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Multiplying and Dividing with Decimals

Multiplying and Dividing with Decimals. by Allison Hendley. Multiplying. Maybe multiplying with decimal points seems a little scary! BUT… There is a simple 3-step trick to multiply decimal point numbers just as if they were whole. While we learn the steps, we will look at the example:.

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Multiplying and Dividing with Decimals

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  1. Multiplying and Dividing with Decimals by Allison Hendley

  2. Multiplying • Maybe multiplying with decimal points seems a little scary! BUT… • There is a simple 3-step trick to multiply decimal point numbers just as if they were whole

  3. While we learn the steps, we will look at the example: 5.8 X 7

  4. Step 1 • Count the number of digits to the right of the decimal point 5.8 X 7 1 digit

  5. Step 2 • Just ignore the decimal point! • Multiply just as if they were normal whole numbers 5 5.8 X 7 5 8 X 7 4 0 6

  6. Step 3 • Use the number of digits from Step 1 to count out where to put the decimal • We counted 1 digit in Step 1, so we move the decimal point by 1 place to the left now 5.8 X 7 4 0 6 . .

  7. That’s It! • Our final answer is: 5.8 X 7 4 0.6

  8. What are we Really Doing? • When we “ignore” a decimal point, we are really multiplying by 10 for each digit to the right of the decimal. 5 8 X 7 5.8 X 7 x 10

  9. What are we Really Doing? • Now you multiply the numbers without decimals 5 8 X 7 4 0 6 • BUT DON’T FORGET WE MULTIPLIED BY 10 EARLIER!

  10. What are we Really Doing? • So now we divide by 10 5 8 X 7 / 10 4 0 6 . . 4 0 6 / 10 • Moving the decimal to the left one place is the same as dividing by 10!

  11. Let’s try it again with more digits to the right of the decimal point this time 0.024 X 0.61

  12. What was Step 1? • Count the digits to the right of the decimal point • From 0.024, how many digits? • What about from 0.61? • That gives a total of: 3 2 5

  13. What was Step 2? • Ignore the decimal points • That means that 0.024 becomes: • In the same way, 0.61 is: 24 61

  14. Now we just multiply that out 2 2 4 X 6 1 2 4 1 4 4 0 1 4 6 4

  15. What was Step 3? • Place the decimal point in our answer • What did we count in Step 1? Now move the decimal that many places to the left • But wait! There are only 4 numbers! 0.024 X 0.61 1 4 6 4 .

  16. Since we need to move the decimal point 5 places to the left but only have 4 numbers, we write the 0 out in front. 0.024 X 0.61 0 1 4 6 4 . .

  17. Don’t forget, its the same as dividing by 10, five times • For our final answer, we have 0.024 X 0.61 0.01464

  18. Why It Works • All we are really doing is multiplying and dividing by powers of 10 as needed to make the problem easier • When we turned 0.024 into 24, we multiplied it by 10 three times 1.) 0.024 x 10 = 0.24 2.) 0.24 x 10 = 2.4 3.) 2.4 x 10 = 24

  19. Also, 0.61 becomes 61 by multiplying by 10 twice • Each time we move the decimal to the right on place we are multiplying by 10 • That’s why we count, so we can divide by 10 the same number of times later

  20. Everybody think of a number • Multiply that number by 10 • Divide that number by 10 • What do you have now?

  21. Canoeing If a group of people set out in 14 canoes, and they each canoe for 8.6 miles, how many total miles were traveled by the canoes? 120.4 miles

  22. Backpacks • The canoers weighed all their packs before leaving and found that all together they weighed 195.2 lbs. If 1 lb = 0.45 kg, how many kilograms of gear have the canoers brought along? 87.84 kgs

  23. Remember the 3 steps: • Count the number of digits to the right of the decimals • Ignore the decimals and multiply • Place the decimal in the answer by moving it back to the left by the same number of digits as before

  24. 6.2 21.08 Dividing • When we divide numbers with decimal points, we use the same idea as multiplying them • Keeping everything lined up is key!

  25. 6.2 62 21.08 210.8 Step 1 • Multiply both the divisor and dividend by whatever power of 10 we need so that the divisor is a whole number

  26. 62 210.8 Step 2 • Divide just like normal • Ignore the decimal point 3 4 1 10 1 0 186 2 4 8 248 0

  27. 3 4 62 210.8 Step 3 • Bring up the decimal point • The decimal point in the quotient is placed directly above where it is in the number being divided • This is why keeping numbers aligned is so important! .

  28. 21.08 21.08 x 10 210.8 6.2 6.2 x 10 62 Why It Works • Just like before, when we multiply and divide by the same number, we don’t change what we started with • Look at the division like this: = =

  29. 10 21.08 21.08 10 6.2 6.2 • Notice that by multiplying both the divisor and the dividend by 10, all we really did is multiply by a special form of 1 1 x x =

  30. Backpacks, Again • If each canoer carries 5.49 kgs of gear while hiking (out of the total 87.84 kgs), how many canoers are there total? Note: some canoes may have more than one canoer. 16 canoers

  31. Kilograms • If 1 lb = 0.45 kg, how many pounds is each canoer carrying when every backpack is 5.49 kgs? 12.2 lbs

  32. 3 Steps of Division: • Multiply both the divisor and the dividend by a power of 10 • Ignore the decimal and divide like normal • Bring up the decimal from its position in the divisor

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