Work out $3 \frac{2}{5} \times 10$. Give your answer in its simplest form.
Answer (2)
The result of multiplying 3 5 2 by 10 is 34. This is found by converting the mixed number to an improper fraction, multiplying, and simplifying the result. The answer is 34 .
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Convert the mixed number to an improper fraction: 3 5 2 = 5 17 .
Multiply the improper fraction by 10: 5 17 × 10 = 5 170 .
Simplify the fraction: 5 170 = 34 .
The final answer is: 34 .
Explanation
Problem Analysis We are asked to calculate 3 5 2 × 10 and give the answer in its simplest form. First, we need to convert the mixed number to an improper fraction.
Convert to Improper Fraction To convert the mixed number 3 5 2 to an improper fraction, we multiply the whole number part (3) by the denominator (5) and add the numerator (2). This gives us the new numerator, and we keep the same denominator (5). So, 3 5 2 = 5 ( 3 × 5 ) + 2 = 5 15 + 2 = 5 17 .
Multiply by 10 Now we multiply the improper fraction 5 17 by 10: 5 17 × 10 = 5 17 × 10 = 5 170 .
Simplify the Fraction To simplify the fraction 5 170 , we divide the numerator (170) by the denominator (5): 170 ÷ 5 = 34 . Therefore, 5 170 = 34 .
Final Answer The result of 3 5 2 × 10 in its simplest form is 34.
Examples
Understanding fractions and multiplication is essential in everyday life. For instance, if you're baking a cake and need to triple a recipe that calls for 3 5 2 cups of flour, you would multiply 3 5 2 by 3. Similarly, if you are calculating distances and need to find out how far a car travels in 10 hours at a speed of 3 5 2 miles per hour, you would perform the same multiplication. These calculations help in accurately measuring ingredients or estimating travel times.
