6th Grade Math Textbook, Fundamentals

Remember:

Rules for Multiplying Two Decimals Rules for Dividing Two Decimals

• The product of likesigns is positive. • The quotient of likesigns is positive.
  
  
  • The product of unlikesigns is negative. • The quotient of unlikesigns is negative.
  
  
  
  

 &KDSWHU

4-13

Solve:y2.5y1. 4

(y2.5y) 1. 4 Add like terms,1y2.5y.



 Simplify.

y0.4

1. 4

3.5

35

35

1

1

.

.

y

1. 4

3.5

3.5y

3.5 Divide both sides by 3.5

to isolate y.

Check: y2.5y1. 4

0.42.5(0.4) 1. 4

0.4 (1) 1. 4

1.4 1. 4 Tr u e

Substitute

0.4 for y.

?

?

Update your skills. See pages 412 XIII, 413 XIV.

Multiplication and Division

Equations with Decimals

Objective To apply the Division Property of Equality to solve multiplication equations with

decimals • To apply the Multiplication Property of Equality to solve division equations with decimals

Carl and his friends made a paper-clip chain 8.05-km long,
an impressive achievement by any standards. The world record,
however, is 32.2 km! How many times greater than the length
of Carl’s chain is the length of the world’s-record chain?

To find how much longer the world’s-record chain is,

write a multiplication equation. Then use the Division

Property of Equality to solve the equation.

Let xthe number of times longer the world’s-record chain is.

Equation: 8.05 km • x32.2 km

Estimate: 8 x32 and 8(4) 32, so xis about 4.

Solve:8.05x32.2

 Divide both sides by 8.05 to isolate x.

Simplify.

x 4

Check:8.05x32.2

8.05(4) 32.2 Substitute 4 for x.

32.2 32.2 Tr u e

The length of the world’s-record paper-clip chain is 4 times greater than

the length of Carl’s 8.05-km chain.

Sometimes you need to combine like terms before solving a

multiplication equation.

The answer is the same as the estimate,

so the answer is reasonable.

32.2

8.05

8.05x

8.05

?

805

805

32 2

805

1

1

4

1

.

.

.

.

x

Remember:

Division Property of Equality:

If ab, then acbc, c0.