de 2.2 [tex]\frac{4}{3} \div 1 \frac{3}{4}=[/tex]
de 3.4 [tex]\frac{3}{6} \div 2 \frac{1}{2}=[/tex]
in 1.2 [tex]\frac{1}{4} \div 3 \frac{4}{5}=[/tex]
i. 5. [tex]\frac{3}{6} \div 2 \frac{1}{2}=[/tex]
i. 6. [tex]\frac{1}{3} \div 1 \frac{3}{6}=[/tex]
i. 7 [tex]\frac{2}{4} \div 2 \frac{1}{3}=[/tex]
Answer (2)
Convert each mixed number to an improper fraction.
Divide the first fraction by the second fraction by multiplying by the reciprocal of the second fraction.
Simplify the resulting fraction to its lowest terms.
Convert the improper fraction to a mixed number: 1) 1 21 19 , 2) 1 5 4 , 3) 76 45 , 4) 2 5 1 , 5) 4 9 2 , 6) 3 14 3 .
Explanation
Understanding the Problem We are given six division problems involving mixed numbers and fractions. Our goal is to evaluate each division problem and express the result as a simplified fraction or mixed number.
Solution Plan First, we need to convert each mixed number to an improper fraction. Then, we will divide the first fraction by the second fraction by multiplying by the reciprocal of the second fraction. Finally, we will simplify the resulting fraction to its lowest terms and convert back to a mixed number.
Solving Problem 1 Problem 1: 2 3 4 ÷ 1 4 3 = 3 10 ÷ 4 7 = 3 10 × 7 4 = 21 40 = 1 21 19
Solving Problem 2 Problem 2: 4 6 3 ÷ 2 2 1 = 6 27 ÷ 2 5 = 6 27 × 5 2 = 30 54 = 5 9 = 1 5 4
Solving Problem 3 Problem 3: 2 4 1 ÷ 3 5 4 = 4 9 ÷ 5 19 = 4 9 × 19 5 = 76 45
Solving Problem 4 Problem 4: 5 6 3 ÷ 2 2 1 = 6 33 ÷ 2 5 = 6 33 × 5 2 = 30 66 = 5 11 = 2 5 1
Solving Problem 5 Problem 5: 6 3 1 ÷ 1 6 3 = 3 19 ÷ 6 9 = 3 19 × 9 6 = 27 114 = 9 38 = 4 9 2
Solving Problem 6 Problem 6: 7 4 2 ÷ 2 3 1 = 4 30 ÷ 3 7 = 4 30 × 7 3 = 28 90 = 14 45 = 3 14 3
Final Answers The solutions to the division problems are:
1 21 19
1 5 4
76 45
2 5 1
4 9 2
3 14 3
Examples
Dividing fractions is a fundamental skill with many real-world applications. For example, if you are baking and need to halve a recipe that calls for 2 2 1 cups of flour, you would divide 2 2 1 by 2. Similarly, if you are splitting a pizza among friends and each person gets 8 3 of the pizza, you can use division to determine how many friends can be fed with a given number of pizzas. These types of calculations are essential in everyday life for managing resources and proportions.
To divide mixed numbers by fractions, first convert the mixed numbers to improper fractions, then multiply by the reciprocal of the second fraction. After calculating, simplify your results and convert them back to mixed numbers if needed. Each calculated problem yields specific simplified fraction results.
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