$1 \frac{3}{4} \div 2 \frac{1}{5} =$
Answer (2)
Convert the mixed fractions to improper fractions: 1 4 3 = 4 7 and 2 5 1 = 5 11 .
Divide the first fraction by the second fraction: 4 7 ÷ 5 11 = 4 7 × 11 5 .
Multiply the fractions: 4 7 × 11 5 = 44 35 .
The final answer is: 44 35 .
Explanation
Problem Setup Let's evaluate the expression 1 4 3 ÷ 2 5 1 .
Converting to Improper Fractions First, we need to convert the mixed fractions to improper fractions. A mixed fraction is a whole number and a proper fraction combined. To convert a mixed fraction to an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator. The result becomes the new numerator, and we keep the same denominator.
First Fraction Conversion For 1 4 3 , we multiply 1 by 4 and add 3, which gives us 1 × 4 + 3 = 4 + 3 = 7 . So, 1 4 3 = 4 7 .
Second Fraction Conversion For 2 5 1 , we multiply 2 by 5 and add 1, which gives us 2 × 5 + 1 = 10 + 1 = 11 . So, 2 5 1 = 5 11 .
Dividing Fractions Now we have the expression 4 7 ÷ 5 11 . To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
Reciprocal and Multiplication The reciprocal of 5 11 is 11 5 . So, we have 4 7 ÷ 5 11 = 4 7 × 11 5 .
Multiplying Numerators and Denominators Now, we multiply the fractions: 4 7 × 11 5 = 4 × 11 7 × 5 = 44 35 .
Simplifying the Fraction The fraction 44 35 is in its simplest form because 35 and 44 do not have any common factors other than 1.
Final Answer Therefore, 1 4 3 ÷ 2 5 1 = 44 35 .
Examples
Understanding fraction division is essential in many real-life scenarios. For instance, if you're baking and need to divide 1 4 3 cups of flour into 2 5 1 batches, you would use this calculation to determine how much flour goes into each batch. Similarly, if you're splitting a workload or resources among a team, knowing how to divide fractions helps ensure fair and accurate distribution. This skill is also valuable in scaling recipes, calculating proportions in construction, and managing finances.
To solve 1 4 3 ÷ 2 5 1 , first convert to improper fractions to get 4 7 and 5 11 . Then, rewrite the division as multiplication by the reciprocal, leading to 44 35 as the final answer. Thus, 1 4 3 ÷ 2 5 1 = 44 35 .
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