Properties of Whole Numbers — Worksheet & Memo

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Grade 8 · Whole Numbers

Properties of Whole Numbers

MARKING GUIDELINE

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 35

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
Which one of the following number sentences shows the COMMUTATIVE property?
(1)
A)7 × (5 + 2) = 7 × 5 + 7 × 2
B)7 × 5 = 5 × 7✓
C)(7 × 5) × 2 = 7 × (5 × 2)
D)7 × 1 = 7
Answer: B — Commutative means the ORDER may be swapped.
- A — that is the distributive property
- C — that is the associative property — the grouping changed, not the order
- D — that is the identity property
1.2
A shop buys 4 boxes of 15 pens and 3 boxes of 12 pens. How many pens does it have altogether?
(1)
A)96✓
B)104
C)81
D)60
Answer: A — 4 × 15 + 3 × 12 = 60 + 36 = 96.
- B — added 4 + 15 and 3 + 12 before multiplying
- C — multiplied only the first pair and added 3 and 12
- D — multiplied only the first pair
1.3
Which one of the following is UNDEFINED?
(1)
A)08
B)81
C)80✓
D)8 × 0
Answer: C — Dividing BY zero is undefined; dividing zero by something is simply 0.
- A — this equals 0, which is defined
- B — this equals 8
- D — this equals 0
1.4
A customer pays for goods costing R372 with a R500 note. What change is due?
(1)
A)R128✓
B)R138
C)R872
D)R228
Answer: A — 500 − 372 = 128.
- B — subtracted the tens wrongly (borrowing error)
- C — ADDED instead of subtracting
- D — subtracted 372 from 600
1.5
Estimate 297 × 4 by rounding to the nearest hundred first.
(1)
A)1 200✓
B)1 188
C)1 000
D)800
Answer: A — 297 rounds to 300, and 300 × 4 = 1 200. (The exact answer is 1 188.)
- B — that is the exact answer, not the estimate
- C — rounded the ANSWER instead of the number
- D — rounded 297 down to 200
1.6
Which one of the following is a WHOLE number but NOT a natural number?
(1)
A)0✓
B)1
C)−3
D)12
Answer: A — The whole numbers are 0; 1; 2; 3; … and the natural numbers are 1; 2; 3; … — 0 is the only difference between them.
- B — 1 is a whole number AND a natural number
- C — −3 is an integer, but not a whole number
- D — a fraction is neither
1.7
Calculate: 40 − 6 × 5 + 2
(1)
A)12✓
B)172
C)10
D)-8
Answer: A — Multiplication first: 40 − 30 + 2 = 12.
- B — worked strictly left to right: (40 − 6) × 5 + 2
- C — did the addition before the subtraction: 40 − (30 + 2)
- D — subtracted 40 from 30 first
1.8
A bus seats 52 people. How many buses are needed for 375 passengers?
(1)
A)7
B)8✓
C)7,2
D)6
Answer: B — 375 ÷ 52 = 7 remainder 11, and the 11 still need a bus, so 8 are needed.
- A — ignored the 11 passengers left over
- C — a number of buses must be a whole number
- D — rounded down twice
1.9
Which one of the following pairs of numbers has a sum of 100 and a difference of 20?
(1)
A)60 and 40✓
B)80 and 20
C)50 and 50
D)70 and 30
Answer: A — 60 + 40 = 100 and 60 − 40 = 20.
- B — sum is 100 but the difference is 60
- C — sum is 100 but the difference is 0
- D — sum is 100 but the difference is 40
1.10
The number 4 807 is written in expanded notation as …
(1)
A)4 000 + 800 + 7✓
B)4 000 + 80 + 7
C)400 + 80 + 7
D)4 + 8 + 0 + 7
Answer: A — The 8 is in the HUNDREDS place, and there are no tens.
- B — placed the 8 in the tens column
- C — placed the 4 in the hundreds column
- D — added the digits instead of expanding

Answer grid — marking guideline

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[13 MARKS]

Answer the following questions on the properties of whole numbers. Show ALL your calculations.

2.1
Name the property shown by 7 × 5 = 5 × 7, and show by ONE example that the same property does NOT hold for subtraction.
(3)
The commutative property of multiplication (1)
7 − 5 = 2 but 5 − 7 = −2 (1)
The two answers differ, so subtraction is NOT commutative (1)
2.2
Use the distributive property to calculate 7 × 98 WITHOUT a calculator.
(3)
7(100 − 2) (1)
= 700 − 14 (1)
= 686 (1)
2.3
Calculate, showing every step: 25 × 104 − 48 ÷ 16
(4)
Multiplication and division first (1)
25 × 104 = 25(100 + 4) = 2 600 (1)
48 ÷ 16 = 3 (1)
2 600 − 3 = 2 597 (1)
2.4
Write down the value of 0 ÷ 8, and explain why 8 ÷ 0 has no answer.
(3)
0 ÷ 8 = 0 (1)
8 ÷ 0 is undefined (1) — no number multiplied by 0 gives 8 (reason 1)

Question 3

[12 MARKS]

A shop buys 3 boxes containing 15 pens each and 4 boxes containing 12 pens each. Each pen is sold for R4.

3.1
Calculate the total number of pens the shop buys.
(3)
3 × 15 = 45 and 4 × 12 = 48 (2)
45 + 48 = 93 pens (1)
3.2
Calculate the total income if every pen is sold, and hence the profit if the shop paid R2,50 for each pen.
(4)
Income = 93 × R4 = R372 (2)
Cost = 93 × R2,50 = R232,50 (1)
Profit = R372 − R232,50 = R139,50 (1)
3.3
A customer pays for all 93 pens with R500. Calculate the change.
(2)
500 − 372 (1) = R128 (1)
3.4
Ann says division is commutative because 12 ÷ 6 = 2. Is Ann correct? Give a reason and support it with an example.
(3)
No (1)
12 ÷ 6 = 2 but 6 ÷ 12 = 12 (1)
The answers differ, so the order matters (reason 1)

TOTAL: 35 marks

This question paper consists of 3 questions.