Question

improper fractions
questions
convert the mixed numbers into improper fractions

1. ( 5\frac{1}{3} = ) ______
2. ( 4\frac{2}{5} = ) ______
3. ( 6\frac{1}{2} = ) ______
4. ( 7\frac{3}{4} = ) ______
5. ( 6\frac{2}{6} = ) ______
6. ( 7\frac{3}{8} = ) ______
7. ( 6\frac{2}{5} = ) ______
8. ( 4\frac{9}{12} = ) ______
9. ( 6\frac{7}{10} = ) ______
10. ( 5\frac{4}{7} = ) ______

Explanation:

Step1: Recall the formula for converting a mixed number \( a\frac{b}{c} \) (where \( a \) is the whole number, \( b \) is the numerator of the fraction, and \( c \) is the denominator) to an improper fraction. The formula is \( \frac{a \times c + b}{c} \).

Step2: Let's take the first problem: \( 5\frac{1}{3} \). Using the formula, \( a = 5 \), \( b = 1 \), \( c = 3 \). So we calculate \( 5 \times 3 + 1 = 15 + 1 = 16 \). Then the improper fraction is \( \frac{16}{3} \).

Step3: Second problem: \( 4\frac{2}{5} \). Here, \( a = 4 \), \( b = 2 \), \( c = 5 \). Calculate \( 4 \times 5 + 2 = 20 + 2 = 22 \). So the improper fraction is \( \frac{22}{5} \).

Step4: Third problem: \( 6\frac{1}{2} \). \( a = 6 \), \( b = 1 \), \( c = 2 \). \( 6 \times 2 + 1 = 12 + 1 = 13 \). Improper fraction: \( \frac{13}{2} \).

Step5: Fourth problem: \( 7\frac{3}{4} \). \( a = 7 \), \( b = 3 \), \( c = 4 \). \( 7 \times 4 + 3 = 28 + 3 = 31 \). Improper fraction: \( \frac{31}{4} \).

Step6: Fifth problem: \( 6\frac{2}{6} \). Simplify the fraction part first (optional, but we can also just use the formula). \( a = 6 \), \( b = 2 \), \( c = 6 \). \( 6 \times 6 + 2 = 36 + 2 = 38 \). So \( \frac{38}{6} \), which can be simplified to \( \frac{19}{3} \), but the question just asks for improper fraction, so \( \frac{38}{6} \) (or simplified).

Step7: Sixth problem: \( 7\frac{3}{8} \). \( a = 7 \), \( b = 3 \), \( c = 8 \). \( 7 \times 8 + 3 = 56 + 3 = 59 \). Improper fraction: \( \frac{59}{8} \).

Step8: Seventh problem: \( 6\frac{2}{5} \). \( a = 6 \), \( b = 2 \), \( c = 5 \). \( 6 \times 5 + 2 = 30 + 2 = 32 \). Improper fraction: \( \frac{32}{5} \).

Step9: Eighth problem: \( 4\frac{9}{12} \). Simplify \( \frac{9}{12} \) to \( \frac{3}{4} \) (optional), but using the formula: \( a = 4 \), \( b = 9 \), \( c = 12 \). \( 4 \times 12 + 9 = 48 + 9 = 57 \). So \( \frac{57}{12} \), which simplifies to \( \frac{19}{4} \), but improper fraction is \( \frac{57}{12} \) (or simplified).

Step10: Ninth problem: \( 6\frac{7}{10} \). \( a = 6 \), \( b = 7 \), \( c = 10 \). \( 6 \times 10 + 7 = 60 + 7 = 67 \). Improper fraction: \( \frac{67}{10} \).

Step11: Tenth problem: \( 5\frac{4}{7} \). \( a = 5 \), \( b = 4 \), \( c = 7 \). \( 5 \times 7 + 4 = 35 + 4 = 39 \). Improper fraction: \( \frac{39}{7} \).

Answer:

s (for each problem in order):

1. \( \frac{16}{3} \)
2. \( \frac{22}{5} \)
3. \( \frac{13}{2} \)
4. \( \frac{31}{4} \)
5. \( \frac{38}{6} \) (or \( \frac{19}{3} \))
6. \( \frac{59}{8} \)
7. \( \frac{32}{5} \)
8. \( \frac{57}{12} \) (or \( \frac{19}{4} \))
9. \( \frac{67}{10} \)
10. \( \frac{39}{7} \)