Lecture from September 29.

1. Agenda 9/29 1. Divisibility Rules 7 and 8 2. Review HW- Exercise 6 3. Item Sets (Longer Word Problems) 4. Formulas CW/HW- Exercises 7 and 8

2. Review: 5 and 6 Which numbers are divisible by five? 54,653,546,435 4,672,231,642 4650

3. Review: 5 and 6 Which numbers are divisible by six? 485,772 312 1340

4. Divisibility Rules Seven A number is divisible by seven if you double the last digit and subtract it from the rest of the number and the answer is: 0, or divisible by 7 672 is evenly divisible by seven (double 2 is 4, subtract 4 from 67. 67-4=63

5. Divisibility Rules Eight A number is evenly divisible by eight if the three rightmost digits are divisible by eight. 109,816 is divisible by 8 because 816 is divisible by 8.

6. Check Which numbers are evenly divisible by seven? 1407 2152 7003

7. Check Which numbers are evenly divisible by eight? 864 7040 3096 4332

8. Item Sets An item set is a passage that gives enough information to produce several questions. To answer each question, you have to be sure you are using only the information that you need.

9. Item Sets Laura and Tim have seen two apartments that they like. Apartment A has monthly rent of $480 for the first year. The rent for the second year will be an additional $48 a month. The rent for apartment A includes heat. The rent for apartment B is $412 a month for 2 years. The rent for apartment B does not include heat. The landlord for apartment B says that the heating bill for the apartment averages $84 a month. 1. Find the yearly rent for apartment A for the second year. Step 1: Add the monthly increase for the second year. $480 + $48 = $528 Step 2: Multiply the monthly rent by 12. $528 x 12 = $6336

10. Item Sets Laura and Tim have seen two apartments that they like. Apartment A has monthly rent of $480 for the first year. The rent for the second year will be an additional $48 a month. The rent for apartment A includes head. The rent for apartment B is $412 a month for 2 years. The rent for apartment B does not include heat. The landlord for apartment B says that the heating bill for the apartment averages $84 a month. 2. Assuming the landlord’s estimate for heating bills is correct, find the total rent and heating costs for one year in apartment B. Step 1: Add the monthly rent and heating bill. $412 + $84 = $496 Step 2: Multiply the monthly total by 12. $496 x 12 = $5952

11. Item Sets- On Your Own Laura and Tim have seen two apartments that they like. Apartment A has monthly rent of $480 for the first year. The rent for the second year will be an additional $48 a month. The rent for apartment A includes heat. The rent for apartment B is $412 a month for 2 years. The rent for apartment B does not include heat. The landlord for apartment B says that the heating bill for the apartment averages $84 a month. 1. For the first year, the monthly rent for apartment A is how much less than the combined monthly rent and heating bill for apartment B? 2. Laura and Tim take home $2230 each month. How much will they have left each month of the second year of their lease if they choose apartment A?

12. Formulas A formula is a mathematical rule. A formula has letters that represent numbers. To use any formula, you substitute values you DO know for certain letters. When you substitute, you replace a letter with a number.

13. Total Cost Formula Total cost = (number of units) x (price per unit) The total cost equals the number of units multiplied by the cost per unit. You have already used this formula in previous exercises. c= nr

14. Distance Formula d= rt Distance equals the rate (speed) multiplied by the time (duration)

15. Examples Use the cost formula to find the cost of 3 pounds of coffee at $5.99 per pound. c=nr Use the distance formula to find the distance a trucker traveled if he drove at an average speed of 65mph for 5 hours. d=rt