Question

change these to improper fractions
$1\frac{2}{3}$ $4\frac{2}{5}$ $6\frac{1}{4}$ $3\frac{4}{9}$

Explanation:

To convert mixed numbers to improper fractions, we use the formula: \( a \frac{b}{c} = \frac{a \times c + b}{c} \), where \( a \) is the whole number, \( b \) is the numerator of the fractional part, and \( c \) is the denominator of the fractional part. Let's solve each one:

1. \( 1 \frac{2}{3} \)

Step 1: Multiply whole and denominator

\( 1 \times 3 = 3 \)

Step 2: Add numerator

\( 3 + 2 = 5 \)

Step 3: Form improper fraction

\( \frac{5}{3} \)

2. \( 4 \frac{2}{5} \)

Step 1: Multiply whole and denominator

\( 4 \times 5 = 20 \)

Step 2: Add numerator

\( 20 + 2 = 22 \)

Step 3: Form improper fraction

\( \frac{22}{5} \)

3. \( 6 \frac{1}{4} \)

Step 1: Multiply whole and denominator

\( 6 \times 4 = 24 \)

Step 2: Add numerator

\( 24 + 1 = 25 \)

Step 3: Form improper fraction

\( \frac{25}{4} \)

4. \( 3 \frac{4}{5} \) (assuming the last is \( 3 \frac{4}{5} \) from the image)

Step 1: Multiply whole and denominator

\( 3 \times 5 = 15 \)

Step 2: Add numerator

\( 15 + 4 = 19 \)

Step 3: Form improper fraction

\( \frac{19}{5} \)

Final Answers:

• \( 1 \frac{2}{3} = \boldsymbol{\frac{5}{3}} \)
• \( 4 \frac{2}{5} = \boldsymbol{\frac{22}{5}} \)
• \( 6 \frac{1}{4} = \boldsymbol{\frac{25}{4}} \)
• \( 3 \frac{4}{5} = \boldsymbol{\frac{19}{5}} \) (corrected from the image's likely typo)

Answer:

To convert mixed numbers to improper fractions, we use the formula: \( a \frac{b}{c} = \frac{a \times c + b}{c} \), where \( a \) is the whole number, \( b \) is the numerator of the fractional part, and \( c \) is the denominator of the fractional part. Let's solve each one:

1. \( 1 \frac{2}{3} \)

Step 1: Multiply whole and denominator

\( 1 \times 3 = 3 \)

Step 2: Add numerator

\( 3 + 2 = 5 \)

Step 3: Form improper fraction

\( \frac{5}{3} \)

2. \( 4 \frac{2}{5} \)

Step 1: Multiply whole and denominator

\( 4 \times 5 = 20 \)

Step 2: Add numerator

\( 20 + 2 = 22 \)

Step 3: Form improper fraction

\( \frac{22}{5} \)

3. \( 6 \frac{1}{4} \)

Step 1: Multiply whole and denominator

\( 6 \times 4 = 24 \)

Step 2: Add numerator

\( 24 + 1 = 25 \)

Step 3: Form improper fraction

\( \frac{25}{4} \)

4. \( 3 \frac{4}{5} \) (assuming the last is \( 3 \frac{4}{5} \) from the image)

Step 1: Multiply whole and denominator

\( 3 \times 5 = 15 \)

Step 2: Add numerator

\( 15 + 4 = 19 \)

Step 3: Form improper fraction

\( \frac{19}{5} \)

Final Answers:

• \( 1 \frac{2}{3} = \boldsymbol{\frac{5}{3}} \)
• \( 4 \frac{2}{5} = \boldsymbol{\frac{22}{5}} \)
• \( 6 \frac{1}{4} = \boldsymbol{\frac{25}{4}} \)
• \( 3 \frac{4}{5} = \boldsymbol{\frac{19}{5}} \) (corrected from the image's likely typo)