Bell Ringers 1. When playing the Integer Game, you have 3 cards in your hand with a sum of −15. Then, you draw a (−5) card. Using addition, how would you write an equation to represent your score? 2. What is the absolute value of 15? 3. What is the sum of −4+(−10)? 4. In what direction does the arrow point on a number line for a negative number? 5. What is an additive inverse of 5? What is the additive inverse of −9? What is the additive inverse of a number? 6. 1 ¼ + (½) 7. ( )

Fractions and decimals

Today I will be able to add rational numbers (fractions and decimals) to solve real world problems.

Adding Fractions with Common Denominators When adding fractions with common denominators you simply add the numerators and the denominator stays the same. Ex: 1/8 + 6/8 Ex: 2 2/ /3

Adding Fractions with Uncommon Denominators When adding fractions with uncommon denominators you must first convert all mixed fractions into improper fractions. Next you will have to find the least common denominator. To find the LCD first list the multiples of the denominators. The first multiple they have in common will be the LCD. Write the equivalent fractions using the LCD. Finally, add the numerators and the denominator stays the same.

Changing Mixed Fractions into Improper Fractions To convert a mixed number to an improper fraction, follow these steps: Multiply the denominator of the fractional part by the whole number, and add the result to the numerator. For example, suppose you want to convert the mixed number. 3 5/6 3x6= =23 Use this result as your numerator, and place it over the denominator you already have. 23/6

Example: Example: ½ + 3/5 Solution: Step 1 :Find the LCD or LCM of 2 and 5 Multiples of 2: 2, 4, 6, 8, 10, 12 Multiples of 5: 5, 10, 15 The LCD or the Least Common Multiple of 2 and 5 is 10 Step 2 : Write both fractions and as equivalent fractions with a common denominator of 10. ½ = 1 x5 =5 = 5/10 2x5=10 3/5 = 3 x 2 = 6 5 x2 = 10 Step 3: Add the 2 equivalent fractions 5/10 + 6/10= 5 +6 = 11 Denominator stays the same Answer: 11/10

Changing Improper Fractions to Mixed Fractions Changing improper fractions to mixed numbers can help you better understand the result of an algebraic problem. Improper fractions are simply top-heavy fractions whose numerators (the numbers on top) are bigger than their denominators. Mixed numbers contain both a whole number and a fraction. Example: Change the improper fraction 25/4 to a mixed number. Divide the numerator by the denominator. Divide 25 by 4, which equals 6 with a remainder of 1. 25/4 = 6 r 1 Find the whole number. The whole number is the number of times the denominator divides into the numerator. 4 (the denominator) divides into 24 (the numerator) 6 times, so 6 is the whole number. Make the remainder the new numerator. Because the remainder (the left over value) of dividing 25 by 4 is 6, 1 is the new numerator. The denominator is still 4. So, the mixed fraction is: 6 ¼

Addition of Integers rules Add rational numbers with the same sign by adding the absolute values and using the common sign. Ex: −+(−) Add rational numbers with opposite signs by subtracting the absolute values and using the sign of the integer with the greater absolute value. Ex: 6 + (-18) (-12) + 65

Listen Carefully Solve the following problem (-2 ¼) Change all whole numbers into fractions and all mixed fractions into improper fractions. 2 x 4 = 8 +1= 9 9/4, 6/1 2. Now find the LCD. Multiples of 4: 4, 8, 12, 16, 20, 24, 28 Multiples of 1: 1, 2, 3, 4, 5, 6, 7, 8 3. Find the equivalent fractions using the LCD. -9/4, 24/4 4. Now subtract the absolute values and use the sign for the rational number with the greatest value. 24/4 - 9/4 = 15/4( the sign will be positive because 24/4 or 6 has the greatest absolute value. 5. Now change the improper fractions back into a mixed number. 15/4 = 3 r 3 so the mixed number is 3 ¾

Let’s Try Again Solve: -3/4 + 1/16

Listen Carefully Solve: Subtract the absolute value of the two rational numbers. (be sure to line up the decimals and add zeros where needed)\ Use the sign of the integer with the greatest absolute value. Answer:

Let’s try again Solve ( )

It’s your turn With a partner solve the problem in your math journal. -2 7/ /6

It’s your turn Solve: 9 + (-3 1/3)

It’s your turn Solve: ( ) + ( )

It’s your turn Solve: ( ) + ( )

Real world problems The Apple stock started at points in the black. After an announcement about a glitch in their new iphone 7 the stock dropped points. At the end of the business day where did the Apple stock end?

Real world problems. I was baking brownies for Mike last night. The recipe called for 2 ¼ cups of flour. I poured 3/8 cup of the flour into the butter and sugar mixture. How much of the flour is left in my measuring cup?

Your turn: real world problems You bought a stock that was in the red. After a month your stock rose by 34.2 points. What is the total points for your stock now?

Your turn: real world problems Jason measured a board to be 12 1/8 feet long. He cut 3 1/6 of the board off. How long is the board now?

Check for understanding On a loose leaf piece of paper write the problems and solve. 1. Solve: (-14 2/6) + 2 1/3 2. Solve: (-3 7/8) + (-3/4) 3. Solve: ( ) 4. Solve: (-10.3) + ( ) 5. You purchased a stock at in the red. The stock fell an additional points. Where does your stock stand in points now? 6. You poured out 5 ¾ cups of flour. Then you poured out an additional 2 2/3 cups of flour. How much flour was poured out?

Exit Ticket In your math journal describe how to solve problems involving the addition of rational numbers with the same signs and with differing signs.