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Envision Math 2.0: Grade 6, Volume 1

EM

Envision Math 2.0: Grade 6, Volume 1 View details

5. Write and Solve Equations with Rational Numbers

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Exercise 19 Page 206

Use the Subtraction Property of Equality isolate m on the right-hand side of the equation.

m=194/45 or m=4 1445

Practice makes perfect

To solve the equation, we can start by rewriting the mixed number as fraction.

7 19=2 45+m

a bc=a* c+b/c

7 * 9 + 1/9=2 * 5 + 4/5+m

Multiply

63 + 1/9=10 + 4/5+m

Add terms

64/9=14/5+m

Now, we have to isolate m on one side. Let's use the Subtraction Property of Equality and subtract 145 from both sides of the equation.

64/9=14/5+m

LHS- 14/5=RHS- 14/5

64/9- 14/5=14/5+m- 14/5

▼

Simplify left-hand side

a/b=a * 5/b * 5

64 * 5/9 * 5-14/5=14/5+m-14/5

a/b=a * 9/b * 9

64 * 5/9 * 5-14 * 9/5 * 9=14/5+m-14/5

Multiply

320/45-126/45=14/5+m-14/5

Subtract fractions

320-126/45=14/5+m-14/5

Subtract terms

194/45=14/5+m-14/5

▼

Simplify right-hand side

CommutativePropAdd

Commutative Property of Addition

194/45=m+14/5-14/5

Subtract fractions

194/45=m+14-14/5

Subtract terms

194/45=m+0/5

0/a=0

194/45=m+0

Identity Property of Addition

194/45=m

Rearrange equation

m=194/45

The value of m is 19445. We can also write our solution as a mixed number.

m=194/45

Rewrite 194 as 180+14

m=180+14/45

Write as a difference of fractions

m=180/45+14/45

Calculate quotient

m=4+14/45

Add terms

m=4 1445

Subchapter links

Do You Understand? p.205

Do You Know How? p.205

Assessment Practice p.208