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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 20 Page 206

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

a=71/36 or a=1 3536

Practice makes perfect

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

a+3 14=5 29

a bc=a* c+b/c

a+3 * 4+ 1/4=5 * 9+2/9

Multiply

a+12 + 1/4=45 + 2/9

Add terms

a+13/4=47/9

Now, we have to isolate a on one side. Let's use the Subtraction Property of Equality and subtract 134 from both sides of the equation.

a+13/4=47/9

LHS- 13/4=RHS- 13/4

a+13/4- 13/4=47/9- 13/4

▼

Simplify left-hand side

Subtract fractions

a+13-13/4=47/9-13/4

Subtract terms

a+0/4=47/9-13/4

0/a=0

a+0=47/9-13/4

Identity Property of Addition

a=47/9-13/4

▼

Simplify right-hand side

a/b=a * 4/b * 4

a=47 * 4/9 * 4-13/4

a/b=a * 9/b * 9

a=47 * 4/9 * 4-13 * 9/4 * 9

Multiply

a=188/36-117/36

Subtract fractions

a=188-117/36

Subtract terms

a=71/36

The value of a is 7136. We can also write our solution as a mixed number.

a=71/36

Rewrite 71 as 36+35

a=36+35/36

Write as a difference of fractions

a=36/36+35/36

Calculate quotient

a=1+35/36

Add terms

a=1 3536

Subchapter links

Do You Understand? p.205

Do You Know How? p.205

Assessment Practice p.208