Math.

24 Step 1: Find/Simplify Anything Involving Parentheses that 7² really means 7× 7, which is 49. 3 (7² + 5) ÷ 6 - 3 Is now … 3(49 + 5) ÷ 6 - 3 Since there is still an expression in parentheses, we add the two numbers in parentheses. 3(49 + 5) ÷ 6, 3 Which is now … 3(54) ÷ 6 - 3 Step 2: Once Parentheses Are Complete, Move On Since there are no more operations in parentheses and no more exponents, we now move on to multiplication and division, whichever comes first working from left to right. 3(54) ÷ 6, 3 Becomes: 162 ÷ 6 - 3 We then perform the division. 162 ÷ 6 - 3 And get: 27 - 3 Step 3: Continue Following Order of Operations Since we only have one operation left, we can solve it. 27, 3 = 24

53.137 Step 1: Line up the numbers by their decimal point. 68.567, 13, 2.43 Would look like: 68.567 13 - 2.43 Now all of our place values are lined up. Step 2: Fill in any empty spots with a placeholder zero. 68.567 13.000 - 2.430 Step 3: Subtract like normal. 68.567 13.000 - 02.430 53.137 68.567, 13, 2.43 is equal to 53.137

17 marbles. Step 1: Interpret the problem First, we must understand what is happening in this situation. To find the number of marbles that Steven has, we need to multiply the number of marbles Max has by 0.2. Step 2: Calculate the number of marbles that Max has Since Max has 2.5 times the number of marbles Jacob has, we can multiply the number of marbles Jacob has by 2.5. with decimals, we pretend as if the decimals are not there. We do not line up numbers by their decimal point. number of marbles of Jacob × number of marbels of Max = total number of marbels Max has 34 × 2.5 Multiply Like Normal and fill in any empty spots with a placeholder zero. 34 × 2.5 170 + 680 850 Put the Decimal Place in the Right Location Since there is 1 number to the right of the decimal point in the problem, there will be 1 number that is behind the decimal in the product. Therefore, the decimal point goes between 5 and 0. 85.0 Since the 0 is after the decimal point, it can also be dropped since it has no value. So, Max has 85 marbles. Step 3: Calculate the number of marbles that Steven has To find the number of marbles Steven has, we can multiply the number of marbles Max has by 0.2. with decimals, we pretend as if the decimals are not there. We do not line up numbers by their decimal point. total number of marbels of Max × number of marbels of Steven = total number of marbels Steven has 85 × 0.2 Multiply Like Normal and fill in any empty spots with a placeholder zero. 85 × 0.2 170 + 000 170 Put the Decimal Place in the Right Location Since there is one number to the right of the decimal point in the problem, there will be one number that is behind the decimal in the product. Therefore, the decimal point goes between the 7 and the 0. 17.0 Since the 0 is after the decimal point, it can also be dropped since it has no value. So, Steven has 17 marbles.

Adding two mixed numbers we can add the whole parts and then the fractional parts. 1 3/10 + 2 ⅝ = (1 + 2) + ( 3/10 + ⅝ ) Step 1: Add the Whole parts Together 1 + 2 = 3 Step 2: Find the Least Common Multiple of the denominators Since 10 and 8 are the denominators of the fractions, we will find the LCM of 10 and 8. Factors of: 10: 10, 20, 30, 40, 50 8: 8, 16, 24, 32, 40 The least common multiple of 10 and 8 is 40. Step 3: Create equivalent fractions using the LCM as the new denominator Each fraction will now have a denominator of 40. Let’s start with 3/10. Since 10 × 4 = 40, we have to multiply the numerator by the same number. 3/10 = (3 × 4)/(10 × 4) = 12/40 Let’s create an equivalent fraction for ⅝ with 40 as the new denominator. Since 8 × 5 = 40, we will multiply the numerator by the same number. ⅝ = (5 × 5)/(8 × 5) = 25/40 Step 4: Add the fractions together (simplify or convert to a mixed number if necessary) Since our fractions now have the same denominator, we can add them together. 12/40 + 25/40 = (12 + 25)/(40) = 37/40 Step 5: Add the whole parts and the fractional parts. 3 + 37/40 = 3 37/40 Answer: 3 37/40

