1. DIVISION ÷÷ DECIMALS

2. MAKING A COMPARISON THE CONCEPT OF WHOLE NUMBER DIVISION IS FAIRLY EASY TO UNDERSTAND AND VISUALIZE THE CONCEPT OF DECIMAL DIVISION CAN BE MORE DIFFICULT TO UNDERSTAND AND VISUALIZE WE WILL TAKE A LOOK AT BOTH TYPES AND THEN COME UP WITH A PROCEDURE WHICH WILL MAKE DECIMAL DIVISION A MUCH SIMPLER PROCESS 12 ÷ 3 1.2 ÷.3

3. DIVISION WITH WHOLE NUMBERS HAVING “12” OF SOMETHING AND DIVIDING IT INTO GROUPS OF “3” IS SOMETHING YOU CAN PROBABLY GRASP IN YOUR MIND WELL A MODEL CAN BE HELPFUL AT TIMES 12 ÷ 3 4 GROUPS

4. LONG DIVISION WHEN THE WHOLE NUMBERS ARE TOO LARGE TO MODEL, YOU CAN USE LONG DIVISION TO FIND THE QUOTIENT 2850 Gallons 3 Gallons = ? 28503 9 27 15 5 0 0

5. DIVISION WITH DECIMAL NUMBERS HAVING “1.2” OF SOMETHING AND DIVIDING IT INTO GROUPS OF “.3” IS SOMETHING YOU COULD HAVE TROUBLE UNDERSTANDING A PICTURE MODEL CAN HELP YOU VISUALIZE THE PROBLEM YOU’RE TRYING TO SOLVE 1.2 ÷.3 1.2 Liters.3 Liters = ?

6. FRACTIONAL MODELING FRACTIONAL MODELING CAN HELP YOU SOLVE THIS PROBLEM SINCE IT’S EASY TO CONVERT DECIMAL NUMBERS INTO FRACTIONS SINCE BOTH NUMBERS ARE TENTHS, MAKING A MODEL WILL NOT BE DIFFICULT FOR THIS PROBLEM 1.2 ÷.3 4 GROUPS

7. WHAT’S THE BEST CHOICE? MODELING DECIMAL DIVISION WORKED WELL FOR THIS PROBLEM, BUT WHAT IF YOUR DECIMAL NUMBERS WENT INTO THE HUNDREDTHS, THOUSANDTHS, OR EVEN MORE DECIMAL PLACES WOULD THIS PROBLEM BE EASY TO MODEL? SINCE LONG DIVISION WORKED FOR LARGER WHOLE NUMBERS, LET’S SEE IF IT WILL WORK FOR DECIMAL NUMBERS AS WELL 1.2 ÷.3.12 ÷.003

8. DECIMALS & LONG DIVISION HERE’S OUR PROBLEM SET UP FOR LONG DIVISION THE PROBLEM CAN BE SOLVED AS IT IS RIGHT NOW USING LONG DIVISION, BUT IT CAN BE VERY DIFFICULT TO UNDERSTAND AND WORK OUT WHEN YOUR DIVISOR IS A DECIMAL NUMBER FORTUNATELY, THERE IS A WAY TO MAKE THINGS EASIER AND STILL USE LONG DIVISION 1.2.3 DIVISOR

9. LONG DIVISION THE PROCESS FOR DECIMAL DIVISORS

10. WHAT WE SHOULD DO IF OUR DIVISOR WERE A WHOLE NUMBER, LONG DIVISION WOULD BE A LOT EASIER COULD THERE BE A WAY TO CHANGE THE PROBLEM SUCH THAT WE WOULD END UP DIVIDING BY A WHOLE NUMBER INSTEAD? YES, WE CAN CHANGE THE PROBLEM THROUGH THE USE OF EQUIVALENT FRACTIONS AND THE RESULTS CAUSED BY MULTIPLYING A DECIMAL NUMBER BY A POWER OF 10 1.2.3 DIVISOR × 10, × 100, × 1000, …

11. HOW TO BEGIN SINCE DIVISION PROBLEMS CAN BE WRITTEN AS FRACTIONS, WE WILL DO THAT FIRST WE WOULD LIKE OUR DIVISOR (THE DENOMINATOR) TO BE CHANGED TO A WHOLE NUMBER THIS CAN BE ACCOMPLISHED BY USING EQUIVALENT FRACTIONS WE MUST MULTIPLY THE NUMERATOR AND DENOMINATOR BY A FACTOR THAT WILL GIVE US A WHOLE NUMBER DIVISOR 1.2.3 × ? DIVISOR

