# 4.5 - Add & Subtract Fractions

The student will

a)  determine common multiples and factors, including least common multiple and greatest common factor;

b)  add and subtract fractions and mixed numbers having like and unlike denominators;*and

c)  solve single-step practical problems involving addition and subtraction with fractions and mixed numbers.

*On the state assessment, items measuring this objective are assessed without the use of a calculator.

### BIG IDEAS

• So that I can use factors and multiples when working with expanding, and reducing fractions as well as finding patterns in numbers

• So that I can use money as one way to use factors in everyday life.  Everyone knows that four quarters equal a dollar.  A twenty-dollar bill can be exchanged for twenty one-dollar bills (factors one and 20), two ten-dollar bills (factors two and 10) or four five-dollar bills (factors four and five)

• So that I can use addition and subtraction with decimals and fractions everyday. If I want to double a recipe, I add the fractions given in the original recipe. I can add the cost of each item I am buying in a store in order to make sure I have enough money

### UNDERSTANDING THE STANDARD

• A factor of a whole number is a whole number that divides evenly into that number with no remainder. A factor of a number is a divisor of the number.
• A common factor of two or more numbers is a divisor that all of the numbers share.
• The greatest common factor of two or more numbers is the largest of the common factors that all of the numbers share.
• The product of the number and any natural number is a multiple of the number.
• Common multiples and common factors can be useful when simplifying fractions.
• The least common multiple of two or more numbers is the lowest number that is a multiple of all of the given numbers.
• Estimation keeps the focus on the meaning of the numbers and operations, encourages reflective thinking, and helps build informal number sense with fractions.  Students can reason with benchmarks to get an estimate without using an algorithm.
• Reasonable answers to problems involving addition and subtraction of fractions can be established by using benchmarks such as 0, , and 1. For example, and are each greater than , so their sum is greater than 1.
• Students should investigate addition and subtraction with fractions, using a variety of models (e.g., fraction circles, fraction strips, lines, pattern blocks).
• While this standard requires instruction in solving problems with denominators of 2, 3, 4, 5, 6, 8, 10, and 12, students would benefit from experiences with other denominators.
• When students use the least common multiple to determine common denominators to add or subtract fractions with unlike denominators, the least common multiple may be greater than 12, but will not exceed 60.
• Proper fractions, improper fractions, and mixed numbers are terms often used to describe fractions. A proper fraction is a fraction whose numerator is less than the denominator.  An improper fraction is a fraction whose numerator is equal to or greater than the denominator.  An improper fraction may be expressed as a mixed number. A mixed number is written with two parts:  a whole number and a proper fraction (e.g., 3).
• Instruction involving addition and subtraction of fractions should include experiences with proper fractions, improper fractions, and mixed numbers as addends, minuends, subtrahends, sums, and differences.
• A fraction is in simplest form when its numerator and denominator have no common factors other than one. The numerator can be greater than the denominator.
• The problem-solving process is enhanced when students create and solve their own practical problems and model problems using manipulatives and drawings.
• In problem solving, emphasis should be placed on thinking and reasoning rather than on key words. Focusing on key words such as in all, altogether, difference, etc.encourages students to perform a particular operation rather than make sense of the context of the problem. It prepares students to solve a very limited set of problems and often leads to incorrect solutions.
• At this level, denominators of fractions resulting from simplification will be limited to 12 or less.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Determine common multiples and common factors of numbers. (a)
• Determine the least common multiple and greatest common factor of no more than three numbers. (a)
• Determine a common denominator for fractions, using common multiples. Common denominators should not exceed 60. (b)
• Estimate the sum or difference of two fractions. (b, c)
• Add and subtract fractions (proper or improper) and/or mixed numbers, having like and unlike denominators limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction. (Subtraction with fractions will be limited to problems that do not require regrouping). (b)
• Solve single-step practical problems that involve addition and subtraction with fractions (proper or improper) and/or mixed numbers, having like and unlike denominators limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fraction. (Subtraction with fractions will be limited to problems that do not require regrouping). (c)

### KEY VOCABULARY

Updated: Aug 22, 2018