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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 22 Page 206

Use the Addition Property of Equality to isolate k on the left-hand side of the equation.

k=629/56 or k=11 1356

Practice makes perfect

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

k-6 38=4 67

a bc=a* c+b/c

k-6 * 8+ 3/8=4 * 7+6/7

Multiply

k-48+3/8=28+6/7

Add terms

k-51/8=34/7

Now, we have to isolate k on one side. Let's use the Addition Property of Equality and add 518 to both sides of the equation.

k-51/8=34/7

LHS+ 51/8=RHS+ 51/8

k-51/8+ 51/8=34/7+ 51/8

▼

Simplify left-hand side

CommutativePropAdd

Commutative Property of Addition

k+51/8-51/8=34/7+51/8

Subtract fractions

k+51-51/8=34/7+51/8

Subtract terms

k+0/8=34/7+51/8

0/a=0

k+0=34/7+51/8

Identity Property of Addition

k=34/7+51/8

▼

Simplify right-hand side

a/b=a * 8/b * 8

k=34 * 8/7 * 8+51/8

a/b=a * 7/b * 7

k=34 * 8/7 * 8+51 * 7/8 * 7

Multiply

k=272/56+357/56

Add fractions

k=272+357/56

Subtract terms

k=629/56

The value of k is 62956. We can also write our solution as a mixed number.

k=629/56

Rewrite 629 as 616+13

k=616+13/56

Write as a difference of fractions

k=616/56+13/56

Calculate quotient

k=11+13/56

Add terms

k=11 1356

Subchapter links

Do You Understand? p.205

Do You Know How? p.205

Assessment Practice p.208