Adding and Subtracting Real Numbers 1 2 Real

Adding and Subtracting Real Numbers 1 -2 Real Numbers Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Warm Up Simplify. 1. |– 3| 3 2. –|4| – 4 Write an improper fraction to represent each mixed number. 6 2 14 55 3. 4 3 4. 7 7 3 7 Write a mixed number to represent each improper fraction. 5. 12 5 Holt Algebra 1 2 2 5 6. 24 9 2 2 3

1 -2 Adding and Subtracting Real Numbers Objectives Add real numbers. Subtract real numbers. Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Vocabulary absolute value opposites additive inverse Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers All the numbers on a number line are called real numbers. You can use a number line to model addition and subtraction of real numbers. Addition To model addition of a positive number, move right. To model addition of a negative number move left. Subtraction To model subtraction of a positive number, move left. To model subtraction of a negative number move right. Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Example 1 A: Adding and Subtracting Numbers on a Number line Add or subtract using a number line. – 4 + (– 7) Start at 0. Move left to – 4. To add – 7, move left 7 units. + (– 7) 11 10 9 8 7 6 5 4 3 – 4+ (– 7) = – 11 Holt Algebra 1 – 4 2 1 0

1 -2 Adding and Subtracting Real Numbers Example 1 B: Adding and Subtracting Numbers on a Number line Add or subtract using a number line. 3 – (– 6) Start at 0. Move right to 3. To subtract – 6, move right 6 units. – 6 +3 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 3 – (– 6) = 9 Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Check It Out! Example 1 a Add or subtract using a number line. – 3 + 7 Start at 0. Move left to – 3. To add 7, move right 7 units. +7 – 3 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 – 3 + 7 = 4 Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Check It Out! Example 1 b Add or subtract using a number line. – 3 – 7 Start at 0. Move left to – 3. To subtract 7 move left 7 units. – 3 – 7 11 10 9 8 7 6 5 4 3 2 1 0 – 3 – 7 = – 10 Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Check It Out! Example 1 c Add or subtract using a number line. – 5 – (– 6. 5) Start at 0. Move left to – 5. To subtract negative 6. 5 move right 6. 5 units. – 5 – (– 6. 5) 8 7 6 5 4 3 2 1 0 1 2 – 5 – (– 6. 5) = 1. 5 Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers The absolute value of a number is the distance from zero on a number line. The absolute value of 5 is written as |5|. 5 units -6 -5 - 4 -3 -2 -1 0 1 2 3 4 5 6 |– 5| = 5 Holt Algebra 1 |5| = 5

1 -2 Adding and Subtracting Real Numbers Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Example 2 A: Adding Real Numbers Add. When the signs of numbers are different, find the difference of the absolute values: Use the sign of the number with the greater absolute value. The sum is negative. Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Example 2 B: Adding Real Numbers Add. y + (– 2) for y = – 6 y + (– 2) = (– 6) + (– 2) – 8 Holt Algebra 1 First substitute – 6 for y. When the signs are the same, find the sum of the absolute values: 6 + 2 = 8. Both numbers are negative, so the sum is negative.

1 -2 Adding and Subtracting Real Numbers Check It Out! Example 2 a Add. – 5 + (– 7) = 5 + 7 = 12 – 12 Holt Algebra 1 When the signs are the same, find the sum of the absolute values. Both numbers are negative, so the sum is negative.

1 -2 Adding and Subtracting Real Numbers Check It Out! Example 2 b Add. – 13. 5 + (– 22. 3) 13. 5 + 22. 3 – 35. 8 Holt Algebra 1 When the signs are the same, find the sum of the absolute values. Both numbers are negative so, the sum is negative.

1 -2 Adding and Subtracting Real Numbers Check It Out! Example 2 c Add. x + (– 68) for x = 52 First substitute 52 for x. x + (– 68) = 52 + (– 68) When the signs of the numbers are different, find the difference of the absolute values. 68 – 52 – 16 Holt Algebra 1 Use the sign of the number with the greater absolute value. The sum is negative.

