1.01 NEGATIVE NUMBERS ____________________________________________________

Understanding Integers 1. What is a positive number? 1.It’s a number greater than zero. * * Represented with a + or no sign 2. What is a negative number? 2. It’s a number less than zero. * Always written with a - sign 3. What are opposites? 3. The same number with a different sign * They are the same distance from 0 but are on different sides of 0 4. Show opposites on a number line:

Understanding Integers 5. What are integers? 5. Integers are the set of all whole numbers and their opposite 6. What is absolute value? 6. An integer’s distance from 0 * Represented by I n I * Never negative * Always positive Negatives are always less than positives Opposites are the same # but one is + and one is -- Absolute values are never negative

Is it positive or negative? Write the integer: A. I owe my friend $10.00 Graphing Opposites. Graph the integer and it’s opposite:. B. I live 100 feet above sea level C. It’s 20 degrees below zero outside D. I gained 15 yards in my football game

Write the absolute value of: 1. I-2I = 2. I0I = 3. I5I = 4. I-4I = 5. I-1I =

1.03 Ordering integers

Comparing and Ordering Integers 1. How do I compare integers? 1.Use a number line. * Numbers to the left are less than number to the right -4 2 Order: 2, -4, -1, 5, Compare the following integers: 3. How do I order integers? 3. GRAPH them on a number line, then order them.

Comparing and Ordering Integers 4. Graph then order the following integers greatest to least: Graph and order the same integers least to greatest. 4. 5, -2, 1, -4, -1, , -2, 1, -4, -1, 3 _____________________________________________ L.L. = LEFT IS LESS * Use a # line to compare or order integers

ALL objectives _________________________________________________

Solving Word Problems 1. How do I solve word problems? Read the problem until you understand what the question is. 2. List the important information 3. Make a plan: how are you going to solve the problem? Draw pictures, diagrams, etc. if necessary 4. Solve the problem 5. Check your answer and look back at the problem. Does your answer make sense?

1.03 Compare & order decimals ____________________________________________________

Ordering and Comparing Decimals: 1. What are the place values for decimals? = hundreds place 0 = tens place 4 = ones place 9 = tenths place 8 = hundredths place 6 = thousandths place 7 = ten-thousandths place 3 = hundred-thousandths place

Ordering and Comparing Decimals: 2. How do I say a decimal number? 2. Always say the decimal as “and” Say the number the same way you would if it wasn’t a decimal, then say the place value of the last digit Example: = Eight two and thirty four hundredths 3. How do I compare decimals? 3. Line up all the decimals then compare each column left to right Example: is greater than 1 so < 2.03

Ordering and Comparing Decimals: 4. How do I order decimals? 4. Line up all the decimals then compare each column left to right Example: 2.4, 1.9, 2.19 (L --> G) 5. Compare these decimals: Order these decimals L -> G: , 1.001, , 2.55, , 5.05, 5.98

Always line up decimals when comparing or ordering Compare columns left to right

1.03 Compare & order fractions ____________________________________________________

1. What are the parts of a fraction? 1. Whole number 2 ¾ 2. How do I compare two fractions? 2. Cross multiply bottom to top and compare the quotients Example: ⅔ ⅝ ⅝ ¾ Numerator Denominator * If the denominators are the same, you can compare the numerators Example: ⅜ ⅞

____________________________________________________ 3. How do I order fractions? 4. How do I change fractions to decimals? 4. Divide the numerator by the denominator 3. Change the fractions into decimals then compare the decimals 1. The nice numerator goes in the house 2. The dorky denominator stays outside the house 3. Add a decimal and two zeros to the nice numerator 4. Divide as usual 5. Bring the decimal straight up into your answer

____________________________________________________ 5. Change these fractions to decimals: 5.⅞⅝⅜⅛⅔⅞⅝⅜⅛⅔

____________________________________________________ 6. Order these fractions least to greatest: 6. ⅞, ⅔, ½, ⅝

____________________________________________________ 7. How else can I order fractions? 7. Find a common denominator (a number all of the denominators can go into evenly) then order the numerators. 1. Find a common denominator 2. Set up each fraction equal to that denominator 3. Whatever # you x the denominator by, you MUST x the numerator by 4. Order fractions based on their numerators Order L  using a common denominator:

____________________________________________________ 9.9. Order G  L using a common denominator:

The nice numerator goes in the house, the dorky denominator stays outside the house Denominator Down Cross multiply to compare TWO fractions Change fractions to decimals or find a common denominator to order fractions or compare more than 2 fractions

1. The run got pushed backwards 12 yards. 2. Andi jumped 12 feet high. 3. Clinton owes $ The city is 1,895 feet below sea level. 5. The diver dove 60 feet under the surface. 6. The temperature was 5 degrees F but then it dropped 7 degrees. What’s the temperature now? 7. In the game of golf, the lowest score wins. Who won the game? Amy = -7 Clinton = -4 Kira = 2 Andi = -9

Clinton dove 45 feet under water. Amy dove 60 feet under water. Kira dove 12 feet under water. Who dove the deepest? 1. What is the opposite of -12? 2. Graph 4 and its opposite: 3. Graph -3 and its opposite:

1. Clinton has 2.3 gallons of gas. He needs 2.76 gallons. Does he have enough? 2. Write in words: Clinton dove feet. Amy dove feet. Andi dove 23.9 feet. Kira dove 23 feet. Put their names in order from the deepest to shallowest dives. 4. What place is the 6 in? Andre has three sticks. Their lengths are 2.21 inches, 2.20 inches and inches. What is the length of the shortest stick?

