1. Find `3 1/2 + 1 3/4`
Solution:
`=3 (1)/(2) + 1 (3)/(4)`
Method-1: Solution by separating whole parts and fraction parts
`=3(1)/(2)+ 1(3)/(4)`
Combine whole parts and fraction parts together
`=(3 + 1)+((1)/(2)+(3)/(4))`
`=4+((1)/(2)+(3)/(4))`
Here, LCM of 2 and 4 is 4. Convert each fractions into like fractions. So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
`=4+(1xx2)/(2xx2)+(3xx1)/(4xx1)`
`=4+(2)/(4)+(3)/(4)`
`=4+(2 + 3)/(4)`
`=4+(5)/(4)`
`=4 + 1(1)/(4)`
`=5 (1)/(4)`
2. Find `2 3/4 + 1 5/6`
Solution:
`=2 (3)/(4) + 1 (5)/(6)`
Method-1: Solution by separating whole parts and fraction parts
`=2(3)/(4)+ 1(5)/(6)`
Combine whole parts and fraction parts together
`=(2 + 1)+((3)/(4)+(5)/(6))`
`=3+((3)/(4)+(5)/(6))`
Here, LCM of 4 and 6 is 12. Convert each fractions into like fractions. So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
`=3+(3xx3)/(4xx3)+(5xx2)/(6xx2)`
`=3+(9)/(12)+(10)/(12)`
`=3+(9 + 10)/(12)`
`=3+(19)/(12)`
`=3 + 1(7)/(12)`
`=4 (7)/(12)`
3. Find `2 3/4 + 1 1/4`
Solution:
`=2 (3)/(4) + 1 (1)/(4)`
Method-1: Solution by separating whole parts and fraction parts
`=2(3)/(4)+ 1(1)/(4)`
Combine whole parts and fraction parts together
`=(2 + 1)+((3)/(4)+(1)/(4))`
`=3+((3)/(4)+(1)/(4))`
`=3+(4)/(4)`
`=3 + 1`
`=4 `
4. Find `1 3/4 + 3/4`
Solution:
`=1 (3)/(4) + (3)/(4)`
Method-1: Solution by separating whole parts and fraction parts
`=1(3)/(4)+ 0(3)/(4)`
Combine whole parts and fraction parts together
`=(1 + 0)+((3)/(4)+(3)/(4))`
`=1+((3)/(4)+(3)/(4))`
`=1+(6)/(4)`
`=1+(3)/(2)`
`=1 + 1(1)/(2)`
`=2 1/2`
This material is intended as a summary. Use your textbook for detail explanation.
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