12. MULTIPLYING BY A POWER OF 10 WHEN YOU MULTIPLY A NUMBER BY 10, THE RESULT IS THE SAME AS TAKING THAT NUMBER AND MOVING THE DECIMAL POINT 1 PLACE TO THE RIGHT WHEN YOU MULTIPLY A NUMBER BY 100, THE RESULT IS THE SAME AS TAKING THAT NUMBER AND MOVING THE DECIMAL POINT 2 PLACES TO THE RIGHT WHEN YOU MULTIPLY A NUMBER BY 1000, THE RESULT IS THE SAME AS TAKING THAT NUMBER AND MOVING THE DECIMAL POINT 3 PLACES TO THE RIGHT … AND SO ON THE NUMBER OF ZEROES MATCHES THE NUMBER OF PLACES MOVED

13. CHANGE THE PROBLEM REMEMBER THAT WE WANT OUR DIVISOR TO BE A WHOLE NUMBER IF THE DECIMAL POINT IS MOVED 1 PLACE TO THE RIGHT, THE DIVISOR WILL BECOME A WHOLE NUMBER SO WHAT SHOULD WE MULTIPLY OUR NUMERATOR & DENOMINATOR BY? 10 WOULD BE THE CORRECT NUMBER NOW WE CAN USE LONG DIVISION TO SOLVE THE NEW PROBLEM × ? DIVISOR 12 3 × 10 =

14. QUICKER METHOD THE METHODS JUST DEMONSTRATED CAN BE PERFORMED QUICKER RIGHT INSIDE OF THE LONG DIVISION PROBLEM ITSELF TO MAKE THE DIVISOR A WHOLE NUMBER, MOVE THE DECIMAL POINT 1 PLACE TO THE RIGHT WHICH IS THE SAME AS MULTIPLYING IT BY 10 THEN MOVE THE DECIMAL POINT 1 PLACE TO THE RIGHT IN THE DIVIDEND SINCE IT MUST BE MULTIPLIED BY 10 AS WELL 1.2.3 DIVISOR DIVIDEND 1.2.3 12 3 NEW PROBLEM

15. SOLVING THE PREVIOUS PROBLEM IF YOU HAVE 1.2 LITERS OF COFFEE AND WILL FILL EACH CUP WITH.3 LITERS, HOW MANY PEOPLE CAN YOU SERVE COFFEE TO? SOLVE THE PROBLEM USING LONG DIVISION 1.2 Liters.3 Liters = ? 1.2.3 WHICH BECOMES 12 3 4 Servings WHICH EQUALS

16. SUMMARY & PRACTICE

17. WHAT TO REMEMBER WHEN YOU HAVE A PROBLEM THAT INVOLVES DIVIDING BY A DECIMAL NUMBER YOU WILL NEED TO CHANGE THE PROBLEM 1)SET UP THE PROBLEM AS LONG DIVISION USING THE NUMBERS GIVEN IN THE ORIGINAL PROBLEM 2)MOVE THE DECIMAL POINT IN THE DIVISOR COMPLETELY TO THE RIGHT TO CHANGE IT TO A WHOLE NUMBER 3)MOVE THE DECIMAL POINT IN THE DIVIDEND TO THE RIGHT THE SAME NUMBER OF PLACES AS YOU MOVED IT IN YOUR DIVISOR a.ADD A DECIMAL POINT TO THE END OF THE DIVIDEND AND AS MANY “0’S” AS NEEDED TO COMPLETE THIS STEP IF NECESSARY 4)SOLVE THE NEWLY CREATED LONG DIVISION PROBLEM

18. SHOW WHAT YOU’VE LEARNED A COMPANY HAS TO MOVE 35 TONS OF DIRT & ROCKS OUT OF THE WAY BEFORE THEY CAN BEGIN TO WORK ON A PROJECT THEIR DUMP TRUCKS CAN CARRY 2.5 TONS OF DIRT & ROCKS AT ONE TIME HOW MANY TRUCKS WILL IT TAKE TO REMOVE ALL OF THE DIRT & ROCKS FROM THE WORK AREA?

19. WERE YOU CORRECT? FINAL ANSWER 14 Trucks. 35 ÷ 2.5 352.5 35025 0 1 0 10 4 100 0