Adding & Subtracting Fractions — Worksheet & Memo

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Grade 8 · Common Fractions

Adding & Subtracting Fractions

MARKING GUIDELINE

Marks

Duration

55 minutes

Questions

Name:

Class:

Date:

Mark

/ 36

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
23 + 14 = …
(1)
A)37
B)1112✓
C)212
D)312
Answer: B — The LCD is 12: 8/12 + 3/12 = 11/12.
- A — added the tops AND the bottoms — the commonest error of all
- C — multiplied instead of adding
- D — added the tops but kept one denominator
1.2
56 − 13 = …
(1)
A)43
B)12✓
C)46
D)23
Answer: B — 5/6 − 2/6 = 3/6 = 1/2.
- A — subtracted the bottoms as well
- C — forgot to change 1/3 into 2/6
- D — subtracted the numerators without a common denominator
1.3
112 + 213 = …
(1)
A)325
B)356✓
C)316
D)256
Answer: B — Add the wholes: 3. Then 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
- A — added the tops and the bottoms of the fractions
- C — SUBTRACTED the fractions
- D — lost a whole number
1.4
Before two fractions can be added, they must have …
(1)
A)the same numerator
B)the same denominator✓
C)the same value
D)whole-number parts
Answer: B — Only pieces of the SAME size can be counted together.
- A — the numerators are what you add
- C — equal fractions would make the question pointless
- D — whole numbers are handled separately
1.5
A tank is 38 full. After 14 more is added, the tank is … full.
(1)
A)412
B)58✓
C)12
D)48
Answer: B — 3/8 + 2/8 = 5/8.
- A — added the tops and the bottoms
- C — guessed at a half
- D — forgot to convert 1/4 to 2/8
1.6
710 − 15 = …
(1)
A)65
B)12✓
C)610
D)35
Answer: B — 7/10 − 2/10 = 5/10 = 1/2.
- A — subtracted the denominators
- C — did not convert 1/5 into 2/10
- D — subtracted 1 from 7 and 5 from 10 separately
1.7
Which one of the following sums is GREATER than 1?
(1)
A)13 + 14
B)34 + 12✓
C)12 + 13
D)25 + 12
Answer: B — 3/4 + 1/2 = 5/4, and 5/4 is more than 1.
- A — 7/12, which is less than 1
- C — 5/6, which is less than 1
- D — 9/10, which is less than 1
1.8
The LOWEST common denominator of 16 and 18 is …
(1)
A)48
B)24✓
C)14
D)2
Answer: B — 24 is the LCM of 6 and 8 — the smallest number both divide into.
- A — 6 × 8 works, but it is not the LOWEST
- C — added the two denominators
- D — that is the HCF, not the LCM
1.9
Thabo walks 14 km, then 23 km. How much further must he walk to complete 2 km?
(1)
A)1112✓
B)1112
C)11112
D)37
Answer: A — 1/4 + 2/3 = 3/12 + 8/12 = 11/12, and 2 − 11/12 = 1 1/12.
- B — that is the distance already walked, not what is left
- C — subtracted from 2 but lost a whole
- D — added the tops and the bottoms
1.10
5 − 234 = …
(1)
A)334
B)214✓
C)234
D)314
Answer: B — 5 = 4 4/4, so 4 4/4 − 2 3/4 = 2 1/4.
- A — added instead of subtracting
- C — subtracted the whole numbers and copied the fraction
- D — borrowed but subtracted the fraction the wrong way

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]

Calculate the following WITHOUT using a calculator. Show ALL your steps and leave your answers in the simplest form.

2.1
34 + 25 − 12
(4)
LCD = 20 (1)
= 1520 + 820 − 1020 (2)
= 1320 (1)
2.2
213 + 112 − 34
(5)
Change to improper fractions: 73 + 32 − 34 (1)
LCD = 12 (1)
= 2812 + 1812 − 912 (2)
= 3712 = 3112 (1)
2.3
56 − (13 + 14)
(4)
Brackets FIRST: 13 + 14 = 712 (2)
1012 − 712 (1) = 14 (1)

Question 3

[13 MARKS]

Answer the word problems below. Show ALL your working.

3.1
A water tank is 23 full. During the day 14 of the FULL tank is used. Determine the fraction of the tank that is left.
(4)
23 − 14 (1)
LCD = 12: 812 − 312 (2)
= 512 of the tank (1)
3.2
Three pipes are 34 m, 23 m and 56 m long. Calculate their total length.
(4)
LCD = 12 (1)
912 + 812 + 1012 (2)
= 2712 = 214 m (1)
3.3
A recipe needs 112 cups of sugar and 34 of a cup of flour. Determine how much MORE sugar than flour is needed.
(3)
32 − 34 (1) = 64 − 34 (1) = 34 of a cup (1)
3.4
A learner writes 12 + 13 = 25. Explain the mistake.
(2)
The learner added the numerators and the denominators (1); the denominators must first be made the same (1)

TOTAL: 36 marks

This question paper consists of 3 questions.