Find each product Perform the indicated operations – ÷ – – 5 – ÷ 6 2 ALGEBRA 1 LESSON 1-2 Exponents and Order of Operations 1-2

= = = = – 7 = (3 + 12) – 7 = 15 – 7 = ÷ 2 = (6 1) ÷ 2 = 6 ÷ 2 = – = (4 – 2) + 9 = = – 5 – 4 = (10 – 5) – 4 = 5 – 4 = = (5 5) + 7 = = ÷ 6 2 = (30 ÷ 6) 2 = 5 2 = 10 ALGEBRA 1 LESSON 1-2 Exponents and Order of Operations Solutions 1-2

Simplify – – 14 3 = – 14 3Simplify the power: 6 2 = 6 6 = 36. = – 42Multiply 14 and 3. = 68 – 42Add and subtract in order from left to right. = 26Subtract. ALGEBRA 1 LESSON 1-2 Exponents and Order of Operations 1-2

Evaluate 5x = 3 2 ÷ p for x = 2 and p = 3. 5x ÷ p = ÷ 3Substitute 2 for x and 3 for p. = ÷ 3Simplify the power. = Multiply and divide from left to right. = 13Add. ALGEBRA 1 LESSON 1-2 Exponents and Order of Operations 1-2

Find the total cost of a pair of jeans that cost $32 and have an 8% sales tax. total cost original price sales tax C=p+r p sales tax rate C = p + r p = Substitute 32 for p. Change 8% to 0.08 and substitute 0.08 for r. = Multiply first. = 34.56Then add. The total cost of the jeans is $ ALGEBRA 1 LESSON 1-2 Exponents and Order of Operations 1-2

Simplify 3(8 + 6) ÷ (4 2 – 10). 3(8 + 6) ÷ (4 2 – 10) = 3(8 + 6) ÷ (16 – 10)Simplify the power. = 3(14) ÷ 6Simplify within parentheses. = 42 ÷ 6Multiply and divide from left to right. = 7Divide. ALGEBRA 1 LESSON 1-2 Exponents and Order of Operations 1-2

Evaluate each expression for x = 11 and z = 16. a. (xz) 2 = (176) 2 Simplify within parentheses. Multiply. = = 2816= 30,976Simplify. (xz) 2 = (11 16) 2 Substitute 11 for x and 16 for z. xz 2 = ALGEBRA 1 LESSON 1-2 Exponents and Order of Operations 1-2 b. xz 2

Simplify 4[(2 9) + (15 ÷ 3) 2 ]. 4[(2 9) + (15 ÷ 3) 2 ] = 4[18 + (5) 2 ]First simplify (2 9) and (15 ÷ 3). = 4[ ]Simplify the power. = 4[43]Add within brackets. = 172Multiply. ALGEBRA 1 LESSON 1-2 Exponents and Order of Operations 1-2

A carpenter wants to build three decks in the shape of regular hexagons. The perimeter p of each deck will be 60 ft. The perpendicular distance a from the center of each deck to one of the sides will be 8.7 ft. = 3(261)Simplify the fraction. = 783Multiply. The total area of all three decks is 783 ft 2. A = 3 ( ) pa 2 = 3 ( ) Substitute 60 for p and 8.7 for a. = 3 ( ) Simplify the numerator. ALGEBRA 1 LESSON 1-2 Exponents and Order of Operations 1-2 Use the formula A = 3 ( ) to find the total area of all three decks. pa 2

ALGEBRA 1 LESSON 1-2 Simplify each expression – ( ) – [(1 + 5) 2 – (18 ÷ 3)] Evaluate each expression. 4. 4x + 3y for x = 2 and y = p 2 + 3s for p = 3 and s = xy 2 + z for x = 3, y = 6 and z = Exponents and Order of Operations 1-2

Write each decimal as a fraction and each fraction as a decimal (For help, go to skills handbook page 725.) ALGEBRA 1 LESSON 1-3 Exploring Real Numbers

