Lesson 17 Rational Numbers Equations Adding Rational Numbers

Lesson 17 Rational Numbers & Equations Adding Rational Numbers

Warm-Up Estimate the value of each expression. 1. – 6. 2 + 9. 9 2. 3. 18. 31 – (22. 9) 4. 5. – 0. 529 + (– 0. 44)

Adding Rational Numbers Target: Add positive and negative fractions and decimals.

Adding Positive and Negative Fractions 1. Write all mixed numbers as improper fractions. 2. Rewrite fractions using the least common denominator. If fractions are negative, place the negative sign on the number in the numerator. 3. Use integer rules to add the numerators and write the sum over the common denominator. 4. Write the fraction in simplest form. If the answer is negative, place the negative sign in front of the sum.

Example 1 Find the sum of � Write . fractions with a common denominator. � Rewrite the problem with the negative in the numerator. � Add the numerators. � Simplify. Move the negative in front of the fraction.

Adding Positive and Negative Decimals 1. Determine the sign of the answer. 2. Find the sum. • If the decimals have the same sign, add the absolute value of the numbers and use the sign determined above. • If the decimals have different signs, subtract the lesser absolute value from the greater absolute value and use the sign determined above.

Example 2 The change in the value of Digimaxx stock last week was points. This week the change in the stock’s value was points. Find the total change in value of Digimaxx stock over the last two weeks. � Write the problem. � Write as improper fractions. � Write with common denominators. � Put the negatives in the numerators. Add and simplify.

Example 3 Find the value of − 3. 52 + 14. 7. � Only one decimal is negative. The answer will have the sign of the number with the larger absolute value. � Line �− up the decimal points and subtract. 3. 52 + 14. 7 = 11. 18

Exit Problems Find each sum. 1. − 8. 2 + (− 2. 3) 2. 3. 4. 0. 49 + (− 0. 6)

Communication Prompt What are the steps you would go through to find the value of ?