**Arkansas Curriculum Frameworks**. 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

AR.Math.Content.7.NS. The Number System

AR.Math.Content.7.NS.A. Apply and extend previous understandings of operations with fractions.

AR.Math.Content.7.NS.A.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

AR.Math.Content.7.NS.A.1.B. Understand p + q as a number where p is the starting point and q represents a distance from p in the positive or negative direction depending on whether q is positive or negative.

AR.Math.Content.7.NS.A.1.C. Interpret sums of rational numbers by describing real-world contexts (e.g., 3 + 2 means beginning at 3, move 2 units to the right and end at the sum of 5. 3 + (-2) means beginning at 3, move 2 units to the left and end at the sum of 1. 70 + (-30) = 40 could mean after earning $70, $30 was spent on a new video game, leaving a balance of $40.).

AR.Math.Content.7.NS.A.1.D. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q).

AR.Math.Content.7.NS.A.1.E. Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in real-world contexts. (e.g., The distance between -5 and 6 is 11. -5 and 6 are 11 units apart on the number line.)

AR.Math.Content.7.NS.A.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

AR.Math.Content.7.NS.A.2.A. Understand that multiplication is extended from fractions to all rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, and the rules for multiplying signed numbers.

AR.Math.Content.7.NS.A.2.B. Interpret products of rational numbers by describing real-world contexts.

AR.Math.Content.7.NS.A.2.D. Interpret quotients of rational numbers by describing real-world contexts.

AR.Math.Content.7.NS.A.2.E. Fluently multiply and divide rational numbers by applying properties of operations as strategies.

AR.Math.Content.7.EE. Expressions and Equations

AR.Math.Content.7.EE.B. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

AR.Math.Content.7.EE.B.3. Solve multi-step, real-life, and mathematical problems posed with positive and negative rational numbers in any form using tools strategically. Apply properties of operations to calculate with numbers in any form (e.g., -(1/4)(n-4)). Convert between forms as appropriate (e.g., 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.). Assess the reasonableness of answers using mental computation and estimation strategies (e.g., If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.).

AR.Math.Content.7.EE.B.4. Use variables to represent quantities in a real-world or mathematical problem. Construct simple equations and inequalities to solve problems by reasoning about the quantities.

AR.Math.Content.7.EE.B.4.A. Solve word problems leading to equations of these forms px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently.

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