ALGEBRA 1 LESSON 1-3 Exploring Real Numbers = = = = = = = 3 = 3 = 3 or = = = 5. = 2 ÷ 5 = = 3 ÷ 8 = = 2 ÷ 3 = = 3 + (5 ÷ 9) = Solutions 1 20

Name the set(s) of numbers to which each number belongs. a. –13b integers rational numbers ALGEBRA 1 LESSON 1-3 Exploring Real Numbers 1-3

Which set of numbers is most reasonable for displaying outdoor temperatures? integers ALGEBRA 1 LESSON 1-3 Exploring Real Numbers 1-3

Determine whether the statement is true or false. If it is false, give a counterexample. All negative numbers are integers. The statement is false. A negative number can be a fraction, such as –. This is not an integer ALGEBRA 1 LESSON 1-3 Exploring Real Numbers 1-3

Write –, –, and –, in order from least to greatest. – = –0.75Write each fraction as a decimal. – = –0.583 – = – From least to greatest, the fractions are –, –, and – –0.75 < –0.625 < –0.583Order the decimals from least to greatest. ALGEBRA 1 LESSON 1-3 Exploring Real Numbers

Find each absolute value. a. |–2.5|b. |7| –2.5 is 2.5 units from 0 on a number line. 7 is 7 units from 0 on a number line. |–2.5| = 2.5 |7| = 7 ALGEBRA 1 LESSON 1-3 Exploring Real Numbers 1-3

ALGEBRA 1 LESSON 1-3 Name the set(s) of numbers to which each given number belongs. 1. – Use to compare Find |– | rational numbersirrational numbersnatural numbers, whole numbers integers, rational numbers –– 7 12 > < 7 12 Exploring Real Numbers

Evaluate – – 4z 2 for x = 4, y = –2, and z = –4. – – 4z 2 = – 4(–4) 2 Substitute 4 for x, –2 for y, and –4 for z. xyxy –4 –2 = – 4(16)Simplify the power. –4 –2 = 2 – 64Divide and multiply. = –62Subtract. ALGEBRA 1 LESSON 1-6 Multiplying and Dividing Real Numbers 1-6 xyxy

Evaluate for p = and r = –. = –2Simplify. = p ÷ rRewrite the equation. prpr = ÷ Substitute for p and – for r ( – ) = Multiply by –, the reciprocal of – ( – ) ALGEBRA 1 LESSON 1-6 Multiplying and Dividing Real Numbers 1-6 prpr

ALGEBRA 1 LESSON 1-6 Simplify. 1. –8(–7)2. –6(–7 + 10) – 4 Evaluate each expression for m = –3, n = 4, and p = – p4. (mp) 3 5. mnp 6.Evaluate 2a ÷ 4b – c for a = –2, b = –, and c = –. 56 – 22 – Multiplying and Dividing Real Numbers 1-6 8mn8mn

ALGEBRA 1 LESSON 1-7 (For help, go to Lessons 1-2 and 1-6.) Use the order of operations to simplify each expression. 1.3(4 + 7)2.–2(5 + 6)3.–1(–9 + 8) 4.–0.5(8 – 6)5. t(10 – 4)6.m(–3 – 1) The Distributive Property

ALGEBRA 1 LESSON 1-7 The Distributive Property 1-7 ( ) 1. 3(4 + 7) = 3(11) = –2(5 + 6) = –2(11) = –22 3. –1(–9 + 8) = –1(–1) = 1 4. –0.5(8 – 6) = –0.5(2) = –1 5. t(10 – 4) = t(6) = (6)t = 6 t = 3t 6. m(–3 – 1) = m(–4) = –4m Solutions

Use the Distributive Property to simplify 26(98). ALGEBRA 1 LESSON (98) = 26(100 – 2)Rewrite 98 as 100 – 2. = 26(100) – 26(2)Use the Distributive Property. = 2600 – 52Simplify. = 2548 The Distributive Property 1-7

Find the total cost of 4 CDs that cost $12.99 each. 4(12.99) = 4(13 – 0.01)Rewrite as 13 – = 4(13) – 4(0.01)Use the Distributive Property. = 52 – 0.04Simplify. = The total cost of 4 CDs is $ ALGEBRA 1 LESSON 1-7 The Distributive Property 1-7

