 ## Grade 5 Math: Applications with Fractions and Decimals

### Applications: Fractions – All Operations

In earlier lessons, students have learned systematic strategies for solving application problems based on a single operation of addition, subtraction, multiplication or division with fractions. These strategies were taught in the context of and applied to three general types of scenarios for addition and subtraction problems: 1) combination situations in which two numbers representing separate groups or measures were either combined or separated, 2) comparison situations in which two numbers representing separate groups or measures were compared to find either the larger or the smaller number, and 3) increase/decrease situations (also referred to as “change” situations), and two types of situations for multiplication and division problems: 1) “fraction of” problems and 2) “times as many” problems. Within each category, the strategies allow students to determine which operation is needed to solve the problem - addition, subtraction, multiplication, or division.

In this lesson, students gain additional proficiency in solving these problems by solving a mixture of these problems that includes all four operations and all five types of situations.

### Applications: Decimals – All Operations

In the prior lesson, students learn to solve a mixture of application problems that require a single operation – either addition, subtraction, multiplication, or division – when one or more of the numbers required to solve the problem were fractions.

In this lesson, students extend what they have learned about solving problems of these types to solve similar problems in which one or more of the numbers are decimals.

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