Fractions of Quantities, Grouping & Sharing — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 8 · Common Fractions

Fractions of Quantities, Grouping & Sharing

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
35 of R200 is …
(1)
A)R120✓
B)R40
C)R333
D)R60
Answer: A — 200 ÷ 5 = 40, and 40 × 3 = 120.
- B — that is only ONE fifth
- C — divided by 3/5 instead of multiplying
- D — used 3/10 of the amount
1.2
R840 is shared between two people in the ratio 3 : 4. The SMALLER share is …
(1)
A)R360✓
B)R480
C)R280
D)R420
Answer: A — 3 + 4 = 7 parts, so one part is R120 and the smaller share is 3 × 120 = R360.
- B — that is the LARGER share
- C — divided by 3 instead of by 7
- D — shared it equally
1.3
A shirt costing R320 is reduced by 14. The new price is …
(1)
A)R80
B)R240✓
C)R400
D)R316
Answer: B — 1/4 of 320 = 80, and 320 − 80 = 240.
- A — that is the DISCOUNT, not the new price
- C — added the discount instead of subtracting
- D — subtracted R4
1.4
23 of a number is 18. The number is …
(1)
A)12
B)27✓
C)36
D)54
Answer: B — Divide by 2/3: 18 × 3/2 = 27. (Check: 2/3 of 27 = 18.)
- A — found 2/3 OF 18 instead of working backwards
- C — doubled 18
- D — multiplied 18 by 3
1.5
In a class of 40 learners, 25 walk to school. How many do NOT walk?
(1)
A)16
B)24✓
C)8
D)20
Answer: B — 2/5 of 40 = 16 walk, so 40 − 16 = 24 do not.
- A — that is the number who DO walk
- C — found 1/5 of 40
- D — halved the class
1.6
Which one of the following is the same as finding 14 of an amount?
(1)
A)multiplying by 4
B)dividing by 4✓
C)subtracting 4
D)dividing by 1/4
Answer: B — One quarter of an amount is that amount split into 4 equal parts.
- A — that makes it 4 times bigger
- C — subtracting removes a fixed amount, not a fraction
- D — dividing by 1/4 multiplies by 4
1.7
Three friends share 12 sweets so that Ann gets 12, Ben 13 and Cara the rest. Cara gets …
(1)
A)6
B)4
C)2✓
D)3
Answer: C — Ann 6 and Ben 4, so Cara gets 12 − 10 = 2.
- A — that is Ann's share
- B — that is Ben's share
- D — shared the 12 equally between three
1.8
A tank holds 60 ℓ. It is 23 full. How much more is needed to fill it?
(1)
A)40 ℓ
B)20 ℓ✓
C)30 ℓ
D)90 ℓ
Answer: B — 2/3 of 60 = 40 already in, so 60 − 40 = 20 more.
- A — that is what is already IN the tank
- C — used a half instead of two thirds
- D — multiplied 60 by 3/2
1.9
Increase R150 by 15.
(1)
A)R30
B)R180✓
C)R120
D)R155
Answer: B — 1/5 of 150 = 30, and 150 + 30 = 180.
- A — that is the increase alone
- C — DECREASED instead of increasing
- D — added 5 instead of one fifth
1.10
Which one of the following is the GREATEST?
(1)
A)12 of 60
B)23 of 42
C)34 of 36
D)45 of 40✓
Answer: D — The four values are 30, 28, 27 and 32.
- A — 30
- B — 28
- C — 27

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

[12 MARKS]

Answer the questions below. Show ALL your calculations.

2.1
Calculate 34 of 60 + 13 of 45.
(4)
34 × 60 = 45 (1)
13 × 45 = 15 (2)
45 + 15 = 60 (1)
2.2
34 of a number is 24. Determine the number.
(3)
34 of the number = 24, so 14 = 8 (1)
The whole = 8 × 4 (1) = 32 (1)
2.3
Sipho is given R120. He spends 14 of it on a book and 13 of it on food. Calculate, in rands, how much he has LEFT.
(5)
Spent: 14 + 13 = 312 + 412 = 712 (2)
Left: 1 − 712 = 512 (1)
512 × 120 (1) = R50 (1)

Question 3

[13 MARKS]

Answer the word problems below.

3.1
A farmer plants 25 of a field with maize and 13 of the field with beans. The rest is left fallow. Determine the fraction left fallow.
(4)
25 + 13 = 615 + 515 = 1115 (2)
1 − 1115 (1) = 415 (1)
3.2
If the field is 45 hectares, calculate how many hectares are left fallow.
(3)
415 × 45 (2) = 12 hectares (1)
3.3
A 7-litre container is used to fill 12-litre bottles. Determine how many bottles can be filled in total, and how much is left after 9 bottles have been filled.
(4)
7 ÷ 12 = 14 bottles (2)
9 bottles use 9 × 12 = 412 ℓ (1)
7 − 412 = 212 ℓ left (1)
3.4
Explain the difference between finding a fraction OF an amount and dividing BY a fraction.
(2)
Finding a fraction of an amount makes it smaller — you multiply (1); dividing by a fraction less than 1 makes it bigger — you count how many pieces fit (1)

TOTAL: 35 marks

This question paper consists of 3 questions.