What is a Mixed Number?

A mixed number is a combination of a whole number and a proper fraction. It is written in the form:

Whole Number + Fraction

For example, 3 1/2 is a mixed number, where 3 is the whole number and 1/2 is the fraction.

Converting Improper Fractions to Mixed Numbers

To convert an improper fraction to a mixed number, follow these steps:

Divide the numerator by the denominator. The quotient is the whole number part of the mixed number.
The remainder becomes the new numerator of the fraction part, with the same denominator.

For example, to convert 7/2 to a mixed number:

7 ÷ 2 = 3 with a remainder of 1

So, 7/2 = 3 1/2

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, follow these steps:

Multiply the whole number by the denominator of the fraction, and then add the numerator.
Write the result as the new numerator over the original denominator.

For example, to convert 4 2/3 to an improper fraction:

4 x 3 + 2 = 12 + 2 = 14

So, 4 2/3 = 14/3

Practice Problems

1. Convert the following improper fraction to a mixed number: 11/4

2. Convert the following mixed number to an improper fraction: 5 1/2

3. Convert the following improper fraction to a mixed number: 9/2

4. Convert the following mixed number to an improper fraction: 3 3/4

5. Convert the following improper fraction to a mixed number: 17/5

6. Convert the following mixed number to an improper fraction: 6 2/3

Answers

1. To convert 11/4 to a mixed number:

11 ÷ 4 = 2 with a remainder of 3

So, 11/4 = 2 3/4

2. To convert 5 1/2 to an improper fraction:

5 x 2 + 1 = 10 + 1 = 11

So, 5 1/2 = 11/2

3. To convert 9/2 to a mixed number:

9 ÷ 2 = 4 with a remainder of 1

So, 9/2 = 4 1/2

4. To convert 3 3/4 to an improper fraction:

3 x 4 + 3 = 12 + 3 = 15

So, 3 3/4 = 15/4

5. To convert 17/5 to a mixed number:

17 ÷ 5 = 3 with a remainder of 2

So, 17/5 = 3 2/5

6. To convert 6 2/3 to an improper fraction:

6 x 3 + 2 = 18 + 2 = 20

So, 6 2/3 = 20/3

◂Math Worksheets and Study Guides Seventh Grade. Decimal Operations

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Work flexibly with fractions, decimals, and percents to solve problems.

Develop meaning for integers and represent and compare quantities with them.

Understand meanings of operations and how they relate to one another.

Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

Compute fluently and make reasonable estimates.

Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.

Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.