Step 1: Convert the mixed numbers into improper fractions 3 ⅝ = (3×8 + 5)/(8) = 29/8 2 ⅖ = (2×5 + 2)/(5) = 12/5 3 ⅝ × 2 ⅖ now becomes 29/8 × 12/5 Step 2: Cross Simplify [If Applicable] and multiply When we look at the fractions to cross-simplify, we find that 12 and 8 have a common factor of 4. We can now reduce the fraction by 4. 29/8 × 12/5 = (29× (12 ÷ 4))/((8 ÷ 4) × 5) =(29× 3)/(2×5) = 87/10 Step 3: Simplify [If Possible] and convert into a mixed number Convert the improper fraction into a mixed number. 87/10 = 87 ÷ 10 8 7/10 Answer: 8 7/10

254,604 Step 1: Determine the population growth in 2020. We need to find what is ⅙ of 155,880. This is the population growth in 2020. The keywords “has grown by ⅙ ” point to multiplication. 155,880 × ⅙ = (155,880)/(1) × ⅙ = (155,880 × 1)/(1 × 6) = (155,880)/(6) =155,880 ÷6 = 25,980 Step 2: Find the total population in 2020. The total population in 2020 is the population in 2019 plus the population growth in 2020. 155,880 + 25,980 = 181,860 Step 3: Determine the population growth in 2021. We need to find what is ⅖ of 181,860. Again, we find the keywords “has grown by ⅖ ” to be sure that we should use multiplication. 181,860 × ⅖ = (181,860)/(1) × ⅖ = (181,860 × 2)/(1 × 5) = (363,720)/(5) =363,720 ÷5 = 72,744 Step 4: Find the total population in 2021. The total population in 2021 is the population in 2020 plus the population growth in 2021. 181,860 + 72,744 = 254,604 The city’s population in 2021 is 254,604 people.

Step 1: Understand the Fraction Pieces The numerator (top number) is 15 and the denominator (bottom number) is 8. The fraction bar shows division. We can write this division problem as: 15 divided by 8 or 15÷ 8. Because 15 can also be written as 15.0, this division problem can be set up as: {array}{r} 8 {longdiv}{15.000} Step 2: Complete the division Eight does not go into 1 so we move to the next number inside the division bar. Eight goes into 15 one time so we put a 1 over the 5. {array}{r} 1 \ 8 {longdiv}{15.000} 8 × 1 = 8 so we subtract 8 from 15 and get 7. {array}{r} 1. \ 8 {longdiv}{15.000} -8 70 {.000} We drop down the 0 and we also keep the decimal point where it is. Then we ask: How many times does 8 go into 70? Because 8× 8 = 64, 8 goes into 70, eight times. {array}{r} 1.8 \ 8 {longdiv}{15.000} -8 70 {.000} -64 6 {.00} We still have a remainder so we bring down the next zero and keep dividing. Because 8× 7 = 56, 8 goes into 60 seven times. {array}{r} 1.87 \ 8 {longdiv}{15.000} -8 70 {.000} -64 60 {.00} -56 {.00} 4 Because 8 × 5 = 40, 8 goes into 40 five times. {array}{r} 1.875 \ 8 {longdiv}{15.000} -8 70 {.000} -64 60 {.00} 56 {-56} 40 -40 {.00} 0 {.00} Forty minus 40 is zero so our answer is 1.875. 15/8 is 1.875 when written as a decimal.

