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First estimate and then use the long division method to find the an Let your partner use a calculator to check your answers. \( \begin{array}{lll}\text { 1. } 2453 \div 312 & \text { 2. } 5876 \div 424 & \text { 3. } 3275 \div 25 \\ \text { 4. } 3772 \div 323 & \text { 5. } 4498 \div 634 & \text { 6. } 6640 \div 30 \\ \text { 7. } 9578 \div 162 & \text { 8. } 7645 \div 502 & \text { 9. } 9200 \div 83\end{array} \)

Ask by Powell Lawson. in South Africa
Feb 25,2025

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Answer

Here are the estimated and long division results for each problem: 1. \( 2453 \div 312 \approx 7.86 \) 2. \( 5876 \div 424 \approx 13.93 \) 3. \( 3275 \div 25 = 131 \) 4. \( 3772 \div 323 \approx 11.68 \) 5. \( 4498 \div 634 \approx 7.08 \) 6. \( 6640 \div 30 \approx 221.33 \) 7. \( 9578 \div 162 \approx 59.06 \) 8. \( 7645 \div 502 \approx 15.24 \) 9. \( 9200 \div 83 \approx 110.84 \) Use a calculator to check these answers.

Solution

Solve the equation by following steps: - step0: Solve for \(x\): \(3772=323x\) - step1: Swap the sides: \(323x=3772\) - step2: Divide both sides: \(\frac{323x}{323}=\frac{3772}{323}\) - step3: Divide the numbers: \(x=\frac{3772}{323}\) Solve the equation \( 6640=30*x \). Solve the equation by following steps: - step0: Solve for \(x\): \(6640=30x\) - step1: Swap the sides: \(30x=6640\) - step2: Divide both sides: \(\frac{30x}{30}=\frac{6640}{30}\) - step3: Divide the numbers: \(x=\frac{664}{3}\) Solve the equation \( 9200=83*x \). Solve the equation by following steps: - step0: Solve for \(x\): \(9200=83x\) - step1: Swap the sides: \(83x=9200\) - step2: Divide both sides: \(\frac{83x}{83}=\frac{9200}{83}\) - step3: Divide the numbers: \(x=\frac{9200}{83}\) Solve the equation \( 9578=162*x \). Solve the equation by following steps: - step0: Solve for \(x\): \(9578=162x\) - step1: Swap the sides: \(162x=9578\) - step2: Divide both sides: \(\frac{162x}{162}=\frac{9578}{162}\) - step3: Divide the numbers: \(x=\frac{4789}{81}\) Solve the equation \( 5876=424*x \). Solve the equation by following steps: - step0: Solve for \(x\): \(5876=424x\) - step1: Swap the sides: \(424x=5876\) - step2: Divide both sides: \(\frac{424x}{424}=\frac{5876}{424}\) - step3: Divide the numbers: \(x=\frac{1469}{106}\) Solve the equation \( 2453=312*x \). Solve the equation by following steps: - step0: Solve for \(x\): \(2453=312x\) - step1: Swap the sides: \(312x=2453\) - step2: Divide both sides: \(\frac{312x}{312}=\frac{2453}{312}\) - step3: Divide the numbers: \(x=\frac{2453}{312}\) Solve the equation \( 4498=634*x \). Solve the equation by following steps: - step0: Solve for \(x\): \(4498=634x\) - step1: Swap the sides: \(634x=4498\) - step2: Divide both sides: \(\frac{634x}{634}=\frac{4498}{634}\) - step3: Divide the numbers: \(x=\frac{2249}{317}\) Solve the equation \( 7645=502*x \). Solve the equation by following steps: - step0: Solve for \(x\): \(7645=502x\) - step1: Swap the sides: \(502x=7645\) - step2: Divide both sides: \(\frac{502x}{502}=\frac{7645}{502}\) - step3: Divide the numbers: \(x=\frac{7645}{502}\) Solve the equation \( 3275=25*x \). Solve the equation by following steps: - step0: Solve for \(x\): \(3275=25x\) - step1: Swap the sides: \(25x=3275\) - step2: