Unit 2 Fraction Operations Pre-Alg.

1. Name two fractions equivalent to 3/4 Unit 2: Fractions! 9/20 DCN # 150 Bell Ringer Concept Builder: Review strategies for adding and subtracting fractions and mixed numbers. Direct Instruction or Explorations: Notes on fraction/mixed number +/- Practice Independent Work/hw: Worksheet Assessment: Teacher obs. Bellringer 1. Name two fractions equivalent to 3/4 Write in standard form 5.06 x 10-7 3. Volume = ____ 2. 0.000000506 3.2 ” 5.1” 4” 3. 65.28 in3

Review of fractions- What is a fraction? We all learned that a fraction was part of a whole. That’s true but fractions are also- A ratio of two numbers An incomplete division problem A way to compare two numbers If one slice is eaten what remains? 1 2 2/3 ? 3

52 2/3 2/12 Both have the digit 2 but the 2 has a different different value here. 52 Both have the digit 2 but the 2 has a different value in 27 than in 52. It’s place value is larger! 2/3 2/12 Would you rather have 2/3 of a pizza or 2/12? Both numbers have a 2 in them! The 2 has a different value here as well! A new way to think about fractions Numerator Digit Denominator Place Value

If you still eat 1/3 of the pizza, what is left on Eating an equal amount of the same size of pizza sliced into 12 pieces. If you still eat 1/3 of the pizza, what is left on the 12 slice pizza? How many smaller slices? 3 Slices 12 Slices 8 2 = ? 3 12 2 x 4 = 3 x 4 12

Two thirds of seventh graders write with Same problem worded differently…. Two thirds of seventh graders write with mechanical pencils. If we select 12 seventh graders at random, how many would prefer to write with a mechanical pencil? 8 2 = ? 3 12 2 x 4 = 3 x 4 12

2 12 21 Adding and subtracting fractions and mixed numbers Find a common denominator + 2. Add the fraction and whole numbers. 3. Reduce your answer 2 12 21

2 3 5 Renaming in subtraction Borrow from the whole number. 7 Borrow from the whole number. Add the denominator to the numerator to make the new numerator. Subtract. 3 2 5

2. Write in scientific notation 304000000 Multiplying Fractions 9/21 DCN # 149 Bell Ringer Concept Builder: Review strategies numbers. for multiplying fractions Direct Instruction or Explorations: Check HW Round Robin problems Independent Work/hw: Assessment: Teacher obs. Bellringer 1. 8 2/5 – 5 5/7 = 2. Write in scientific notation 304000000 3. Compare √ 34 _____ 650% 1. 2 24/35 2. 3.04 x 108 3. <

Multiplying with numbers greater than 1 result in products larger than their factors. For example- Think “3 sets of 4 equals 12 ” X = OF Multiplying with fractions less than 1 result in products smaller than one or more of their factors. For example- ½ x 4 = 2 ½ x ¼ = 1/8 Think “ ½ set of 4 equals 2”

1 2 1 x 2 = 2 1 x 5 = 5 5 1 Reduce first if possible Multiplying fractions and mixed numbers. Reduce first if possible Multiply the numerators Multiply the denominators 1 5 2 1 1 x 2 = 2 1 x 5 = 5

Change mixed numbers to improper fractions. Reduce if possible Multiply numerators and denominators. Multiplying mixed numbers 4 2 1 3

Dividing Fractions 9/22 DCN # 148 Bell Ringer Concept Builder: Understand the meaning of multiplying fractions; applying the multiplication algorithm Direct Instruction or Explorations: Demonstrate fraction division using modeling Notes on the algorithm Class practice text pp 144 problems 1-27 Independent Work/hw: Worksheet Assessment: Teacher obs. Bellringer 1. Under what conditions can I multiply a number by a fraction and get a larger number? Explain. 2. 1/5 – 5/6 = 3. 3 1/4 + 7 4/5 =

One way to divide fractions. . . 4 ÷ ½ = 8 Another way …

Dividing fractions and mixed numbers Change any mixed numbers to improper fractions. 2. Keep, change, flip to make it a multiplication problem. 3. Reduce first if possible and multiply.

The easiest way . . . A number multiplied by it’s multiplicative inverse equals 1. For example: Multiplicative inverse *Also called the reciprocal Why is this important? In the operation of division, multiplying with the divisor’s multiplicative inverse results in the same answer. For example, 4 ÷ 2 = 4 x ½ So when you have a division problem with fractions or mixed numbers, keep change flip and make it a multiplication problem.

199 is between perfect squares 196 and 225 or Multiplying and Dividing Fractions 9/23 DCN # 147 Bell Ringer Concept Builder: Multiplying mixed numbers by applying the multiplication algorithm Direct Instruction or Explorations: Check HW Drill and kill problems Independent Work/hw: Worksheet Assessment: Teacher obs. 800/40=20 783/37=21.2 Bellringer 1. Quickly estimate: 783 ÷ 37 2. 2/5 – 5/7 = 3. Estimate √199 -11/35 199 is between perfect squares 196 and 225 or 14 < √199 < 15 but closer to 14 than 15 so estimate 14.1 or 14.2

Place in order from least to greatest | -5 + 3 | -17 -√3 9 x 10-3 Multiplying and Dividing Fractions 9/28 DCN # 145 Bell Ringer Concept Builder: Applying the multiplication and division algorithm Direct Instruction or Explorations: Check homework Amateur Arch. Independent Work/hw: Worksheet Assessment: Teacher obs. Bellringer: Place in order from least to greatest | -5 + 3 | -17 -√3 9 x 10-3

Bellringer: Test Review Choose the correct answer for Multiplying and Dividing Fractions 9/29 DCN # 144 Bell Ringer Concept Builder: Applying the multiplication and division algorithm to fractions and mixed numbers Direct Instruction or Explorations: Review fraction operations on desk Word problems in groups Independent Work/hw: Worksheet Assessment: Teacher obs. Quiz grade Bellringer: Test Review Choose the correct answer for A. 2 ½ B. - 2 ½ C. 3 29 /32 D. - 3 29 /32 2. Choose the correct answer for A. 5 B. -5 C. 12 2 /4 D. - 12 2 /4 3. 4. What is 4/7 of 28? 5. Babs had 12 ½ yards of ribbons that she cut into pieces ¾ yd. long. How many pieces did she have?

Renaming in subtraction