Exercise 53 Page 98

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

6 23

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side of the equation and all of the constant terms on the other side using the Properties of Equality. In this case, the variable term is already on the left-hand side of the equation, so we will start by subtracting 415 from both sides.

a/20+4/15=9/15

SubEqn

LHS-4/15=RHS-4/15

a/20+4/15-4/15=9/15-4/15

SubFrac

Subtract fractions

a/20+4/15-4/15=9-4/15

SubTerms

Subtract terms

a/20=5/15

ReduceFrac

a/b=.a /5./.b /5.

a/20=1/3

Now that we have isolated the variable term on the left-hand side, we can continue solving the equation by multiplying both sides by 20.

a/20=1/3

MultEqn

LHS * 20=RHS* 20

a/20*20=1/3*20

FracMultDenomToNumber

a/20* 20 = a

a=1/3*20

MoveRightFacToNum

a/c* b = a* b/c

a=20/3

Since 20 and 3 share no common factors, this is as simplified as this fraction can be. The solution to the equation is a= 203. Although it is a perfectly valid solution, we can also rewrite it as a mixed number.

a=20/3

WriteSum

Write as a sum

a=18+2/3

WriteSumFrac

Write as a sum of fractions

a=18/3+2/3

CalcQuot

Calculate quotient

a=6+2/3

Rewrite

Rewrite 6+2/3 as 6 23