Divide both sides: \(\frac{25x}{25}=\frac{3275}{25}\) - step3: Divide the numbers: \(x=131\) Let's estimate and then perform long division for each of the given problems. ### 1. \( 2453 \div 312 \) **Estimation:** - \( 2453 \approx 2500 \) - \( 312 \approx 300 \) - Estimated quotient: \( \frac{2500}{300} \approx 8.33 \) **Long Division:** - \( 2453 \div 312 \approx 7.86 \) ### 2. \( 5876 \div 424 \) **Estimation:** - \( 5876 \approx 5900 \) - \( 424 \approx 400 \) - Estimated quotient: \( \frac{5900}{400} \approx 14.75 \) **Long Division:** - \( 5876 \div 424 \approx 13.93 \) ### 3. \( 3275 \div 25 \) **Estimation:** - \( 3275 \approx 3300 \) - \( 25 \approx 25 \) - Estimated quotient: \( \frac{3300}{25} = 132 \) **Long Division:** - \( 3275 \div 25 = 131 \) ### 4. \( 3772 \div 323 \) **Estimation:** - \( 3772 \approx 3800 \) - \( 323 \approx 300 \) - Estimated quotient: \( \frac{3800}{300} \approx 12.67 \) **Long Division:** - \( 3772 \div 323 \approx 11.68 \) ### 5. \( 4498 \div 634 \) **Estimation:** - \( 4498 \approx 4500 \) - \( 634 \approx 600 \) - Estimated quotient: \( \frac{4500}{600} = 7.5 \) **Long Division:** - \( 4498 \div 634 \approx 7.08 \) ### 6. \( 6640 \div 30 \) **Estimation:** - \( 6640 \approx 6600 \) - \( 30 \approx 30 \) - Estimated quotient: \( \frac{6600}{30} = 220 \) **Long Division:** - \( 6640 \div 30 \approx 221.33 \) ### 7. \( 9578 \div 162 \) **Estimation:** - \( 9578 \approx 9600 \) - \( 162 \approx 160 \) - Estimated quotient: \( \frac{9600}{160} = 60 \) **Long Division:** - \( 9578 \div 162 \approx 59.06 \) ### 8. \( 7645 \div 502 \) **Estimation:** - \( 7645 \approx 7600 \) - \( 502 \approx 500 \) - Estimated quotient: \( \frac{7600}{500} = 15.2 \) **Long Division:** - \( 7645 \div 502 \approx 15.24 \) ### 9. \( 9200 \div 83 \) **Estimation:** - \( 9200 \approx 9200 \) - \( 83 \approx 80 \) - Estimated quotient: \( \frac{9200}{80} = 115 \) **Long Division:** - \( 9200 \div 83 \approx 110.84 \) ### Summary of Results 1. \( 2453 \div 312 \approx 7.86 \) 2. \( 5876 \div 424 \approx 13.93 \) 3. \( 3275 \div 25 = 131 \) 4. \( 3772 \div 323 \approx 11.68 \) 5. \( 4498 \div 634 \approx 7.08 \) 6. \( 6640 \div 30 \approx 221.33 \) 7. \( 9578 \div 162 \approx 59.06 \) 8. \( 7645 \div 502 \approx 15.24 \) 9. \( 9200 \div 83 \approx 110.84 \) You can use a calculator to verify these results.

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The Deep Dive

To estimate the results of these divisions, you can round the numbers to the nearest hundreds or simpler values. For example, for \(2453 \div 312\), you might round 2453 to 2400 and 312 to 300, leading to an estimated answer of approximately 8. For \(3275 \div 25\), you can keep it straightforward since 25 goes into 100 smoothly; therefore, it gives an estimated answer of around 130. Now, let's demonstrate the long division for \(2453 \div 312\) step-by-step. First, determine how many times 312 fits into the beginning portion of 2453. 312 goes approximately 7 times, giving \(7 \times 312 = 2184\). Subtract this from 2453 to find the remainder. Bring down the next digit if needed, and repeat this to find the final quotient. You can double-check with your partner's calculator to see how close your estimates were!

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