Multiplication and Division Equations with Decimals

Honors Math – Grade 6

Problem of the Day

Carl and his friends made a paper-clip chain 8.05 km long. 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?

What are the important facts?

Write an equation to show the original depth. Define a variable first!

Let’s take a closer look…

KEY CONCEPT Solving Multiplication EquationsRECALL: To solve a multiplication equation, we use the inverse operation—division. This is known as The Division Property of Equality.

The length of the world’s-record chain is 4 times greater than Carl’s chain.

Solve each equation.

Do not forget the rules for dividing signed decimals…quotient of like signs is positive, quotient of unlike signs is negative.Do not forget the rules for dividing signed decimals…quotient of like signs is positive, quotient of unlike signs is negative.

Solve each equation.

Do not forget the rules for dividing signed decimals…quotient of like signs is positive, quotient of unlike signs is negative.Do not forget the rules for dividing signed decimals…quotient of like signs is positive, quotient of unlike signs is negative.

Solve each equation.

Do not forget the rules for dividing signed decimals…quotient of like signs is positive, quotient of unlike signs is negative.Do not forget the rules for dividing signed decimals…quotient of like signs is positive, quotient of unlike signs is negative.

KEY CONCEPT Solving Division Equations

RECALL: To solve a division equation, we use the inverse operation—multiplication. This is known as The Multiplication Property of Equality.

Do not forget the rules for multiplying signed decimals…product of like signs is positive; product of unlike signs is negative!Do not forget the rules for multiplying signed decimals…product of like signs is positive; product of unlike signs is negative!

Solve each equation.

Do not forget the rules for multiplying signed decimals…product of like signs is positive; product of unlike signs is negative!Do not forget the rules for multiplying signed decimals…product of like signs is positive; product of unlike signs is negative!

Solve each equation.

Do not forget the rules for multiplying signed decimals…product of like signs is positive; product of unlike signs is negative!Do not forget the rules for multiplying signed decimals…product of like signs is positive; product of unlike signs is negative!

Do not forget the rules for multiplying signed decimals…product of like signs is positive; product of unlike signs is negative!Do not forget the rules for multiplying signed decimals…product of like signs is positive; product of unlike signs is negative!

KEY CONCEPT Combining Like Algebraic Terms

Sometimes you need to combine like terms before solving an equation. To combine like algebraic terms, add or subtract the coefficients.

Solve each equation.

First combine like terms then solve the equation using inverse operations.First combine like terms then solve the equation using inverse operations.