# 6.6 and *6.5 - Add, Subtract, Multiply, Divide Fractions (No Calc)

6.6  The student will

a)   multiply and divide fractions and mixed numbers;

b)  estimate solutions and then solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions.

6.5  The student will

a)  multiply and divide fractions and mixed numbers;*  (with NO CALCULATOR)

b)  solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers; and

Bloom's Level:  Remember, Understand

### BIG IDEAS

• I can adjust recipes for the number of servings needed, cut ribbon into equal portions, and determine how much wood is needed to build a dog house.
• I will be able to determine approximations in real world situations that involve fractions.

### UNDERSTANDING THE STANDARD

• Simplifying fractions to simplest form assists with uniformity of answers.
• Addition and subtraction are inverse operations as are multiplication and division.
• It is helpful to use estimation to develop computational strategies. For example, 2 7/8 • 3/4 is about of 3/4 of 3, so the answer is between 2 and 3.
• When multiplying a whole by a fraction such as  3 • 1/2 , the meaning is the same as with multiplication of whole numbers: 3 groups the size of  of 1/2 the whole.
• When multiplying a fraction by a fraction such as 2/3 • 3/4, we are asking for part of a part.
• When multiplying a fraction by a whole number such as 1/2 • 6, we are trying to find a part of the whole.

·  A fraction can be expressed in simplest form (simplest equivalent fraction) by dividing the numerator and denominator by their greatest common factor.

·  When the numerator and denominator have no common factors other than 1, then the fraction is in simplest form.

·  Addition and subtraction are inverse operations as are multiplication and division.

·  Models for representing multiplication and division of fractions may include arrays, paper folding, repeated addition, repeated subtraction, fraction strips, fraction rods, pattern blocks, and area models.

·  It is helpful to use estimation to develop computational strategies.

-  Example:   is about  of 3, so the answer is between 2 and 3.

·  When multiplying a whole number by a fraction such as   , the meaning is the same as with multiplication of whole numbers: 3 groups the size of  of the whole.

·  When multiplying a fraction by a fraction such as  , we are asking for part of a part.

·  When multiplying a fraction by a whole number such as   6, we are trying to determine a part of the whole.

·  A multistep problem is a problem that requires two or more steps to solve.

·  Different strategies can be used to estimate the result of computations and judge the reasonableness of the result.

-  Example: What is an approximate answer for 2.19 ¸ 0.8? The answer is around 2 because
2.19  0.8 is about 2 ¸ 1 = 2.

·  Understanding the placement of the decimal point is important when determining quotients of decimals. Examining patterns with successive decimals provides meaning, such as dividing the dividend by 6, by 0.6, and by 0.06.

·  Solving multistep problems in the context of practical situations enhances interconnectedness and proficiency with estimation strategies.

·  Examples of practical situations solved by using estimation strategies include shopping for groceries, buying school supplies, budgeting an allowance, and sharing the cost of a pizza or the prize money from a contest.

### ESSENTIALS

• How are multiplication and division of fractions and multiplication and division of whole numbers alike? Fraction computation can be approached in the same way as whole number computation, applying those concepts to fractional parts.
• What is the role of estimation in solving problems?  Estimation helps determine the reasonableness of answers.

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

6.6a1  Multiply and divide with fractions and mixed (No Calc) numbers. Answers are expressed in simplest form.

·  6.5a2  Multiply and divide fractions (proper or improper) and mixed numbers. Answers are expressed in simplest form.

6.6b1  Solve single‐step and multi‐step practical problems that involve addition and subtraction with fractions and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form.

·  6.5b1  Solve single-step and multistep practical problems that involve addition and subtraction with fractions (proper or improper) and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form.

6.6b2  Solve single‐step and multi‐step practical problems that involve multiplication and division with fractions and mixed numbers, with and without regrouping, that include denominators of 12 or less. Answers are expressed in simplest form.

·  6.5b2  Solve single-step and multistep practical problems that involve multiplication and division with fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.

### KEY VOCABULARY

multiplication, division, product, quotient, dividend, divisor, remainder, simplest form, fraction, mixed numbers, numerator, denominator, reciprocal, inverse operations, whole numbers, estimation, solution, reasonableness

SOME KEY WORDS FOR SOLVING WORD PROBLEMS:

Addition:  sum, how much, in all, total, how many

Subtraction:  difference, less than, how much more “er” words (i.e longer, shorter, etc…)

Multiplication:  product, in all, total,

Division:  each, equally, share, every, per

Updated: Oct 27, 2017