\( \begin{aligned} 238 \times 35 & =238 \times(30+5) \\ & =(238 \times 30)+(238 \times 5) \\ & =(238 \times 3 \times 10)+(238 \div 2 \times 10) \\ & =(714 \times 10)+(119 \times 10) \\ & =7140+1190 \\ & =8330\end{aligned} \) EXerciseta. Do these multiplications by breaking down one of the numbers as the example above: \( \begin{array}{ll}\text { 1. } 343 \times 25 & \text { 2. } 4001 \times 43 \\ \text { 3. } 453 \times 72 & \text { 4. } 3200 \times 66\end{array} \)
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Certainly! Here’s how you can break down the multiplications using a similar method: 1. For \( 343 \times 25 \): \[ 343 \times 25 = 343 \times (20 + 5) = (343 \times 20) + (343 \times 5) \] \[ = (343 \times 2 \times 10) + (343 \div 2 \times 10) = (686 \times 10) + (171.5 \times 10) \] \[ = 6860 + 1715 = 8575. \] 2. For \( 4001 \times 43 \): \[ 4001 \times 43 = 4001 \times (40 + 3) = (4001 \times 40) + (4001 \times 3) \] \[ = (4001 \times 4 \times 10) + (4001 \div 3) \times 10 = (16004 \times 10) + (12003) \] \[ = 160040 + 12003 = 172043. \] 3. For \( 453 \times 72 \): \[ 453 \times 72 = 453 \times (70 + 2) = (453 \times 70) + (453 \times 2) \] \[ = (453 \times 7 \times 10) + (906) = (3171 \times 10) + 906 \] \[ = 31710 + 906 = 32616. \] 4. Finally, for \( 3200 \times 66 \): \[ 3200 \times 66 = 3200 \times (60 + 6) = (3200 \times 60) + (3200 \times 6) \] \[ = (192000) + (19200) = 211200. \] Feel free to play around with these steps—math can be super fun when you break it down!
