4. [tex]$\frac{1}{4} \div 3 \frac{4}{5}$[/tex]
5. [tex]$1 \frac{3}{6} \div 2 \frac{1}{2}$[/tex]
6. [tex]$2 \frac{1}{3} \div 1 \frac{3}{6}$[/tex]
Answer (2)
Convert each mixed number to an improper fraction.
Divide the fractions by multiplying by the reciprocal of the second fraction.
Simplify the resulting fraction.
Convert any improper fractions back to mixed numbers: 1 76 9 , 2 15 2 , 1 9 5 .
1 76 9 , 2 15 2 , 1 9 5
Explanation
Understanding the Problem We are given three division problems involving mixed numbers. We need to convert each mixed number to an improper fraction and then perform the division. Remember that to divide fractions, we multiply by the reciprocal of the second fraction. Finally, we simplify the result.
Solving the First Problem Let's solve the first problem: 4 4 1 ÷ 3 5 4 . First, convert the mixed numbers to improper fractions:
4 4 1 = 4 4 × 4 + 1 = 4 16 + 1 = 4 17
3 5 4 = 5 3 × 5 + 4 = 5 15 + 4 = 5 19
Now, divide the fractions:
4 17 ÷ 5 19 = 4 17 × 19 5 = 4 × 19 17 × 5 = 76 85
Convert the improper fraction back to a mixed number:
76 85 = 1 76 9
Solving the Second Problem Now, let's solve the second problem: 5 3 1 ÷ 2 2 1 . First, convert the mixed numbers to improper fractions:
5 3 1 = 3 5 × 3 + 1 = 3 15 + 1 = 3 16
2 2 1 = 2 2 × 2 + 1 = 2 4 + 1 = 2 5
Now, divide the fractions:
3 16 ÷ 2 5 = 3 16 × 5 2 = 3 × 5 16 × 2 = 15 32
Convert the improper fraction back to a mixed number:
15 32 = 2 15 2
Solving the Third Problem Finally, let's solve the third problem: 2 3 1 ÷ 1 6 3 . First, convert the mixed numbers to improper fractions:
2 3 1 = 3 2 × 3 + 1 = 3 6 + 1 = 3 7
1 6 3 = 6 1 × 6 + 3 = 6 6 + 3 = 6 9 = 2 3
Now, divide the fractions:
3 7 ÷ 2 3 = 3 7 × 3 2 = 3 × 3 7 × 2 = 9 14
Convert the improper fraction back to a mixed number:
9 14 = 1 9 5
Final Answer Therefore, the solutions are:
4 4 1 ÷ 3 5 4 = 1 76 9
5 3 1 ÷ 2 2 1 = 2 15 2
2 3 1 ÷ 1 6 3 = 1 9 5
Examples
Mixed number division is useful in everyday situations such as cooking, where you might need to divide a recipe in half or in other fractional parts. For example, if a recipe calls for 2 2 1 cups of flour and you only want to make half the recipe, you would need to divide 2 2 1 by 2 to find out how much flour you need. This skill is also useful in construction, where you might need to divide lengths of materials into fractional parts.
We solved three division problems involving mixed numbers by converting them into improper fractions, dividing by the reciprocal, and converting back to mixed numbers. The answers are: 1 \frac{9}{76} for the first, \frac{3}{5} for the second, and 1 \frac{5}{9} for the last problem. This process involves understanding fractions and the operations of multiplication and division.
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