045. Dividing Decimals

Learning Intentions

• divide decimals by whole numbers
• divide decimals by other decimals

Pre-requisite Summary

• Understand the meaning of the decimal point and decimal place value
• Be able to divide whole numbers Use mental or written methods
• Know that a decimal can be written with extra zeros without changing its value, for example
• Understand multiplication and division by powers of ten
• Be able to estimate answers to Check whether a quotient is reasonable
• Understand that dividing by a decimal can be turned into division by a whole number by multiplying both numbers by a power of ten

Worked Examples

Worked Example 1

Divide a decimal by a whole number:

a)

b)

Worked Example 2

Divide a decimal by a whole number:

a)

b)

Worked Example 3

Divide a decimal by a whole number when extra zeros may help:

a)

b)

Worked Example 4

Divide a decimal by another decimal by rewriting the divisor as a whole number:

a)

b)

Worked Example 5

Divide a decimal by another decimal:

a)

b)

Worked Example 6

Solve and check by estimation:

a)

b)

c) Explain how estimation helps check the answer.

Problems

Problem 1

Divide a decimal by a whole number:

a)

b)

Problem 2

Divide a decimal by a whole number:

a)

b)

Problem 3

Divide a decimal by a whole number when extra zeros may help:

a)

b)

Problem 4

Divide a decimal by another decimal by rewriting the divisor as a whole number:

a)

b)

Problem 5

Divide a decimal by another decimal:

a)

b)

Problem 6

Solve and check by estimation:

a)

b)

c) Explain how estimation helps check the answer.

Exercises

Understanding and Fluency

Exercise 1.

Divide each decimal by a whole number:

a)

b)

c)

Exercise 2.

Divide each decimal by a whole number:

a)

b)

c)

Exercise 3.

Divide each decimal by a whole number:

a)

b)

c)

Exercise 4.

Divide each decimal by another decimal:

a)

b)

c)

Exercise 5.

Divide each decimal by another decimal:

a)

b)

c)

Exercise 6.

Divide each decimal by another decimal:

a)

b)

c)

Exercise 7.

Estimate first, then divide:

a)

b)

c)

Exercise 8.

Estimate first, then divide:

a)

b)

c)

Reasoning

Exercise 9.

Explain why can be rewritten as .

Exercise 10.

A student says . Explain the mistake.

Exercise 11.

Explain why dividing by a decimal less than can make the answer larger than the starting number.

Exercise 12.

A student rewrites as . Explain why this is incorrect.

Problem-solving

Exercise 13.

A rope is m long and is cut into equal pieces. How long is each piece?

Exercise 14.

A L bottle of juice is poured equally into cups. How much juice is in each cup?

Exercise 15.

A ribbon of length m is cut into pieces of length m. How many pieces are made?

Exercise 16.

A runner travels km in hours at a constant rate. What is the average distance per hour?

Exercise 17.

A tank contains L of water and is filled into bottles holding L each. How many bottles can be filled?

Exercise 18.

A packet of seeds weighs kg in total and is divided equally into kg bags. How many bags are made?

Potential Misunderstandings

• Students may line up decimals incorrectly when dividing by a whole number
• Students may forget that extra zeros can be added to a decimal without changing its value
• Students may place the decimal point in the quotient incorrectly
• Students may think dividing by a decimal always makes the answer smaller
• Students may multiply only the divisor by a power of ten instead of multiplying both dividend and divisor
• Students may not Recognise that dividing by is the same as finding how many halves fit into the number
• Students may estimate poorly and fail to notice an unreasonable answer
• Students may confuse dividing by with dividing by

Next: 046. Decimals, Fractions and Recurring Decimals