Conversion Between Improper Fractions and Mixed Numbers

Steps to Convert an Improper Fraction to a Mixed Number:
1. Divide the numerator by the denominator.
Example: 8 ÷ 5 = 1 with remainder 3

2. Write the quotient as the whole number.
Quotient = 1

3. Write the remainder as the numerator of the fraction.
Remainder = 3

4. Keep the same denominator.
Denominator = 5

5. Final Answer:
`"8"/"5"`= 1`"3"/"5"`Example: If 7 apples are divided equally between 2 people, how many will each one get?
`"7"/"2"` = 7 ÷ 2

     3
`2")"overline(    7    )`
–   6     
     1
(Where , 2 = Divisor, 7 = Dividend, 3 = Quotient, 1 = Remainder)

`"7"/"2"` =3`"1"/"2"`
Each will get 3 full apples and `"1"/"2"`  an apple.

Steps to Convert a Mixed Number into an Improper Fraction:

1. Start with the mixed number.
Example: 2`"3"/"5"`​

2. Multiply the whole number by the denominator.
2 × 5 = 10

3. Add the numerator to the product.
10 + 3 = 13

4. Keep the same denominator.
Denominator = 5

5. Write the improper fraction.
Final answer: `"13"/"5"`

Example:  3 `"2"/"5"` is a mixed number. Convert this into an improper fraction.
3 `"2"/"5"` = 3 + `"2"/"5"` = `"3"/"1"` + `"2"/"5"` = `"3 × 5"/"1 × 5"` + `"2"/"5"`=`"3 × 5 + 2" / "5"` = `"15+ 2 "/"5" ` = `"17"/"5"`