 ## Grade 4 Math: Operations with Fractions

This series illustrates the meaning of addition and subtraction of fractions, using fractions with the same denominator. A key feature of these lessons is that they illustrate that the operations of addition and subtraction are the same for fractions as they are for whole numbers.

### Adding and Subtracting Fractions with Pictures

Students have learned previously to write fractions represented by drawings of objects. They’ve also learned to create drawings to represent fractions.

In this lesson, they learn to add and subtract fractions with the same denominator using fractions represented with drawings.

### Adding and Subtracting Fractions: All Steps

In this lesson, students learn to add and subtraction fractions without drawings when the denominators are the same. They first write the new fraction as the sum of the original numbers, using the common denominator as the denominator of the new fraction.

They then write the final fraction by adding the terms in the numerator.

Each step is evaluated separately.

In this lesson, students add and subtract fractions with a common denominator without writing the interim steps. They write the final answer only.

### Multiplying Fractions by Whole Numbers

Earlier, students have learned to understand multiplication of whole numbers using arrays. In this lesson, students begin to learn about multiplying fractions by learning to multiply a fraction by a whole number.

The concept of multiplication of a fraction is illustrated using arrays like those used earlier for whole numbers. This begins the extension of the student’s understanding of the multiplication of whole numbers to the understanding of the multiplication of fractions. This same approach is later extended to understanding the multiplication of a fraction by a fraction.

The concepts involved in multiplying a fraction by a whole number using arrays are used to explain the rationale for the standard algorithm for multiplying a fraction by a whole number, and later, multiplying a fraction by a fraction.

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