Question

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improper fractions
convert the mixed numbers into improper fractions
2)
$4 \frac{2}{5} = $
4)
$7 \frac{3}{4} = $
6)
$7 \frac{3}{8} = $
8)
$4 \frac{9}{12} = $
10)
$5 \frac{4}{7} = $

Explanation:

Step1: Recall the formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction. The formula is \( a\frac{b}{c}=\frac{a\times c + b}{c} \).

Step2: Solve for \( 4\frac{3}{5} \) (problem 2).

Using the formula, \( a = 4 \), \( b = 3 \), \( c = 5 \).
So, \( 4\times5 + 3 = 20 + 3 = 23 \).
Thus, \( 4\frac{3}{5}=\frac{23}{5} \).

Step3: Solve for \( 7\frac{3}{4} \) (problem 4).

Here, \( a = 7 \), \( b = 3 \), \( c = 4 \).
\( 7\times4 + 3 = 28 + 3 = 31 \).
So, \( 7\frac{3}{4}=\frac{31}{4} \).

Step4: Solve for \( 7\frac{3}{8} \) (problem 6).

For this, \( a = 7 \), \( b = 3 \), \( c = 8 \).
\( 7\times8 + 3 = 56 + 3 = 59 \).
Thus, \( 7\frac{3}{8}=\frac{59}{8} \).

Step5: Solve for \( 4\frac{9}{12} \) (problem 8).

Simplify the fraction first (optional, but can make calculation easier). \( \frac{9}{12}=\frac{3}{4} \), but we can also use the formula directly. \( a = 4 \), \( b = 9 \), \( c = 12 \).
\( 4\times12 + 9 = 48 + 9 = 57 \).
So, \( 4\frac{9}{12}=\frac{57}{12}=\frac{19}{4} \) (after simplifying by dividing numerator and denominator by 3).

Step6: Solve for \( 5\frac{4}{7} \) (problem 10).

Using the formula, \( a = 5 \), \( b = 4 \), \( c = 7 \).
\( 5\times7 + 4 = 35 + 4 = 39 \).
Thus, \( 5\frac{4}{7}=\frac{39}{7} \).

Answer:

s (for each problem):

1. \( \frac{23}{5} \)
2. \( \frac{31}{4} \)
3. \( \frac{59}{8} \)
4. \( \frac{19}{4} \) (or \( \frac{57}{12} \))
5. \( \frac{39}{7} \)