Work out \( \frac{16gh^2}{5k} \div \frac{24h}{25gk} \). Give your answer in its simplest form.
Answer (2)
The simplified form of the expression 5 k 16 g h 2 ÷ 25 g k 24 h is 3 10 g 2 h . We achieved this by multiplying by the reciprocal and simplifying step by step. Common factors were canceled out to reach the final result.
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To solve the problem 5 k 16 g h 2 ÷ 25 g k 24 h and express it in its simplest form, we should follow these steps:
Understand the Division of Fractions : Dividing by a fraction is equivalent to multiplying by its reciprocal. Thus, b a ÷ d c = b a × c d .
Apply the Principle to the Given Problem : Change the division into a multiplication by using the reciprocal of the second fraction:
5 k 16 g h 2 ÷ 25 g k 24 h = 5 k 16 g h 2 × 24 h 25 g k
Multiply the Fractions : Multiply the numerators and the denominators separately:
Numerator: 16 g h 2 × 25 g k = 16 ⋅ 25 ⋅ g ⋅ g ⋅ h 2 ⋅ k = 400 g 2 h 2 k
Denominator: 5 k × 24 h = 5 ⋅ 24 ⋅ k ⋅ h = 120 kh
So, we have:
120 kh 400 g 2 h 2 k
Simplify the Expression : Cancel out common factors in the numerator and denominator.
The common factor k appears in both.
Simplifying the coefficients 120 400 = 3 10
h 2 and h results in h in the numerator.
Therefore, the simplified form is:
3 10 g 2 h
Thus, 5 k 16 g h 2 ÷ 25 g k 24 h simplifies to 3 10 g 2 h . This process involves understanding the properties of fractions and basic algebraic manipulation.