1 -2 Adding and Subtracting Real Numbers Two numbers are opposites if their sum is 0. A number and its opposite are on opposite sides of zero on a number line, but are the same distance from zero. They have the same absolute value. Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers A number and its opposite are additive inverses. To subtract signed numbers, you can use additive inverses. Subtracting 6 is the same as adding the inverse of 6. Additive inverses 11 – 6 = 5 11 + (– 6) = 5 Subtracting a number is the same as adding the opposite of the number. Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Example 3 A: Subtracting Real Numbers Subtract. – 6. 7 – 4. 1 = – 6. 7 + (– 4. 1) To subtract 4. 1, add – 4. 1. When the signs of the numbers are the same, find the sum of the absolute values: 6. 7 + 4. 1 = 10. 8. = – 10. 8 Holt Algebra 1 Both numbers are negative, so the sum is negative.

1 -2 Adding and Subtracting Real Numbers Example 3 B: Subtracting Real Numbers Subtract. 5 – (– 4) 5 − (– 4) = 5 + 4 9 Holt Algebra 1 To subtract – 4 add 4. Find the sum of the absolute values.

1 -2 Adding and Subtracting Real Numbers Example 3 C: Subtracting Real Numbers Subtract. First substitute To subtract Rewrite of 10. Holt Algebra 1 for z. , add . with a denominator

1 -2 Adding and Subtracting Real Numbers Example 3 C Continued When the signs of the numbers are the same, find the sum of the absolute values: . Write the answer in the simplest form. Both numbers are negative, so the sum is negative. Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Check It Out! Example 3 a Subtract. 13 – 21 = 13 + (– 21) To subtract 21 add – 21. When the signs of the numbers are different, find the difference of the absolute values: 21 – 13 = 8. – 8 Holt Algebra 1 Use the sign of the number with the greater absolute value.

1 -2 Adding and Subtracting Real Numbers Check It Out! Example 3 b Subtract. To subtract – 3 1 add 3 1. 2 2 4 Holt Algebra 1 When the signs of the numbers are the same, find the sum of the absolute values: 3 1 + 1 = 4. 2 2 Both numbers are positive so, the sum is positive.

1 -2 Adding and Subtracting Real Numbers Check It Out! Example 3 c Subtract. x – (– 12) for x = – 14 x – (– 12) = – 14 – (– 12) – 14 + (12) First substitute – 14 for x. To subtract – 12, add 12. When the signs of the numbers are different, find the difference of the absolute values: 14 – 12 = 2. – 2 Holt Algebra 1 Use the sign of the number with the greater absolute value.

1 -2 Adding and Subtracting Real Numbers Example 4: Oceanography Application An iceberg extends 75 feet above the sea. The bottom of the iceberg is at an elevation of – 247 feet. What is the height of the iceberg? Find the difference in the elevations of the top of the iceberg and the bottom of the iceberg. elevation at top of iceberg 75 Minus – elevation at bottom of iceberg – 247 75 – (– 247) = 75 + 247 To subtract – 247, add 247. Find the sum of the = 322 absolute values. The height of the iceberg is 322 feet. Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Check It Out! Example 4 What if…? The tallest known iceberg in the North Atlantic rose 550 feet above the oceans surface. How many feet would it be from the top of the tallest iceberg to the wreckage of the Titanic, which is at an elevation of – 12, 468 feet? elevation at top of iceberg 550 Minus – elevation of the Titanic – 12, 468 550 – (– 12, 468) To subtract – 12, 468, 550 – (– 12, 468) = 550 + 12, 468 add 12, 468. Find the sum of the = 13, 018 absolute values. Distance from the iceberg to the Titanic is 13, 018 feet. Holt Algebra 1

1 -2 Adding and Subtracting Real Numbers Lesson Quiz Add or subtract using a number line. 2. – 5 – (– 3) – 2 1. – 2 + 9 7 Add or subtract. 3. – 23 + 42 19 4. 4. 5 – (– 3. 7) 8. 2 5. 6. The temperature at 6: 00 A. M. was – 23°F. At 3: 00 P. M. it was 18°F. Find the difference in the temperatures. 41°F Holt Algebra 1