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Sample Answers
1. a) About 5, 5.404
5.404 5 27.02
b) About 0.5, 0.57
0.57 6 3.42
c) About 0.1, 0.105
0.105 7 0.735
d) About 0.01, 0.009
0.009 8 0.072
e) About 6, 6.25
6.25 8 50
f) About 0.5, 0.573
0.573 6 3.438
Work through the examples in Connect together.
Ensure students understand that using Base
Ten Blocks to divide is only feasible when the
dividend is small; for example, it would take
a lot of blocks to model 73.984.
Practice
The second method shown may be difficult for
some students to grasp quickly. If necessary, work
through several other examples on the board or
overhead projector. The question 3 4 presents
a good opportunity to help students realize that
all numbers can be written as decimals; for
example, 3 can be written as 3.0.
Assessment Focus: Question 9
Some students may feel more comfortable with
recording the numbers without the decimal
point, dividing as they would whole numbers,
then using an estimate to place the decimal
point in the quotient.
Have Base Ten Blocks available for students
who wish to use them. The Numbers Every Day
feature requires a calculator.
Students should immediately realize that the
answer is incorrect because the dividend is
about 1 and 1 divided by 4 will result in a
quotient less than 1.
Students may guess that the decimal point was
misplaced. Some students may perform the
division to verify their assumption.
Ensure students understand that when the
dividend is a 2-digit whole number, they are
expected to use a calculator.
Unit 4 • Lesson 11 • Student page 155
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3. 2.25 km 5 0.45 km; Eric cycled 0.45 km each minute.
2.76 km 8 0.345 km; Josie cycled 0.345 km each minute.
0.45 0.345, so Eric travelled faster.
5. $58.50 5 $11.70; Sharma paid $11.70 each day.
Miles paid $12.50 each day.
$11.70 $12.50, so Sharma got the better deal.
6. Eight friends shared 3 L of juice equally. How much juice did
each person get?
3 L 8 0.375 L
Each person got 0.375 L of juice.
9. a) The answer is incorrect because 1.374 is a little more than
0.661 km
Eric
$2.33
$27.96
Sharma
1
4
1. 1 4 , or 0.25
So, the quotient will be a little more than 0.25.
b) 1.374 4 0.3435, so the student placed the decimal
point in the wrong place.
3.746 km
$0.24
$3.56
REFLECT: Since the divisor, 5, is greater than the dividend, 4,
the quotient will be less than 1. Write 4 as a decimal: 4.0
To divide 4.0 by 5: Divide the ones.
5 4.40
There are 4 ones left over.
0. 8
This is 40 tenths. Divide the tenths.
4 5 0.8
13.5 km
Numbers Every Day
If the final digit of the number were 4 or 6 it would be divisible
by 2 and therefore not prime. Once students realize this, they
can record the 3 as the ones digit. They can write two numbers
by arranging the other two digits as tens and hundreds and
confirm that both numbers are prime by trying to find divisors
with a calculator.
463, 643
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Reasoning; Applying concepts
✔ Students understand that dividing a
decimal by a whole number involves
the same process as dividing a whole
number by a whole number.
✔ Students understand that dividing a
whole number by a greater number
results in a quotient less than 1.
✔ Students understand that all numbers
can be written as decimals.
Extra Support: Students who have difficulty dividing
decimals to thousandths by a whole number may benefit from
practice with decimals to tenths and later decimals to
hundredths.
Students can use Step-by-Step 11 (Master 4.23) to complete
question 9.
Accuracy of procedures
✔ Students can divide a decimal to
thousandths by a whole number, and
multiply to check their answers.
Extra Practice: Students can complete Extra Practice 6
(Master 4.32).
Extension: Have students measure the heights of 4 classmates,
then calculate the average height in metres, decimetres,
centimetres, and millimetres.
Recording and Reporting
Master 4.2 Ongoing Observations:
Decimals
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Unit 4 • Lesson 11 • Student page 156