a) Write $2 \frac{1}{4}$ as an improper fraction in its simplest form.
b) Work out $2 \frac{1}{4} \times 5$
Give your answer as a fraction in its simplest form.
Answer (2)
To convert the mixed fraction 2 4 1 to an improper fraction, it becomes 4 9 . When multiplying 4 9 by 5, the result is 4 45 , which is already in its simplest form.
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Convert the mixed fraction 2 4 1 to an improper fraction: 4 ( 2 × 4 ) + 1 = 4 9 .
Multiply the improper fraction 4 9 by 5: 4 9 × 5 = 4 45 .
Simplify the resulting fraction (if possible). In this case, 4 45 is already in its simplest form.
The final answer is 4 45 .
Explanation
Problem Overview We are given a mixed fraction and asked to convert it into an improper fraction and then multiply the resulting fraction by a whole number.
Converting to Improper Fraction To convert the mixed fraction 2 4 1 to an improper fraction, we multiply the whole number part (2) by the denominator (4) and add the numerator (1). The result becomes the new numerator, and we keep the same denominator (4). So, we have:
4 ( 2 × 4 ) + 1 = 4 8 + 1 = 4 9
Thus, 2 4 1 as an improper fraction is 4 9 .
Multiplying by 5 Now, we need to multiply the improper fraction 4 9 by 5. To do this, we multiply the numerator (9) by 5 and keep the same denominator (4):
4 9 × 5 = 4 9 × 5 = 4 45
So, 2 4 1 × 5 = 4 45 .
Simplifying the Result The improper fraction 4 45 is already in its simplest form because 45 and 4 have no common factors other than 1. We can also express 4 45 as a mixed number: 11 4 1 . However, the question asks for the answer as a fraction in its simplest form, so we leave it as 4 45 .
Final Answer Therefore, 2 4 1 × 5 = 4 45 .
Examples
Understanding fractions is crucial in everyday situations, such as cooking. For instance, if a recipe calls for 2 4 1 cups of flour and you want to make five times the recipe, you need to calculate 2 4 1 × 5 . Converting 2 4 1 to 4 9 and then multiplying by 5 gives you 4 45 cups, which is 11 4 1 cups. This ensures you have the correct amount of flour for the enlarged recipe, demonstrating a practical application of fraction manipulation.
