(4) [tex]\frac{4}{5} \div \frac{3}{4}[/tex]
Answer (1)
Dividing by a fraction is equivalent to multiplying by its reciprocal.
Rewrite the division as a multiplication: 5 4 ÷ 4 3 = 5 4 × 3 4 .
Multiply the fractions: 5 4 × 3 4 = 15 16 .
The final answer is 15 16 .
Explanation
Understanding the problem We are asked to evaluate the expression 5 4 ÷ 4 3 . Dividing by a fraction is the same as multiplying by its reciprocal.
Rewriting the division as multiplication To divide 5 4 by 4 3 , we multiply 5 4 by the reciprocal of 4 3 , which is 3 4 . So we have: 5 4 ÷ 4 3 = 5 4 × 3 4
Multiplying the fractions Now, we multiply the two fractions: 5 4 × 3 4 = 5 × 3 4 × 4 = 15 16
Simplifying the fraction The fraction 15 16 is already in its simplest form, as 16 and 15 have no common factors other than 1.
Final Answer Therefore, the result of the division is 15 16 .
Examples
In cooking, if a recipe calls for 4 3 cup of flour and you only have 5 4 cup, you might want to know what fraction of the recipe you can make. This problem is a direct application of dividing one fraction by another. Understanding how to divide fractions helps in scaling recipes and adjusting ingredient quantities.