Step 1: Read the Decimal Out Loud A few reminders: a. We read everything to the left of the decimal by itself. b. The decimal says the word “and”. c. We then read everything to the right of the decimal. d. We end it by saying the place value of the last number. Therefore, 0.932 is said as: Nine Hundred Thirty-two Thousandths Step 2: Write the Fraction You Read Out Loud Zero came before the decimal, so there is no whole number. We also said nine hundred thirty-two thousandths out loud. Nine hundred thirty-two would be our numerator and one thousand would be our denominator. 932/1000 Let’s check and see if the fraction can be simplified. 932 and 1000 have a factor of 4 in common so we can simplify the fraction by dividing both the numerator and denominator by a common factor, 4. 932/1000 ÷ 4/4 = (932 ÷ 4)/(1000 ÷ 4) = 233/250 Let’s check and see if the fraction can be further simplified. Because the only factor that 233 and 250 have in common is 1, the fraction is completely simplified. 0.932 is 233/250 when written as a fraction.

Step 1: Interpret the Problem In this problem, we are given a monetary value that incurs a fee percentage and a tip percentage to find the final cost amount. We will do this in two parts. First, we will determine the fee percentage amount and add that to the initial monetary value. When calculating a percentage amount, we multiply the percentage by the given total. Fee Percentage × Initial Total = Fee Percentage Amount Step 2: Convert the fee percent to a decimal We do not use actual percentages when solving math problems, so we have to change 7% into a decimal. To change a percent into a decimal, we divide the percent by 100, which is the same as moving the decimal two spots to the left. Since there is no decimal in 7, we assume it is to the right of the ones place, so: 7 % = 7. % Now we can slide the decimal point two spaces left. Note that there will be a space between the decimal and the 7 that is filled by a 0. 7. % → 0.07 7% as a decimal is 0.07 Step 3: Determine the fee percentage amount and find the first total Now that our percent has been turned into a decimal, we can multiply: 0.07 × 122.19 = 8.5533 *Note: We will not be rounding here; we round at the end of the problem. To determine our first total, we add the percentage fee amount to our initial amount. 122.19 + 8.5533 = 130.7433 Step 4: Convert the tip percent to a decimal We do not use actual percentages when solving math problems, so we have to change 15% into a decimal. To change a percent into a decimal, we divide the percent by 100, which is the same as moving the decimal two spots to the left. Since there is no decimal in 15, we assume it is to the right of the ones place, so: 15 % = 15. % Now we can slide the decimal point two spaces left. 15. % → 0.15 15% as a decimal is 0.15. Step 5: Determine the tip percentage amount and find the final total that we are finding the tip based on the bill after the service fee, so we will use the total amount calculated in Step 3 here. Now that our percent has been turned into a decimal, we can multiply it with our first total: 0.15 × 130.7433 = 19.611495 *Note: We will not be rounding here; we round at the end of the problem. To determine our final total, we add the tip percentage amount to our first total. 130.7433 + 19.611495 = 150.354795 When a math problem has a final answer representing a monetary quantity, the final answer must be rounded to the nearest hundredth, unless otherwise directed. 150.354795 = $ 150.35 The final total of Oscar’s order was $150.35.

Step 1: Interpret the Problem Calculating the patient’s original heart rate before the drop requires some manipulation of the percentages. We need to consider that the original heart rate represents 100%. If the original heart rate represents 100% we must calculate how much of the original heart rate is remaining after a percent drop. Given the heart rate dropped by 30%, we know, 100%, 30% = 70 % Therefore, the remaining heart rate percent is 70%. Step 2: Turn The Percent Into a Decimal We never use percentages in our actual math problems, so we first must turn our percentages into a decimal. To turn a percentage into a decimal, we divide by 100, which is the same as moving the decimal point two spaces to the left. 70% = 70. % 70. % ÷ 100 = 0.70 70% as a decimal is 0.70. zeros at the end of a number after a decimal does not add any value, so we can just write it as.70. 0.70 = 0.7 Step 3: Determine the Original Heart Rate We know 63 = 70 %, and we are looking for the value that represents 100%. This means whatever 100% is, will be more than 63. Once you calculate the percent paid and turn that into a decimal, we can use the rule below to calculate the original price of an item by using division. Current Heart Rate ÷ Decimal = Original Heart Rate 63 ÷ 0.7 = 90 The patient’s heart rate before the drop was 90 beats per minute.

