Equivalent Fractions & Simplifying — Worksheet & Memo

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Grade 8 · Common Fractions

Equivalent Fractions & Simplifying

MARKING GUIDELINE

Marks

Duration

50 minutes

Questions

Name:

Class:

Date:

Mark

/ 33

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 fractions is equivalent to 27?
(1)
A)49
B)621✓
C)221
D)914
Answer: B — Multiply the top and the bottom by the SAME number: 2 × 3 = 6 and 7 × 3 = 21.
- A — added 2 to both parts instead of multiplying
- C — multiplied only the denominator
- D — added 7 to the top and 7 to the bottom
1.2
4254 written in its simplest form is …
(1)
A)2127
B)79✓
C)68
D)1418
Answer: B — The HCF of 42 and 54 is 6, and 42 ÷ 6 = 7 while 54 ÷ 6 = 9.
- A — divided by 2 only, so it can still be simplified
- C — divided by 7 and 6, which are different numbers
- D — divided by 3 only
1.3
Which one of the following is the LARGEST fraction?
(1)
A)35
B)23✓
C)58
D)712
Answer: B — Over a denominator of 120: 72, 80, 75 and 70 — so 2/3 is the largest.
- A — 72 out of 120
- C — 75 out of 120
- D — 70 out of 120, the smallest
1.4
A fraction is in its lowest terms when …
(1)
A)the numerator is smaller than the denominator
B)the denominator is a prime number
C)the only common factor of the two parts is 1✓
D)the numerator is 1
Answer: C — Nothing except 1 divides into both, so there is nothing left to cancel.
- A — 3/4 and 6/8 both satisfy that, yet 6/8 is not in its lowest terms
- B — 6/7 is simplest and 7 is prime, but 4/9 is simplest too and 9 is not
- D — 1/2 is simplest, but so is 3/4
1.5
34 of the learners in a class of 32 are present. How many are ABSENT?
(1)
A)24
B)8✓
C)12
D)4
Answer: B — Present = 3/4 × 32 = 24, so absent = 32 − 24 = 8.
- A — that is the number PRESENT, not absent
- C — used 1/3 of 32 rather than 1/4
- D — divided 32 by 8
1.6
Which one of the following is NOT equal to 12?
(1)
A)36
B)714
C)46✓
D)2550
Answer: C — 4/6 simplifies to 2/3, not 1/2.
- A — 3 ÷ 3 = 1 and 6 ÷ 3 = 2
- B — 7 ÷ 7 = 1 and 14 ÷ 7 = 2
- D — 25 ÷ 25 = 1 and 50 ÷ 25 = 2
1.7
25 written as a percentage is …
(1)
A)25%
B)40%✓
C)2,5%
D)52%
Answer: B — 2 ÷ 5 = 0,4 and 0,4 × 100 = 40%.
- A — turned the fraction upside down first
- C — divided 5 by 2 and moved the comma the wrong way
- D — wrote the digits down in the order they appear
1.8
Multiplying the numerator and the denominator of a fraction by 3 …
(1)
A)makes the fraction 3 times bigger
B)leaves its value unchanged✓
C)makes the fraction 3 times smaller
D)makes it a whole number
Answer: B — You have multiplied by 3/3, which is 1, and multiplying by 1 changes nothing.
- A — only multiplying the NUMERATOR by 3 would do that
- C — only multiplying the denominator by 3 would do that
- D — nothing about it forces a whole number
1.9
Which of the following lists is arranged from SMALLEST to largest?
(1)
A)12 ; 23 ; 34✓
B)34 ; 23 ; 12
C)23 ; 12 ; 34
D)12 ; 34 ; 23
Answer: A — Over a denominator of 12: 6, 8 and 9.
- B — that is largest to smallest
- C — compared the numerators only
- D — compared the denominators only
1.10
In a test Sipho scored 1824 and Ann scored 1520. Which statement is TRUE?
(1)
A)Sipho did better
B)Ann did better
C)They scored the same✓
D)It cannot be compared
Answer: C — Both simplify to 3/4, so the two scores are equal.
- A — 18 is bigger than 15, but the totals differ too
- B — Ann's denominator is smaller, but that does not make her score lower
- D — fractions with different denominators can always be compared

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

[14 MARKS]

Answer the questions below WITHOUT using a calculator. Leave all answers in their simplest form.

2.1
Fill in the missing number: 27 = ?21, and hence write 27 with a denominator of 63.
(3)
21 ÷ 7 = 3, so the numerator is multiplied by 3 as well (1)
27 = 621 (1)
63 ÷ 7 = 9, so 27 = 1863 (1)
2.2
Simplify 84126 to its lowest terms.
(4)
Both are even: 4263 (1)
Both divide by 3: 1421 (1)
Both divide by 7: 23 (1)
(Or divide once by the HCF, 42) (1)
2.3
Arrange in ASCENDING order: 23; 58; 712; 34
(4)
LCD = 24 (1)
1624; 1524; 1424; 1824 (2)
712; 58; 23; 34 (1)
2.4
Is 79 in its lowest terms? Give a reason for your answer, and simplify 4254 fully.
(3)
Yes (1)
The only common factor of 7 and 9 is 1 (reason 1)
4254 = 79, dividing top and bottom by 6 (1)

Question 3

[9 MARKS]

Answer the questions below.

3.1
A learner writes 1218 = 69 = 34. Identify the step where the learner went wrong and give the correct answer.
(3)
69 is correct (1)
The last step is wrong: 6 and 9 divide by 3, not by 2 (1)
69 = 23 (1)
3.2
Explain why multiplying the numerator and the denominator by the same number does not change the value of a fraction.
(2)
You are multiplying by nn, which is 1 (1), and multiplying by 1 leaves the value unchanged (1)
3.3
Determine which is larger, 57 or 710, and show how you decided.
(4)
LCD = 70 (1)
57 = 5070 and 710 = 4970 (2)
57 is larger (1)

TOTAL: 33 marks

This question paper consists of 3 questions.