Multiplication with Decimals Reminder: Multiplying with the grid method: 65 x 23 This can be re written as (60 + 5) x (20 + 3) 60 5 20 3 We now put this into the grid: Add the answers together: x Multiply out the numbers to fill the grid + 180 100 15 12 10 18 15 1495

Multiplication with Decimals Now do these: 26 x 42 5. 563 x 59 86 x 40 6. 24 x 437 50 x 86 7. 907 x 649 35 x 77 8. 576 x 430 x 20 6 40 800 240 2 40 12 + 240 40 12 1092 x 500 60 3 50 25000 3000 150 9 4500 540 27 33,217 x 80 6 40 3200 240 3200 + 240 3440 x 20 4 400 8000 1600 30 600 120 7 140 28 10,488 x 50 4000 6 300 4000 + 300 4300 x 900 7 600 540000 4200 40 36000 280 9 8100 63 588,643 x 30 5 70 2100 350 7 210 35 2100 + 350 210 35 2695 x 500 70 6 400 200,000 28,000 2400 30 15,000 2,100 180 247,680

Multiplication with Decimals To multiply decimals we use the same method, but we have to think about the place value: To multiply as this is can cause confusion so we think about the denomination 6.5 x 2.3 0.1 = 1 tenth so 6.5 = 65 tenths 1.0 = 10 tenths also 2.3 = 23 tenths Therefore as long as we remember the denomination we can multiply using the grid method:

Multiplication with Decimals This answer was found by multiplying tenths x tenths 60 5 20 3 x 1200 + 180 100 15 1200 100 1 x 1 10 10 1 100 180 15 = 1495 1 100 So the denomination of the answer is The numerical answer is 1495, so the place value of the 5 is 1 100 Therefore the correct answer in denomination of 1’s is: 14.95

Multiplication with Decimals We can check that the answer is correct by estimating 6.5 x 2.3 Estimate to 7 x 3 = 14 Therefore we expect an answer about 14. Inspect the answer 1495 If we put the decimal point here 1.495 the answer is clearly too small If we put the decimal point here 149.5 the answer is clearly too big The answer must be 14.95

Multiplication with Decimals Now do these: 26 x 4.2 5. 5.63 x 5.9 8.6 x 40 6. 2.4 x 4.37 50 x 8.6 7. 90.7 x 64.9 3.5 x 7.7 8. 5.76 x 4.30 x 20 6 40 800 240 2 40 12 + 240 40 12 109.2 x 500 60 3 50 25000 3000 150 9 4500 540 27 33.217 x 80 6 40 3200 240 3200 + 240 344.0 x 20 4 400 8000 1600 30 600 120 7 140 28 10.488 x 50 4000 6 300 4000 + 300 430.0 x 900 7 600 540000 4200 40 36000 280 9 8100 63 5,886.43 x 30 5 70 2100 350 7 210 35 2100 + 350 210 35 26.95 x 500 70 6 400 200,000 28,000 2400 30 15,000 2,100 180 24.7680

Multiplication with Decimals Points to note: What happens when you have a number less than 1 multiplied by another number less than 1? 0.1 is called a decimal fraction because it is 1 written in decimal notation 10 Therefore 0.1 x 10 is finding 1 of 10 (a fraction of a quantity) 10 0.1 x 10 = 1 Therefore 0.1 x 0.1 is finding 1 of 1 10 10 1 x 1 10 10 = 1 100 0.1 x 0.1 = 0.01 When a number less than 1 is squared the answer is even smaller Therefore 0.12 = 0.01

Multiplication with Decimals Now do these: 0.2 x 0.3 8. 0.42 0.4 x 0.2 9. 0.52 0.3 x 0.3 10. 0.62 0.6 x 0.3 11. 0.72 0.8 x 0.7 12. 1.5 x 0.6 0.22 13. 0.23 0.32 14. 0.43 0.06 0.16 0.08 0.25 0.09 0.36 0.18 0.49 0.56 0.9 0.04 0.008 0.09 0.064