Work out $3 \times 2 \frac{5}{12}$ Give your answer as a fraction in its simplest form.
Answer (2)
To calculate 3 × 2 12 5 , convert the mixed number to an improper fraction, which gives 12 29 . Then, multiply by 3 to get 12 87 and simplify this to 4 29 . The answer is 4 29 .
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Convert the mixed number 2 12 5 to an improper fraction: 2 12 5 = 12 29 .
Multiply the improper fraction by 3: 3 × 12 29 = 12 87 .
Simplify the resulting fraction by dividing both numerator and denominator by their greatest common divisor (GCD), which is 3: 12 ÷ 3 87 ÷ 3 = 4 29 .
The simplified fraction is 4 29 .
Explanation
Problem Analysis We are asked to multiply a whole number, 3, by a mixed number, 2 12 5 , and express the result as a simplified fraction.
Convert Mixed Number to Improper Fraction First, we need to convert the mixed number 2 12 5 into an improper fraction. To do this, we multiply the whole number part (2) by the denominator (12) and add the numerator (5). This gives us the new numerator, and we keep the same denominator. So, we have:
2 12 5 = 12 ( 2 \tims 12 ) + 5 = 12 24 + 5 = 12 29
Multiply by 3 Next, we multiply the improper fraction 12 29 by 3:
3 \tims 12 29 = 12 3 \tims 29 = 12 87
Simplify the Fraction Now, we need to simplify the fraction 12 87 . To do this, we find the greatest common divisor (GCD) of the numerator (87) and the denominator (12) and divide both by the GCD.
The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 87 are 1, 3, 29, and 87.
The greatest common divisor of 87 and 12 is 3. So, we divide both the numerator and the denominator by 3:
12 87 = 12 ÷ 3 87 ÷ 3 = 4 29
Final Answer The simplified fraction is 4 29 .
Examples
In baking, if a recipe calls for 2 12 5 cups of flour and you want to triple the recipe, you need to calculate 3 × 2 12 5 . Converting the mixed number to an improper fraction and then multiplying helps you find the total amount of flour needed, which is 4 29 cups. This ensures you have the correct proportions for your tripled recipe.
