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Answer/Explanation:

6.

a. ¾ of ²/9

"of" is the same as multiplication

= ¾ × ²/9

= ½ × ⅓

= (1 × 1)/(2 × 3)

= ⅙

b. ⅖ of ⁷/12

= ⅖ × ⁷/12

= ⅕ × ⁷/6

= (1 × 7)/(5 × 6)

= ⁷/30

7.

a. HCF of 243 and 246 using the matching factors method:

State out all factors that are integers that will divide 243 and 246 each without any remainder

243 = 1, [3,] 9, 27, 81, and 243

246 = 1, 2, [3,] 6, 41, 82, 123, and 246

Next, find the greatest factor that is common to both:

The greatest common factor that is common is 3

Therefore,

HCF = 3

b. HCF of 72 and 96 using the matching factors method:

State out all factors that are integers that will divide 72 and 96 each without any remainder

72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, [24,] 36, and 72

96 = 1, 2, 3, 4, 6, 8, 12, 16, [24,] 32, 48, and 96

Next, find the greatest factor that is common to both:

The greatest common factor that is common is 24

Therefore,

HCF = 24

8.

a. LCM of 12, 18, 36 using Prime Factorization Method:

First, list out the prime factorization of each of the numbers in exponential form:

12 = 2² × 3¹

18 = 2¹ × 3²

36 = 2² × 3²

Next, multiple the highest exponent prime factors to find the LCM:

The highest exponent prime are 2² and 3²

Therefore, the LCM would be:

2² × 3² = 4 × 9 = 36

LCM = 36

b. LCM of 9, 27, 18 using Prime Factorization Method:

First, list out the prime factorization of each of the numbers in exponential form:

9 = 3²

27 = 3³

18 = 2¹ × 3²

Next, multiple the highest exponent prime factors to find the LCM:

The highest exponent prime are 2¹ and 3³

Therefore, the LCM would be:

2¹ × 3³ = 2 × 27 =

LCM = 54

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