1. Our gas tank has 4/9 of a gallon in it. We need 7/13 of a gallon for the lawn mower. Do we have enough? 2. Order least to greatest: 3/6, 2/7, 4/5 3. The store has 3 nails left. One is 3/5 inches, one is 8/11 inches, and one is 6/9 inches. Which one is shortest? 4. Turn this fraction into a decimal: 5/9 5. The recipe calls for 1/3 cups of sugar. I have 3/9 cups of sugar. Is that enough?

1.Put all cards face down on your desk 2.Mix them all up (please)! be gentle so the cards don’t bend or rip 3.Distribute them evenly between you and your partner 4.Flip them over one at a time 5.The LOWEST number wins 6.The first player with all of the cards wins

1.03 Fractions ____________________________________________________

1. What are like fractions? 1. They’re fractions with the same denominator (de nomber on de bottom) 2. What are unlike fractions? 2. They’re fractions with different denominators 3. What are proper fractions? 3. Fractions in which the numerator is less than the denominator 4. What are improper fractions? 4. Fractions in which the numerator is greater than the denominator EX: ⅝ ⅞ ⅛ EX: ⅛,, ½ EX: ½ ⅞ ⅛ EX:,,

5. What are equivalent fractions? 5. Fractions that have the same value 6. How do I make an equivalent fraction? 6. * Multiply the numerator and denominator by the same number OR EX: EX: x = x = = = = = * Divide by a number that goes into the numerator AND denominator evenly EX: ÷ = ÷ =

7. What does simplest form mean? 7. The fraction cannot be reduced * No numbers other than 1 can go into the numerator and denominator evenly 8. How do I change a whole number into fraction? EX: ⅝, ⅔, ⅞ 8. Put the whole number over 1 EX: = 1 = 1 = 1 EX: 7= 10= 5= 9. How do I make a fraction equal to 1? 9. The numerator must be the same as the denominator

10. What is a mixed number? 10. A whole number with a fraction 11. How do I change a mixed number into an improper fraction? EX: 4⅝, 7⅔, 3⅞ Multiply the whole number and denominator 2. Add the numerator to your answer 3. The sum becomes the numerator 4. The denominator stays the same EX: 4⅝ 7⅔ 3⅞ Multiply Then add.

11. How do I change an improper fraction into a mixed number? 1 4 __ 1. Divide the numerator by the denominator. 2. The remainder becomes the numerator, the denominator stays the same = 12. Change the improper fractions to mixed numbers:

1.03 Multiply fractions 2. How do I multiply a fraction by a whole number? 2.A. Change the whole number into a fraction ** put it over 1 B. Multiply the numerators C. Multiply the denominators D. Write your answer in simplest form Example: 4 * 7/8 1. How do I multiply fractions? 1.A. Multiply the numerators B. Multiply the denominators C. Write the answer in simplest form Example: 1/3 * 3/5

1.03 Multiply fractions 3. How do I multiply mixed numbers? 3.A. Change the mixed numbers to improper fractions B. Multiply the numerators C. Multiply the denominators D. Write the answer in simplest form or as a mixed number Example 1: 1/3 * 1 1/2 Example 2: 2 1/2 * 1 1/3 4. How do I evaluate fraction expressions? 4.A. Replace x with the given number B. Multiply C. Write your answer in simplest form Example: x = 5/8 1/3 * x

1.03 Multiply fractions 6. How do I multiply a whole number by a mixed number? 6. A.Write both numbers as improper fractions B.Multiply the numerators and denominators C.Change your answer to a mixed number

1.03 Divide fractions 1. What is a reciprocal? 1.It’s when you flip a fraction upside down * Two fractions are reciprocals if their product is 1 2. How do I find the reciprocal of a fraction? 2. Switch the numerator and denominator Example: 2/5 = 8/9 =

1.03 Divide fractions 3. How do I divide fractions? Copy the first fraction 2. Change the division sign to multiplication 3. Flop (flip) the second fraction 4. Multiply 5. Write your answer in simplest form Example: 4/5 - 5 Example 2: 1/2 - 1/4

1. How do I add like fractions? 1.A. Add the numerators B. Keep the same denominator C. Write your answer in simplest form Example: 2/7 + 3/7 2.How do I subtract like fractions? 2. A. Subtract the numerators B. Keep the same denominator C. Write your answer in simplest form Example 1: 4/5 - 1/5 = Example 2: 1- 4/5= 3. How do I subtract like mixed numbers? 3. A. Subtract the fractions B. Subtract the whole numbers C. Write your answer in simplest form Example: 2 3/ /4 = 1.03 Add & subtract fractions

4. How do I evaluate expressions with fractions? 4. A. Write the expression B. Replace x with the given number C. Subtract/Add the numerators D. Keep the same denominator E. Write your answer in simplest form Example 1 : x = 5/8 x - 2/8 Example 2: x = 3/8 x + 1 1/8