Simplify 3(4m – 7). 3(4m – 7) = 3(4m) – 3(7)Use the Distributive Property. = 12m – 21Simplify. ALGEBRA 1 LESSON 1-7 The Distributive Property 1-7

Simplify –(5q – 6). –(5q – 6) = –1(5q – 6)Rewrite the expression using –1. = –1(5q) – 1(–6)Use the Distributive Property. = –5q + 6Simplify. ALGEBRA 1 LESSON 1-7 The Distributive Property 1-7

Simplify –2w 2 + w 2. –2w 2 + w 2 = (–2 + 1)w 2 Use the Distributive Property. = –w 2 Simplify. ALGEBRA 1 LESSON 1-7 The Distributive Property 1-7

Relate: –6 times the quantity 7 minus m Write:–6 (7 – m) Write an expression for the product of –6 and the quantity 7 minus m. –6(7 – m) ALGEBRA 1 LESSON 1-7 The Distributive Property 1-7

ALGEBRA 1 LESSON 1-7 Simplify each expression (299) 2. 4(x + 8) 3. – 3(2y – 7) 4. –(6 + p) a + 2b – 4c + 3.1b – 4a 6. Write an expression for the product of and the quantity b minus x + 32– 6y + 21 – 6 – p –2.7a + 5.1b – 4c b – ( ) The Distributive Property

ALGEBRA 1 LESSON 1-8 (For help, go to Lessons 1-4 and 1-6.) Simplify each expression (9 + 2)2.3 (–2 5) –4(7)(–5)5.– (–4) x – 28.2t – 8 + 3t9.–5m + 2m – 4m Properties of Real Numbers 1-8

ALGEBRA 1 LESSON (9 + 2) = 8 + (2 + 9) = (8 + 2) + 9 = = (–2 5) = 3 (–10) = – = = = –4(7)(–5) = –4(–5)(7) = 20(7) = – (–4) = –6 + (–4) + 9 = – = – = = 1 3 = x – 2 = 3 + (–2) + x = 1 + x 8. 2t – 8 + 3t = 2t + 3t – 8 = (2 + 3)t – 8 = 5t – 8 9. –5m + 2m – 4m = (–5 + 2 – 4)m = –7m Properties of Real Numbers Solutions 1-8

Name the property each equation illustrates. a. 3 a = a 3 b. p 0 = 0 c. 6 + (–6) = 0 ALGEBRA 1 LESSON 1-8 Properties of Real Numbers 1-8 Commutative Property of Multiplication, because the order of the factors changes Multiplication Property of Zero, because a factor multiplied by zero is zero Inverse Property of Addition, because the sum of a number and its inverse is zero

Suppose you buy a shirt for $14.85, a pair of pants for $21.95, and a pair of shoes for $ Find the total amount you spent = Commutative Property of Addition = ( ) Associative Property of Addition = Add within parentheses first. = 61.95Simplify. The total amount spent was $ ALGEBRA 1 LESSON 1-8 Properties of Real Numbers 1-8

Simplify 3x – 4(x – 8). Justify each step. 3x – 4(x – 8) = 3x – 4x + 32Distributive Property = (3 – 4)x + 32Distributive Property = –1x + 32Subtraction = –x + 32Identity Property of Multiplication ALGEBRA 1 LESSON 1-8 Properties of Real Numbers 1-8

ALGEBRA 1 LESSON 1-8 Name the property that each equation illustrates. 1. 1m = m2. (– 3 + 4) + 5 = – 3 + (4 + 5) 3. –14 0 = 0 4. Give a reason to justify each step. Iden. Prop. Of Mult.Assoc. Prop. Of Add. Mult. Prop. Of Zero a. 3x – 2(x + 5) = 3x – 2x – 10Distributive Property b.= 3x + (– 2x) + (– 10) Definition of Subtraction c.= [3 + (– 2)]x + (– 10)Distributive Property d.= 1x + (– 10)Addition e.= 1x – 10Definition of Subtraction f. = x – 10 Identity Property of Multiplication Properties of Real Numbers 1-8