2. [tex] \frac{4}{3} \div 1 \frac{3}{4}= [/tex]
3. [tex] \frac{3}{6} \div 2 \frac{1}{2}= [/tex]
4. [tex] 2 \frac{1}{4} \div 3 \frac{4}{5}= [/tex]
Answer (2)
Convert each mixed number to an improper fraction.
Divide the first improper fraction by the second improper fraction by multiplying by its reciprocal.
Simplify the resulting fraction to its lowest terms or convert to a mixed number.
The solutions are: 21 40 , 5 9 , and 76 45 , which can also be written as 1 21 19 , 1 5 4 , and 76 45 respectively. 21 40 , 5 9 , 76 45
Explanation
Problem Overview and Strategy We are given three division problems involving mixed numbers. Our goal is to convert these mixed numbers to improper fractions and then perform the division. Remember that dividing by a fraction is the same as multiplying by its reciprocal. Finally, we will simplify the resulting fractions.
Solving the First Problem Let's tackle the first problem: 2 3 4 ÷ 1 4 3 . First, we convert the mixed numbers to improper fractions:
2 3 4 = 3 2 × 3 + 4 = 3 6 + 4 = 3 10
1 4 3 = 4 1 × 4 + 3 = 4 4 + 3 = 4 7
Now we divide the improper fractions:
3 10 ÷ 4 7 = 3 10 × 7 4 = 3 × 7 10 × 4 = 21 40
We can convert this improper fraction to a mixed number:
21 40 = 1 21 19
Solving the Second Problem Now let's solve the second problem: 4 6 3 ÷ 2 2 1 . First, we convert the mixed numbers to improper fractions:
4 6 3 = 6 4 × 6 + 3 = 6 24 + 3 = 6 27 = 2 9
2 2 1 = 2 2 × 2 + 1 = 2 4 + 1 = 2 5
Now we divide the improper fractions:
2 9 ÷ 2 5 = 2 9 × 5 2 = 2 × 5 9 × 2 = 10 18 = 5 9
We can convert this improper fraction to a mixed number:
5 9 = 1 5 4
Solving the Third Problem Finally, let's solve the third problem: 2 4 1 ÷ 3 5 4 . First, we convert the mixed numbers to improper fractions:
2 4 1 = 4 2 × 4 + 1 = 4 8 + 1 = 4 9
3 5 4 = 5 3 × 5 + 4 = 5 15 + 4 = 5 19
Now we divide the improper fractions:
4 9 ÷ 5 19 = 4 9 × 19 5 = 4 × 19 9 × 5 = 76 45
Final Answers Therefore, the solutions to the three division problems are:
2 3 4 ÷ 1 4 3 = 21 40 = 1 21 19
4 6 3 ÷ 2 2 1 = 5 9 = 1 5 4
2 4 1 ÷ 3 5 4 = 76 45
Examples
Understanding how to divide mixed numbers is useful in many real-life situations. For example, if you are baking and need to divide a recipe in half, you might need to divide mixed number quantities of ingredients. Or, if you are calculating how many pieces of wood you can cut from a longer board, you might need to divide mixed numbers to find the answer. These skills are also helpful in understanding proportions and ratios, which are used in many fields, including science, engineering, and finance.
To solve the division problems involving mixed numbers, we convert them to improper fractions, then perform the division by multiplying by the reciprocal, and finally simplify the results. The answers are: 1) 21 40 , 2) 5 9 , and 3) 76 45 .
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