$ make $3{,}480$, the quotient is $580$.
   $$3{,}480 \div 6 = 580$$
3. Check
   Multiply by the original divisor, $0.6$. The result is the original dividend, $348$.
   $$580 \times 0.6 = 348$$

Worked example

Groups of four tenths

1. Make a whole-number divisor
   Multiply both numbers by $10$. The divisor $0.4$ becomes $4$, and the dividend $728$ becomes $7{,}280$.
   $$728 \div 0.4 = 7{,}280 \div 4$$
2. Divide
   Divide $7{,}280$ by $4$. Since $4$ times $1{,}820$ equals $7{,}280$, the quotient is $1{,}820$.
   $$7{,}280 \div 4 = 1{,}820$$
3. Check
   Use the original divisor, $0.4$. Multiplying the quotient by it returns $728$.
   $$1{,}820 \times 0.4 = 728$$

Worked example

A divisor greater than one

1. Change both numbers
   The divisor has one digit after the decimal point. Multiply both numbers by $10$. The divisor becomes $12$, and the dividend becomes $9{,}360$.
   $$936 \div 1.2 = 9{,}360 \div 12$$
2. Divide
   Since $12$ times $780$ equals $9{,}360$, the quotient is $780$.
   $$9{,}360 \div 12 = 780$$
3. Check
   Multiply by the original divisor, $1.2$. The product is the original dividend, $936$.
   $$780 \times 1.2 = 936$$

Common mistakes and how to avoid them

Lesson summary

• Multiply the dividend and divisor by $10$ to make a one-decimal-place divisor a whole number.
• Divide the changed numbers to find the quotient.
• Check by multiplying the quotient by the original divisor.

Check your understanding

Key terms

Dividend

The number being divided.

Divisor

The number we divide by.

Quotient

The answer to a division question.

Tenths

The ten equal parts made when one whole is split into ten equal parts.

Continue through Grade 6 Math

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

• B2.7 · Multiply three-digit whole numbers by decimal tenths
• B2.9 · Multiply whole numbers by proper fractions
• 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 B2.8. 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.

Official curriculum reference

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