$10 \div 2 \frac{2}{9}$
Answer (1)
Convert the mixed number to an improper fraction: 2 9 2 = 9 20 .
Rewrite the division as multiplication by the reciprocal: 10 ÷ 9 20 = 10 × 20 9 .
Multiply the fractions: 10 × 20 9 = 20 90 .
Simplify the fraction: 20 90 = 2 9 = 4.5 . The final answer is 4.5 .
Explanation
Understanding the problem We are asked to divide 10 by the mixed number 2 9 2 .
Converting to an improper fraction First, we need to convert the mixed number 2 9 2 into an improper fraction. To do this, we multiply the whole number part (2) by the denominator (9) and add the numerator (2). This gives us 2 × 9 + 2 = 18 + 2 = 20 . So, the improper fraction is 9 20 .
Dividing by a fraction Now we can rewrite the original problem as 10 ÷ 9 20 . Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 9 20 is 20 9 . So, we have 10 × 20 9 .
Multiplying the fractions To multiply 10 × 20 9 , we can write 10 as a fraction: 1 10 . Then we multiply the numerators and the denominators: 1 10 × 20 9 = 1 × 20 10 × 9 = 20 90 .
Simplifying the result Finally, we simplify the fraction 20 90 . Both the numerator and denominator are divisible by 10, so we can divide both by 10: 20 ÷ 10 90 ÷ 10 = 2 9 . We can also express this as a mixed number: 4 2 1 or as a decimal 4.5 .
Final Answer Therefore, 10 ÷ 2 9 2 = 2 9 = 4.5 .
Examples
Imagine you are baking a cake and the recipe calls for 2 9 2 cups of flour per cake. If you have 10 cups of flour, you can calculate how many cakes you can bake by dividing 10 by 2 9 2 . This problem demonstrates how division with mixed numbers can be used in everyday situations like cooking or measuring ingredients.
