**Kansas Academic Education Standards**. Fraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. Read More...

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Study GuideFraction OperationsWorksheet/Answer key

Fraction OperationsWorksheet/Answer key

Fraction OperationsWorksheet/Answer key

Fraction Operations

KS.7.NS. The Number System

Apply and extend previous understandings of operations with positive rational numbers to add, subtract, multiply, and divide all rational numbers.

7.NS.1. Represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.1b. Show p + q as the number located a distance |ݑ| from p, in the positive or negative direction depending on whether q is positive or negative.

7.NS.1c. Model subtraction of rational numbers as adding the additive inverse, p − ݑ=p + (ޢȒݑ).

7.NS.1d. Model subtraction as the distance between two rational numbers on the number line where the distance is the absolute value of their difference.

7.NS.1e. Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2. Apply and extend previous understandings of multiplication and division of positive rational numbers to multiply and divide all rational numbers.

7.NS.2a. Describe how multiplication is extended from positive rational numbers to all rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (−1)(−1) = 1 and the rules for multiplying signed numbers.

7.NS.2c. Apply properties of operations as strategies to multiply and divide rational numbers.

7.NS.3. Solve and interpret real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

KS.7.EE. Expressions and Equations

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

7.EE.3. Solve multi-step real-life and mathematical problems with rational numbers. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50.

7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct two-step equations and inequalities to solve problems by reasoning about the quantities.

7.EE.4a. Solve word problems leading to equations of the form pݑ+Űݑ =r, and p(ްݑ +Űݑ)=r where p, q, and r are specific rational numbers. Solve equations of these forms fluently (efficiently, accurately, and flexibly). Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Standards