Describe Relationship Between Expressions with Fractions and Decimals

This lesson explains how to describe relationships between expressions with fractions or decimals using multiplication and division. It addresses common misunderstandings, such as the belief that multiplication always results in a larger number and division always results in a smaller number. Through examples, it demonstrates that multiplying by a fraction can yield a smaller result, while dividing by a fraction can yield a larger result. The lesson also covers comparing expressions without actual calculation by understanding the effects of multiplying or dividing by fractions.

What is a common misunderstanding about multiplication?

• It always results in a smaller number.

• It always results in a larger number.

• It has no effect on the number.

• It always results in a negative number.

If you multiply a number by a fraction less than one, what happens to the number?

• It becomes smaller.

• It remains the same.

• It becomes larger.

• It becomes negative.

What happens when you divide a number by a fraction less than one?

• The result is smaller.

• The result is negative.

• The result is larger.

• The result is the same.

How does multiplying by 1/2 compare to multiplying by 1?

• It makes the expression negative.

• It makes the expression the same size.

• It makes the expression half as large.

• It makes the expression twice as large.

What is the effect of dividing by 1/3 compared to dividing by 1?

• It makes the expression negative.

• It makes the expression three times smaller.

• It makes the expression three times larger.

• It makes the expression the same size.