Multiply $12 \cdot \frac{3}{5}$. Simplify the answer and express it as a mixed number.
Answer (2)
Multiply the whole number 12 by the numerator of the fraction: 12 × 3 = 36 .
Keep the same denominator: 5 36 .
Convert the improper fraction 5 36 to a mixed number by dividing 36 by 5.
The result is 7 5 1 .
Explanation
Understanding the Problem We need to multiply the whole number 12 by the fraction 5 3 . The result needs to be simplified and expressed as a mixed number.
Multiplying by a Fraction To multiply a whole number by a fraction, we can rewrite the whole number as a fraction with a denominator of 1. So, we have: 12 ⋅ 5 3 = 1 12 ⋅ 5 3
Calculating the Improper Fraction Now, we multiply the numerators and the denominators: 1 12 ⋅ 5 3 = 1 × 5 12 × 3 = 5 36
Converting to a Mixed Number Now we convert the improper fraction 5 36 to a mixed number. To do this, we divide 36 by 5. The quotient will be the whole number part, and the remainder will be the numerator of the fractional part. The denominator remains 5.
Finding the Mixed Number We perform the division: 36 ÷ 5 = 7 with a remainder of 1. Therefore, the mixed number is 7 5 1 .
Examples
Imagine you are baking cookies and the recipe calls for 5 3 of a cup of sugar per batch. If you want to make 12 batches of cookies, you need to calculate how much sugar you need in total. This is where multiplying a whole number by a fraction comes in handy. In this case, you would multiply 12 (batches) by 5 3 (cup of sugar per batch) to find the total amount of sugar needed, which is 7 5 1 cups.
The multiplication of 12 by 5 3 results in the improper fraction 5 36 , which can be converted to the mixed number 7 5 1 .
;
