a) Write $2 \frac{3}{4}$ as an improper fraction in its simplest form.
b) Work out $2 \frac{3}{4} \times 5$
Give your answer as a fraction in its simplest form.
Answer (1)
Convert the mixed fraction 2 4 3 to an improper fraction: 4 ( 2 × 4 ) + 3 = 4 11 .
Multiply the improper fraction by 5: 4 11 × 5 = 4 55 .
Simplify the fraction (if needed): 4 55 is already in simplest form.
The final answers are: 4 11 and 4 55 .
Explanation
Problem Analysis We are given a mixed fraction 2 4 3 and asked to convert it into an improper fraction and then multiply the result by 5.
Converting to Improper Fraction To convert the mixed fraction 2 4 3 to an improper fraction, we multiply the whole number part (2) by the denominator (4) and add the numerator (3). The result is placed over the original denominator (4). So, we have: 4 ( 2 × 4 ) + 3 = 4 8 + 3 = 4 11 Thus, the improper fraction is 4 11 .
Multiplying by 5 Now, we need to multiply the improper fraction 4 11 by 5: 4 11 × 5 = 4 11 × 5 = 4 55 So, the result of the multiplication is 4 55 .
Simplifying the Result The fraction 4 55 is already in its simplest form because 55 and 4 have no common factors other than 1. We can also express this improper fraction as a mixed number: 4 55 = 13 4 3 .
Final Answer Therefore, 2 4 3 as an improper fraction is 4 11 , and 2 4 3 × 5 = 4 55 .
Examples
Understanding fractions and their operations is crucial in everyday situations, such as cooking and baking. For instance, if a recipe calls for 2 4 3 cups of flour and you want to make 5 times the recipe, you need to calculate 2 4 3 × 5 . Converting the mixed fraction to an improper fraction, 4 11 , and then multiplying by 5 gives you 4 55 or 13 4 3 cups of flour needed. This ensures you have the correct proportions for your recipe.
