Mixed Numbers

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

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

Converting Improper Fractions to Mixed Numbers

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator. For example:

7/2 = 3 1/2 (7 ÷ 2 = 3 with a remainder of 1)

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, then add the numerator. Place the result over the original denominator. For example:

4 2/3 = (4 × 3) + 2 / 3 = 14/3

Adding and Subtracting Mixed Numbers

When adding or subtracting mixed numbers, first convert them to improper fractions, perform the operation, and then convert the result back to a mixed number if needed.

Multiplying and Dividing Mixed Numbers

When multiplying mixed numbers, convert them to improper fractions, multiply the numerators and denominators, then simplify the result. When dividing mixed numbers, convert them to improper fractions, then multiply by the reciprocal of the divisor.

Practice Questions

Convert the improper fraction 11/4 to a mixed number.
Convert the mixed number 5 1/3 to an improper fraction.
Add the mixed numbers 2 2/5 and 3 3/4.
Subtract the mixed numbers 7 1/2 and 4 3/8.
Multiply the mixed numbers 2 1/3 and 3 1/4.
Divide the mixed number 4 1/2 by 2 1/3.

Remember to show your work and simplify your answers where possible.

◂Math Worksheets and Study Guides Fifth Grade. Multiplication

Vocabulary/Answer key

Multiplication

The resources above cover the following skills:

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.

Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Connections to the Grade 5 Focal Points (NCTM)

Number and Operations: Building on their work in grade 4, students extend their understanding of place value to numbers through millions and millionths in various contexts. They apply what they know about multiplication of whole numbers to larger numbers. Students also explore contexts that they can describe with negative numbers (e.g., situations of owing money or measuring elevations above and below sea level).