Work out:
$4 \frac{1}{9}-3 \frac{3}{5}$
Give your answer in its simplest form.
Answer (2)
Convert the mixed numbers to improper fractions: 4 9 1 = 9 37 and 3 5 3 = 5 18 .
Find a common denominator for the fractions, which is 45.
Convert the fractions to equivalent fractions with the common denominator: 9 37 = 45 185 and 5 18 = 45 162 .
Subtract the fractions: 45 185 − 45 162 = 45 23 . The answer is 45 23 .
Explanation
Understanding the Problem We need to subtract two mixed numbers: 4 9 1 and 3 5 3 . The answer should be given in its simplest form.
Converting to Improper Fractions First, convert the mixed numbers to improper fractions.
Calculating Improper Fractions 4 9 1 = 9 4 × 9 + 1 = 9 36 + 1 = 9 37
3 5 3 = 5 3 × 5 + 3 = 5 15 + 3 = 5 18
Finding a Common Denominator Now, subtract the two improper fractions: 9 37 − 5 18 . To do this, we need a common denominator, which is the least common multiple (LCM) of 9 and 5. Since 9 and 5 have no common factors other than 1, their LCM is simply their product: 9 × 5 = 45 .
Converting Fractions to Common Denominator Convert both fractions to have the denominator 45: 9 37 = 9 × 5 37 × 5 = 45 185 5 18 = 5 × 9 18 × 9 = 45 162
Subtracting the Fractions Now subtract the fractions: 45 185 − 45 162 = 45 185 − 162 = 45 23
Simplifying the Result The resulting fraction 45 23 is already in its simplest form because 23 is a prime number and does not divide 45.
Final Answer Therefore, the final answer is 45 23 .
Examples
Understanding fractions is crucial in many real-life situations, such as cooking, where you might need to adjust ingredient quantities. For example, if a recipe calls for 4 9 1 cups of flour, but you only want to make a portion that's 3 5 3 cups smaller, calculating the difference using fraction subtraction helps you determine the exact amount of flour needed. This ensures your recipe turns out perfectly, demonstrating the practical application of fraction arithmetic in everyday tasks.
We converted the mixed numbers 4 9 1 and 3 5 3 to improper fractions, found a common denominator of 45, and subtracted to get the answer 45 23 in its simplest form. This result represents the difference between the two amounts. The final answer is 45 23 .
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