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Rational Numbers & Equations

This lesson focuses on multiplying and dividing decimals. Learn how to multiply decimals as if they are whole numbers, count decimal places, and move decimal points. Also, explore dividing decimals by changing the divisor and moving the decimal point. Practice with real-world scenarios and complete exit problems to reinforce learning.

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Rational Numbers & Equations

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  1. Lesson 7 Rational Numbers & Equations Multiplying and Dividing Decimals

  2. Warm-Up • Sara spent $3.44 at one store and $6.89 at another store. How much did she spend in all? • Lars gave the cashier $20 for an item that cost $8.30. How much change should he receive? • It rained 1.37 inches yesterday and 0.8 inches today. How much total rain fell over the past two days?

  3. Multiplying and Dividing Decimals Target: Multiply and divide decimals.

  4. Multiplying with Decimals • Multiply as if the numbers are whole numbers. • Add the number of digits after the decimal point in each factor to find the number of decimal places in the product. • Insert zeros, if necessary, to hold place value. Delete zeros that are not necessary.

  5. Example 1 Find the value of 4.13(5.2). • Multiply as if whole numbers. • Count digits after the decimal. There are three. • Move the decimal point three spaces to the left and insert.

  6. Dividing with Decimals • If the divisor is not a whole number, change the divisor into a whole number by moving the decimal point to the right. • If the decimal point in the divisor was moved, move the decimal point in the dividend the same number of places to the right as it was moved in the divisor. • Divide the dividend by the divisor. • Move the decimal point in the quotient directly above the decimal point in the dividend. • If necessary, insert zeros to hold place value.

  7. Example 2 Find the value of 15.12 ÷ 3.6. • Move decimal in dividend so it is a whole number. Move the decimal the same amount of spaces in the divisor. 151.2 ÷ 36 • Divide and move decimal up.

  8. Example 3 Isaiah developed 30 pictures from his digital camera. He was charged $2.70. What price did he pay per picture? • Divide. • Move decimal up and add zeros. • Isaiah paid $0.09 per picture.

  9. Example 4 Find the value of 5 ÷ 8. • Insert zeros into the problem after the decimal point. • Divide.

  10. Exit Problems Find the value of each expression. • 8.4(1.3) • 5(0.72) • 0.25(1.9) • 19.6 ÷ 7 • 7.2 ÷ 0.3

  11. Communication Prompt What part of dividing with decimals is the most challenging for you?

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