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Question:- 4/5 of (4/9 + 2/3) ÷ 2 2/3

Answer↘

⭐Step 1 : Find the Least Common Denominator (LCD) of 4/9 ,2/3

Method 1: By Listing Multiples

List out all multiples of each denominator, and find the first common one.

Multiples of 9 : 9, ...

Multiples of 3 : 3, 6, 9, ...

Therefore, the LCD is 99.

Method 2: By PRIME Factors

List all prime factors of each denominator, and find the union of these primes.

Prime Factors of 9 : 3, 3

Prime Factors of 3 : 3

Therefore, the LCD is 3×3=9

LCD=9

⭐Step 2 : Make the denominators the same as the LCD

4/9+2×3/3×3

⭐Step 3 : Simplify. Denominators are now the same

4\9 +6\9

⭐Step 4 : Join the denominators

4+6/9

⭐Step 5 simplify 5/9 +2/3 to 10/9

4/5×10/9÷2 2/3

⭐Step 6: convert 2 2/3 to improper fraction USING the method a b/c= ac+b/c

4/5×10/9÷2×3+2/3

⭐Step 7 : Simplify 2×3 to 6

4/5×10/9÷6+2/3

⭐Step 8: Simplify 6+2 to 8

4/5×10/9÷8/3

⭐Step 9: use the rule a ÷ b/c= a × c/b

4/5×10/9×3/8

⭐Step 10: use the rule a+b × c/d = ac/bd

4×10×3/5×9×8

⭐Step 11 : Simplify 4×10×3 to 120

120/5×9×8

⭐Step 12:  Simplify 5×9×8 to 360

120/360

⭐Step 13 : Simplify 120/360 to 1/3

Final answer 1/3

Decimal FORM: 0.333333

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