Multiply. $6 \frac{1}{4} \times 3 \frac{3}{5}=$
Answer (2)
Convert the mixed numbers to improper fractions: 6 4 1 = 4 25 and 3 5 3 = 5 18 .
Multiply the improper fractions: 4 25 × 5 18 = 20 450 = 2 45 .
Convert the resulting improper fraction back to a mixed number: 2 45 = 22 2 1 .
The final answer is 22 2 1 .
Explanation
Convert to Improper Fractions We are asked to multiply two mixed numbers: 6 4 1 × 3 5 3 . To do this, we first convert each mixed number to an improper fraction.
Converting Mixed Numbers The first mixed number, 6 4 1 , can be converted to an improper fraction as follows: 6 4 1 = 4 6 × 4 + 1 = 4 24 + 1 = 4 25 The second mixed number, 3 5 3 , can be converted to an improper fraction as follows: 3 5 3 = 5 3 × 5 + 3 = 5 15 + 3 = 5 18
Multiply Improper Fractions Now, we multiply the two improper fractions: 4 25 × 5 18 = 4 × 5 25 × 18 We can simplify this by canceling common factors. Both 25 and 5 are divisible by 5, and both 18 and 4 are divisible by 2: 4 25 × 5 18 = 2 × 1 5 × 9 = 2 45
Convert back to Mixed Number Now, we convert the resulting improper fraction, 2 45 , back to a mixed number: 2 45 = 22 2 1
Final Answer Comparing our result, 22 2 1 , with the given options, we see that it matches the third option.
Examples
Mixed number multiplication is useful in everyday situations, such as when you need to calculate the area of a rectangular garden that measures 6 4 1 meters in length and 3 5 3 meters in width. By multiplying these mixed numbers, you can determine the total area of the garden, which helps in planning how much soil or fencing you might need. This skill is also applicable in cooking, carpentry, and other practical fields where precise measurements are required.
To multiply 6 4 1 and 3 5 3 , convert them to improper fractions, which gives you 4 25 and 5 18 . Multiplying these results in 2 45 , which converts back to the mixed number 22 2 1 . Thus, the final answer is 22 2 1 .
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