045. Dividing Decimals

Learning Intentions

Understand the meaning of the decimal point and decimal place value
Be able to divide whole numbers using mental or written methods
Know that a decimal can be written with extra zeros without changing its value, for example $3.6 = 3.60$
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

Divide a decimal by a whole number:
a) $8.4 \div 2$
b) $15.6 \div 3$

Divide a decimal by a whole number:
a) $3.75 \div 5$
b) $12.48 \div 4$

Divide a decimal by a whole number when extra zeros may help:
a) $4.2 \div 8$
b) $0.96 \div 6$

Divide a decimal by another decimal by rewriting the divisor as a whole number:
a) $3.6 \div 0.6$
b) $4.8 \div 0.2$

Divide a decimal by another decimal:
a) $2.75 \div 0.5$
b) $7.56 \div 1.2$

Solve and check by estimation:
a) $5.04 \div 0.7$
b) $0.81 \div 0.09$
c) Explain how estimation helps check the answer.

Divide a decimal by a whole number:
a) $9.6 \div 2$
b) $18.9 \div 3$

Divide a decimal by a whole number:
a) $4.25 \div 5$
b) $14.64 \div 4$

Divide a decimal by a whole number when extra zeros may help:
a) $5.4 \div 8$
b) $0.84 \div 6$

Divide a decimal by another decimal by rewriting the divisor as a whole number:
a) $4.2 \div 0.7$
b) $6.4 \div 0.4$

Divide a decimal by another decimal:
a) $3.25 \div 0.5$
b) $8.64 \div 1.2$

Solve and check by estimation:
a) $6.3 \div 0.9$
b) $0.72 \div 0.08$
c) Explain how estimation helps check the answer.

Divide each decimal by a whole number:
a) $7.2 \div 2$
b) $9.6 \div 3$
c) $12.5 \div 5$
Divide each decimal by a whole number:
a) $6.84 \div 4$
b) $3.6 \div 8$
c) $0.72 \div 6$
Divide each decimal by a whole number:
a) $15.75 \div 3$
b) $4.08 \div 2$
c) $2.4 \div 6$
Divide each decimal by another decimal:
a) $2.4 \div 0.6$
b) $4.2 \div 0.7$
c) $5.6 \div 0.8$
Divide each decimal by another decimal:
a) $3.5 \div 0.5$
b) $7.2 \div 1.2$
c) $9.6 \div 0.4$
Divide each decimal by another decimal:
a) $4.95 \div 0.9$
b) $8.64 \div 1.8$
c) $0.63 \div 0.07$
Estimate first, then divide:
a) $5.04 \div 0.7$
b) $7.92 \div 1.1$
c) $1.44 \div 0.3$
Estimate first, then divide:
a) $0.96 \div 0.12$
b) $6.25 \div 0.5$
c) $3.24 \div 0.9$

Explain why $3.6 \div 0.6$ can be rewritten as $36 \div 6$ .
A student says $4.8 \div 0.2 = 2.4$ . Explain the mistake.
Explain why dividing by a decimal less than $1$ can make the answer larger than the starting number.
A student rewrites $2.75 \div 0.5$ as $27.5 \div 0.5$ . Explain why this is incorrect.

A rope is $8.4$ m long and is cut into $2$ equal pieces. How long is each piece?
A $3.6$ L bottle of juice is poured equally into $6$ cups. How much juice is in each cup?
A ribbon of length $4.5$ m is cut into pieces of length $0.5$ m. How many pieces are made?
A runner travels $7.2$ km in $1.2$ hours at a constant rate. What is the average distance per hour?
A tank contains $5.04$ L of water and is filled into bottles holding $0.7$ L each. How many bottles can be filled?
A packet of seeds weighs $0.81$ kg in total and is divided equally into $0.09$ kg bags. How many bags are made?

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 $0.5$ 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 $0.2$ with dividing by $2$