number AnD AlgebrA • Number aNd plaCe value
33 Janet is a land developer and has bought 10 450 square metres of land. She intends to
subdivide the land into 11 separate blocks.
a How many square metres will each block be?
b If she sells each block for $72 250, how much will she receive for the subdivided land?
34 Shea has booked a beach house for a week over the summer period for a group of 12 friends.
The house costs $1344 for the week. If all 12 people stayed for 7 nights, how much will the
house cost each person per night?
reASoning
35 In AFL football, a goal scores 6 points and a behind scores 1 point. Find a score which is
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2D
the same as the product of the number of goals and the number of behinds. For example,
2 goals 12 behinds = 2 ì 6 + 12 = 24 points. Also 2 ì 12 = 24. Find two other similar
results.
36 a Consider numbers with 2 identical digits multiplied by 99. Work out each of the following.
11 ì 99 =
22 ì 99 =
33 ì 99 =
Can you see a pattern? Without using long multiplication or a calculator, write down the
answers to 44 ì 99, 55 ì 99, 66 ì 99, 77 ì 99, 88 ì 99 and 99 ì 99.
b Try it again but this time multiply numbers
with 3 identical digits by 99. Use only long
multiplication or a calculator with the first
3 calculations. Look for a pattern and then
write down the answers to the remaining
reFleCtioN
multiplications.
How
are multiplication and
c What about numbers with 4 or 5 identical
division
related?
digits which are multiplied by 99? Try these
as well.
long division
■
■
Long division uses the same process as short division, but all the calculations are recorded.
As a general rule, when dividing by numbers greater than 12, use long division.
WorkeD exAmPle 12
Calculate 2685 ó 15.
Think
WriTe
)
1
15 >12, so long division is needed.
2
As 15 > 2, divide 15 into the first 2 digits, as shown in
red.
185
15 − 2685
3
To find the remainder, multiply 1 by 15, write the result
under the digits 26 and subtract.
186
15 − 2685
15 2685
)
)
− 15
− 11
Chapter 2 Positive integers
41
number AND algebra • Number and place value
4
5
6
7
Bring the remaining digits down next to the 11.
As 15 > 11, divide 15 into the first 3 digits.
185
15 − 2685
)
− 15↓↓
− 1185
175
15 − 2685
)
− 15
− 1185
Multiply 7 by 15 and write the result under the digits
118. Subtract the numbers and bring the 5 down next
to the 3.
175
15 − 2685
Divide 15 into 135 and repeat.
179
15 − 2685
)
− 15
− 1185
− 105↓
− 1135
)
− 15
− 1185
− 105
− 1135
1 − 135
− 1110
8
Write the answer.
22685 ó 15 = 179 = 179
Worked Example 13
Calculate 2297 ó 17.
Think
42
1
17 >12, so long division is needed.
2
Divide 17 into the first 2 digits. Multiply this result by 17
and subtract.
Maths Quest 7 for the Australian Curriculum
Write
)
17 2297
197
17 − 2297
)
− 17
− 15
number AND algebra • Number and place value
3
4
Bring the remaining digits down next to the 5.
Divide 17 into the first 2 digits. Multiply this result by 17
and subtract.
197
17 − 2297
)
− 17↓↓
− 1597
137
17 − 2297
)
− 17
− 1597
1 − 51
− 318
5
6
Bring the remaining digit 7 down next to the 8.
Divide 17 into 87 and repeat.
137
17 − 2297
)
− 17
− 1597
− 51↓
− 18 7
135
17 − 2297
)
− 17
−1 597
− 51
− 1187
− 85
− 1112
7
Write the answer.
2297 ó 17 = 135 remainder 2 or
2
2297 ó 17 = 135 17
remember
1. Long division uses the same processes as short division, but all the steps are recorded.
2. Use long division when the divisor is greater than 12.
Chapter 2 Positive integers
43
number AnD AlgebrA • Number aNd plaCe value
eXerCiSe
2D
iNdividual
PAThWAYS
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Activity 2-D-1
Long division
doc-1096
Activity 2-D-2
More long division
doc-1097
Activity 2-D-3
Advanced long
division
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long division
FlueNCy
1 We12 Using long division, evaluate the following.
a 195 ó 13
b 308 ó 22
d 589 ó 31
e 9683 ó 23
g 5525 ó 17
h 9050 ó 25
j 11 004 ó 2
c 544 ó 17
f 8554 ó 13
i 1302 ó 21
2 We13 Using long division, evaluate the following.
a 847 ó 13
b 951 ó 15
d 1600 ó 19
e 5050 ó 41
g 6831 ó 21
h 7721 ó 31
j 20 011 ó 27
c 1210 ó 17
f 8289 ó 33
i 14 997 ó 23
unDerSTAnDing
3 Complete the following long division problems.
216
a
19 448 1
)
b
c
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)
17 82 1 9
)
2 1 3 r 17
21 512 1
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game
2e
48 1
reFleCtioN
order of operations
■
■
■
■
Why would you use long division
instead of short division?
In mathematics, conventions are followed so that we all have a common understanding of
mathematical operations.
Consider the question 6 + 6 ó 3. If you perform the addition first the answer is 4. If you
perform the division first the answer is 8. The correct answer is 8.
There is a set order in which mathematicians calculate problems. The order is:
1. Brackets
2. Indices or square roots
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right).
The acronym BIDMAS can be used to remember the correct order of operations.
WorkeD exAmPle 14
Calculate 6 + 12 ó 4.
Think
44
WriTe
6 + 12 ó 4
1
Write the question.
2
Perform the division before the addition.
=6+3
3
Calculate the answer.
=9
maths Quest 7 for the australian Curriculum