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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 14 Page 205

Use the Subtraction Property of Equality to isolate z on the left-hand side of the equation.

z=11/12

Practice makes perfect

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

1 34+z=2 23

a bc=a* c+b/c

1 * 4 + 3/4+z=2 * 3 + 2/3

Identity Property of Multiplication

4 + 3/4+z=2 * 3 + 2/3

Multiply

4 + 3/4+z=6 + 2/3

Add terms

7/4+z=8/3

Now, we have to isolate z on one side. Let's use the Subtraction Property of Equality and subtract 74 from both sides of the equation.

7/4+z=8/3

LHS- 7/4=RHS- 7/4

7/4+z- 7/4=8/3- 7/4

▼

Simplify left-hand side

CommutativePropAdd

Commutative Property of Addition

7/4-7/4+z=8/3-7/4

Subtract fractions

7-7/4+z=8/3-7/4

Subtract terms

0/4+z=8/3-7/4

0/a=0

0+z=8/3-7/4

Identity Property of Addition

z=8/3-7/4

▼

Simplify right-hand side

a/b=a * 4/b * 4

z=8 * 4/3 * 4-7/4

a/b=a * 3/b * 3

z=8 * 4/3 * 4-7 * 3/4 * 3

Multiply

z=32/12-21/12

Subtract fractions

z=32-21/12

Subtract terms

z=11/12

Subchapter links

Do You Understand? p.205

Do You Know How? p.205

Assessment Practice p.208