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