\frac{5 a b}{c d} \div 2 \frac{1}{7}
Answer (2)
Convert the mixed number to an improper fraction: 2 7 1 = 7 15 .
Rewrite the division as multiplication by the reciprocal: c d 5 ab ÷ 7 15 = c d 5 ab × 15 7 .
Multiply the fractions: c d 5 ab × 15 7 = 15 c d 35 ab .
Simplify the fraction: 15 c d 35 ab = 3 c d 7 ab .
The simplified expression is 3 c d 7 ab .
Explanation
Understanding the Problem We are asked to simplify the expression c d 5 ab ÷ 2 7 1 . This involves dividing a fraction by a mixed number. To do this, we will first convert the mixed number to an improper fraction, then rewrite the division as multiplication by the reciprocal of the improper fraction, and finally simplify the resulting expression.
Converting Mixed Number to Improper Fraction First, we convert the mixed number 2 7 1 to an improper fraction. To do this, we multiply the whole number part (2) by the denominator (7) and add the numerator (1). This gives us 2 × 7 + 1 = 14 + 1 = 15 . So, the improper fraction is 7 15 .
Rewriting Division as Multiplication Now we rewrite the division as multiplication by the reciprocal. The reciprocal of 7 15 is 15 7 . Therefore, we have c d 5 ab ÷ 7 15 = c d 5 ab × 15 7
Multiplying the Fractions Next, we multiply the fractions: c d 5 ab × 15 7 = c d × 15 5 ab × 7 = 15 c d 35 ab
Simplifying the Fraction Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5: 15 c d 35 ab = 15 ÷ 5 35 ÷ 5 × c d ab = 3 c d 7 ab
Final Answer Therefore, the simplified expression is 3 c d 7 ab .
Examples
Understanding how to simplify expressions involving fractions and mixed numbers is crucial in various real-life scenarios, such as calculating proportions in recipes, determining ratios in construction projects, or adjusting quantities in scientific experiments. For instance, if you need to scale a recipe that calls for 2 7 1 cups of flour and you only want to make 3 5 of the recipe, you would use similar simplification techniques to find the new amount of flour needed. This ensures accurate and consistent results in practical applications.
To simplify c d 5 ab ÷ 2 7 1 , first convert the mixed number to an improper fraction 7 15 , change the division to multiplication by its reciprocal, and then simplify the resulting fraction. The final simplified expression is 3 c d 7 ab .
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