frac 41 7 - Math Solver AI

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--- ## Question (Assumed: Convert \( 5\frac{6}{7} \) to an improper fraction) **Question content**: Convert the mixed number \( 5\frac{6}{7} \) to an improper fraction. **Discipline**: Mathematics **Grade**: 4th - 5th grade (elementary school) ### Correct answer \( \frac{41}{7} \) ### Detailed problem-solving steps 1. **Recall the conversion formula**: For a mixed number \( a\frac{b}{c} \) (where \( a \) is the whole number, \( b \) is the numerator, and \( c \) is the denominator), the improper fraction is \( \frac{a \times c + b}{c} \). 2. **Identify parts of the mixed number**: In \( 5\frac{6}{7} \), \( a = 5 \), \( b = 6 \), and \( c = 7 \). 3. **Apply the formula**: Calculate \( a \times c + b \): \( 5 \times 7 + 6 = 35 + 6 = 41 \). 4. **Form the improper fraction**: Place the result (41) over the original denominator (7), so the improper fraction is \( \frac{41}{7} \). ### Knowledge points involved 1. **Mixed Numbers** - Interpretation: A mixed number represents a quantity as a sum of a whole number and a proper fraction (e.g., \( 5\frac{6}{7} = 5 + \frac{6}{7} \)). It is used to express values between whole numbers in a more intuitive way. 2. **Improper Fractions** - Interpretation: A fraction where the numerator is greater than or equal to the denominator (e.g., \( \frac{41}{7} \)). Improper fractions represent values greater than or equal to 1 and are useful for arithmetic operations (e.g., addition/subtraction of fractions). 3. **Conversion between Mixed Numbers and Improper Fractions** - Interpretation: The process relies on the meaning of fractions (parts of a whole) and equivalent fractions. For a mixed number \( a\frac{b}{c} \), the whole number \( a \) is equivalent to \( \frac{a \times c}{c} \) (since \( a = \frac{a \times c}{c} \) for any non - zero \( c \)). Adding the proper fraction \( \frac{b}{c} \) gives \( \frac{a \times c}{c}+\frac{b}{c}=\frac{a \times c + b}{c} \), which is the improper fraction form. ---

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