Work out $10 \times 5 \frac{1}{3}$. Give your answer as a fraction in its simplest form.
Answer (1)
Convert the mixed number to an improper fraction: 5 3 1 = 3 16 .
Multiply the improper fraction by 10: 10 × 3 16 = 3 160 .
Simplify the fraction (if needed). In this case, 3 160 is already in its simplest form.
The final answer is 3 160 .
Explanation
Problem Analysis and Conversion to Improper Fraction We need to calculate 10 × 5 3 1 and express the answer as a fraction in its simplest form. First, we need to convert the mixed number to an improper fraction.
Converting Mixed Number to Improper Fraction To convert the mixed number 5 3 1 to an improper fraction, we multiply the whole number part (5) by the denominator (3) and add the numerator (1). This gives us 5 × 3 + 1 = 15 + 1 = 16 . So, 5 3 1 = 3 16 .
Multiplication Now we multiply the improper fraction 3 16 by 10: 10 × 3 16 = 3 10 × 16 = 3 160
Simplifying the Fraction The fraction 3 160 is already in its simplest form because 160 and 3 have no common factors other than 1.
Final Answer Therefore, the answer is 3 160 .
Examples
Imagine you are baking cookies for a bake sale. The recipe calls for 5 3 1 cups of flour, but you want to make 10 batches of cookies. To find out how much flour you need in total, you would multiply 10 × 5 3 1 . This calculation helps you determine that you need 3 160 cups of flour, which is approximately 53.33 cups. Knowing this, you can accurately measure the ingredients and bake the cookies successfully.
