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Mastering Division with Expanded Notation: 1,315 ÷ 5 Explained

In this lesson, you’ll learn how to effectively divide using expanded notation. We’ll dissect challenging problems into manageable parts, showing you step-by-step solutions for division. For example, we will break down the division of 1,315 by 5 using smart estimation techniques, expanded notation, and multiplication concepts. You’ll also discover how to apply these methods in real-life scenarios, such as distributing items evenly among groups. By the end of this lesson, you’ll be equipped with skills to tackle complex division problems confidently.

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Mastering Division with Expanded Notation: 1,315 ÷ 5 Explained

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  1. How would you divide 1,315 ÷ 5?

  2. In this lesson you will learn how to divide by using expanded notation.

  3. Challenging problems can be broken into smaller parts Then I can multiply 26 x 10 and get 260 20 x 13 I know that 20 is 2 times 10 20 = 2 x 10 I can multiply 13 x 2 and get 26 13 x 2 = 26 26 x 10 = 260 20 x 13 = 260

  4. Expanded notation 2,615 = 2,000 + 10 + 600 + 5

  5. 1,315 ÷5 1,500 divides easily by 5 Smart rounding ≈ 1,500 ÷ 5 Smart estimate less than 300

  6. 1,315 ÷ 5 10 ÷5 = 2 = 1,000 1,315 + 10 +300 +5 5 ÷5 = 1 This makes sense since our smart estimate was less than 300 ÷5 200 10 ÷ 5= 2 100 ÷ 5= 20 1000 1,000 ÷ 5= 200 ÷5 300 60 ÷5 2 10 30 ÷ 5 = 6 300 ÷ 5 = 60 1 ÷5 5 0 263 x 5 = 1,315 1,315 ÷ 5 = 263

  7. There are 1,520 pencils for 10 students. How many pencils does each student get? Smart rounding ≈ 1,500 ÷ 10 1,500 divides easily by 10 Smart estimate ≈150

  8. 1,520 ÷ 10 20 ÷10 = 2 = 1,000 1,520 + 20 +500 +0 This makes sense since our smart estimate was 150 10 ÷ 10= 1 100 ÷ 10= 10 ÷10 100 1,000 1,000 ÷ 10= 100 ÷10 500 50 ÷10 2 20 50 ÷ 10 = 5 500÷ 10 = 50 0 152 x 10 = 1,520 1,520 ÷ 10 = 152

  9. In this lesson you have learned how to divide by using expanded notation.

  10. What is 1,250 ÷ 5?

  11. Use expanded notation to show the division of 1,845÷ 5. Make a chart to show your work. • Sidney has 2,125 paper plates to put in 25 boxes. She estimated that she would put 100 plates in each box. Using expanded notation and a chart, show whether or not this is a good estimate.

  12. Which of the following shows the division of 3510 ÷ 5 by using expanded notation? A = 3000 3,510 + 10 +500 +5 C B 0

  13. Sandra needs to store 2,125 paper clips seeds. Only 25 fit in each box. Which chart uses expanded notation to show how many boxes she will need? A = 2,000 2,1 2 5 + 20 +100 +5 C B 0

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