Step-by-step explanation:

To simplify the expression 4 ⅓ : 3 ½, we need to convert the mixed numbers into improper fractions and then perform the division.

4 ⅓ can be written as an improper fraction as follows:

4 ⅓ = (4 * 3 + 1) / 3 = 13 / 3

Similarly, 3 ½ can be written as an improper fraction as follows:

3 ½ = (3 * 2 + 1) / 2 = 7 / 2

Now, we can perform the division of the fractions:

(13 / 3) / (7 / 2) = (13 / 3) * (2 / 7)

To multiply fractions, we multiply the numerators together and the denominators together:

(13 * 2) / (3 * 7) = 26 / 21

Therefore, the simplified form of 4 ⅓ : 3 ½ is 26/21.

4 ⅓ : 3 ½.

= [tex]\frac{13}{3} : \frac{7}{2}[/tex]

Now multiply the ratio by the LCM of the denominators 3 and 2, that is 6.

The ratio becomes [tex]13 \times 2: 7 \times 3[/tex]

= 26 : 21.

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