The sum of ( [tex]\frac{2}{5}[/tex] x + [tex]\frac{5}{8}[/tex] ) + ( [tex]\frac{1}{5}[/tex] x - [tex]\frac{1}{4}[/tex] ) is [tex]\frac{3}{5}[/tex] x + [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
To add or subtract 2 fractions, they must have same denominators, if they not do that
- Find the Lowest common multiple of the two denominators (LCM)
- Replace each denominator by it
- Divide The LCM by each denominator and multiply the numerator of each fraction by its quotient
∵ ( [tex]\frac{2}{5}[/tex] x + [tex]\frac{5}{8}[/tex] ) + ( [tex]\frac{1}{5}[/tex] x - [tex]\frac{1}{4}[/tex] )
- Let us start with adding the like terms
∴ ( [tex]\frac{2}{5}[/tex] x + [tex]\frac{5}{8}[/tex] ) + ( [tex]\frac{1}{5}[/tex] x - [tex]\frac{1}{4}[/tex] ) = (
∵ ( [tex]\frac{2}{5}[/tex] x + [tex]\frac{1}{5}[/tex] x ) have same denominators, then we can add them
∴ ( [tex]\frac{2}{5}[/tex] x + [tex]\frac{1}{5}[/tex] x ) = [tex]\frac{3}{5}[/tex] x
∵ ( [tex]\frac{5}{8}[/tex] - [tex]\frac{1}{4}[/tex] ) do not have the same denominators, then we must find
LCM of 8 and 4
- The LCM of 8 and 4 is 8 because 8 is the first common multiple
of 8 and 4
∵ LCM of 8 and 4 is 8
- Divide 8 by the denominator 4
∵ 8 ÷ 4 = 2
- Multiply the numerator of the fraction by 2
∴ [tex]\frac{1}{4}=\frac{2}{8}[/tex]
∴ ( [tex]\frac{5}{8}[/tex] - [tex]\frac{1}{4}[/tex] ) = ( [tex]\frac{5}{8}[/tex] - [tex]\frac{2}{8}[/tex] ) = [tex]\frac{3}{8}[/tex]
∴ ( [tex]\frac{2}{5}[/tex] x + [tex]\frac{5}{8}[/tex] ) + ( [tex]\frac{1}{5}[/tex] x - [tex]\frac{1}{4}[/tex] ) = [tex]\frac{3}{5}[/tex] x + [tex]\frac{3}{8}[/tex]
The sum of ( [tex]\frac{2}{5}[/tex] x + [tex]\frac{5}{8}[/tex] ) + ( [tex]\frac{1}{5}[/tex] x - [tex]\frac{1}{4}[/tex] ) is [tex]\frac{3}{5}[/tex] x + [tex]\frac{3}{8}[/tex]
Learn more:
You can learn more about the fractions in brainly.com/question/2456302
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