1. Find Mixed Number to Improper Fraction of `1 2/3`

Solution:
Method-1:
`1 (2)/(3)=((1 xx 3)+2)/3=(3+2)/3=5/3`

---

Method-2:
`1 (2)/(3)`

Step-1 : Multiply the denominator(3) by the whole number(1)
`3 xx 1=3`

Step-2 : Add the product(3) to the numerator(2)
`3+2=5`

Step-3 :Write the sum(5) over the denominator(3)
`5/3`

So, `1 (2)/(3)=5/3`

---

Method-3:
`1 (2)/(3)`

Step-1 : Multiply the whole number(1) by the denominator(3)
`(1 xx 3+"[ ]")/("[ ]")`

Step-2 : Simplify
`(3+"[ ]")/("[ ]")`

Step-3 : Add the product(3) to the numerator(2)
`(3+2)/("[ ]")`

Step-4 : Simplify
`(5)/("[ ]")`

Step-5 : Write the sum(5) over the denominator(3)
`5/3`

So, `1 (2)/(3)=5/3`

---

2. Find Mixed Number to Improper Fraction of `2 3/4`

Solution:
Method-1:
`2 (3)/(4)=((2 xx 4)+3)/4=(8+3)/4=11/4`

---

Method-2:
`2 (3)/(4)`

Step-1 : Multiply the denominator(4) by the whole number(2)
`4 xx 2=8`

Step-2 : Add the product(8) to the numerator(3)
`8+3=11`

Step-3 :Write the sum(11) over the denominator(4)
`11/4`

So, `2 (3)/(4)=11/4`

---

Method-3:
`2 (3)/(4)`

Step-1 : Multiply the whole number(2) by the denominator(4)
`(2 xx 4+"[ ]")/("[ ]")`

Step-2 : Simplify
`(8+"[ ]")/("[ ]")`

Step-3 : Add the product(8) to the numerator(3)
`(8+3)/("[ ]")`

Step-4 : Simplify
`(11)/("[ ]")`

Step-5 : Write the sum(11) over the denominator(4)
`11/4`

So, `2 (3)/(4)=11/4`

---

3. Find Mixed Number to Improper Fraction of `3 4/5`

Solution:
Method-1:
`3 (4)/(5)=((3 xx 5)+4)/5=(15+4)/5=19/5`

---

Method-2:
`3 (4)/(5)`

Step-1 : Multiply the denominator(5) by the whole number(3)
`5 xx 3=15`

Step-2 : Add the product(15) to the numerator(4)
`15+4=19`

Step-3 :Write the sum(19) over the denominator(5)
`19/5`

So, `3 (4)/(5)=19/5`

---

Method-3:
`3 (4)/(5)`

Step-1 : Multiply the whole number(3) by the denominator(5)
`(3 xx 5+"[ ]")/("[ ]")`

Step-2 : Simplify
`(15+"[ ]")/("[ ]")`

Step-3 : Add the product(15) to the numerator(4)
`(15+4)/("[ ]")`

Step-4 : Simplify
`(19)/("[ ]")`

Step-5 : Write the sum(19) over the denominator(5)
`19/5`

So, `3 (4)/(5)=19/5`

---

4. Find Mixed Number to Improper Fraction of `1 2/7`

Solution:
Method-1:
`1 (2)/(7)=((1 xx 7)+2)/7=(7+2)/7=9/7`

---

Method-2:
`1 (2)/(7)`

Step-1 : Multiply the denominator(7) by the whole number(1)
`7 xx 1=7`

Step-2 : Add the product(7) to the numerator(2)
`7+2=9`

Step-3 :Write the sum(9) over the denominator(7)
`9/7`

So, `1 (2)/(7)=9/7`

---

Method-3:
`1 (2)/(7)`

Step-1 : Multiply the whole number(1) by the denominator(7)
`(1 xx 7+"[ ]")/("[ ]")`

Step-2 : Simplify
`(7+"[ ]")/("[ ]")`

Step-3 : Add the product(7) to the numerator(2)
`(7+2)/("[ ]")`

Step-4 : Simplify
`(9)/("[ ]")`

Step-5 : Write the sum(9) over the denominator(7)
`9/7`

So, `1 (2)/(7)=9/7`

---