79.4 % Step 1: Calculate Part (Non-100 %) In reading the prompt, the first step is to identify the amounts needed to be added to calculate the portion of the budget that has already been spent, which represents the part (non-100%). 75 + 65 = 140 Making 140 the part (non-100 %). Step 2: Divide the Part (Non-100 %) by the Whole (100 %) To find the percentage, we have to divide the part of the total available amount by the total amount available. In this case, the non-100 % part that we have, 140, will be divided by the total amount available, which represents 100 %, which is 680 140 ÷ 680 = 0.2058823529 We can round this off to the third-place value. Check your answer choices to see if numbers were rounded to a different place value. So let’s look at the third-place value: 0.2058823529 We look to the right and see an 8. Since an 8 is 5 or more, that means the underlined digit goes up by one so the 5 becomes a 6 . 0.206 Every other number to the right of the 5 would turn to 0, and since they would have no value, we can get rid of them. Step 3: Multiply by 100 Now that we have our decimal, we have to turn it into a percent. we turn a decimal into a percent by multiplying it by 100, which is the same as moving the decimal point two spots to the right. 0.206 × 100 = 20.6 % This tells us how much of the budget has already been spent. Finally, we have to find the percentage of what she has left. Step 4: Subtract Budget Spent from Total Budget The event coordinator spent 20.6 % of her budget. In order to find the percentage that is left we will subtract the percentage she spent from 100 %. 100 %, 20.6 % = 79.4 % The event coordinator has 79.4 % of her budget left.

When solving equations, remember to use: Inverse Operations, operations that undo one another. So if subtraction is present, we use addition, etc. What we do to one side we MUST do to the other Our goal is to ISOLATE the variable which means to have JUST one of the variables. Step 1: Distribute In this problem, we are first going to remove the parentheses from the equation. To do this we must multiply the term in front of each parenthesis by each term inside its respective parenthesis. 2(3x, 1), 2 (x + 5) = 12 6x, 2, 2x, 10 = 12 Step 2: Combine Any Like Terms Now we can rearrange the equation so that we can combine all whole numbers and all terms with the same variable. Also, remember to include the sign IN FRONT of each term. 6x, 2, 2x, 10 = 12 If we rearrange, it becomes: 6x, 2x, 2, 10 = 12 This simplifies to: 4x, 12 =12 Step 3: Solve the Equation When we solve equations, we can start by applying the inverse of the constant term on both sides of the equation. The constant is the term with no variable attached to it. We see that 12 is being subtracted from 4x, the -12 is the constant term because there is no x attached, so we have to undo subtraction using addition. Therefore we are going to add 12 to both sides. 4x, 12 + 12 = 12 + 12 Which then becomes: 4x = 24 Now we can solve: Since 4 is being multiplied by x, we have to undo the multiplication using division. Therefore we are going to divide both sides by 4. (4x)/(4) = 24/4 This simplifies to: 1x = 6 Since 1x and x are the same thing, our final answer is: x = 6

Step 1: Manipulate the Equations so that a term can cancel out When we have a system of equations in which both equations are written in the form ax + by = c, we can solve the system using the method called ELIMINATION. To use elimination we need to make sure that one of the pairs of variables cancels up to zero. Looking at the system we notice that the two x terms are 2x and 4x and the two y -terms are 5y and 3y. Neither of the pairs cancels up to zero so there is some work to do. We need to decide what to multiply the equations by so that we can make one pair cancel up to zero. If we look at the x -terms we can multiply 2x by -2 and it will become -4x which if added to the other term, 4x, will cancel up to zero. This means that we will multiply all terms in the top equation by -2: -2× (2x + 5y) = 19× -2 -4x, 10y = -38 So our system becomes, -4x, 10y = -38 4x + 3y = 17 Step 2: Add the Equations and solve Once we have one pair of the variable terms cancel up to zero we can add the equations to each other. We add x-term to x -term and y-term to y -term vertically. {ccc}-4x, 10y = -38 4x + 3y = 17 x - 7y = -21 So our x -terms zero out (cancel out) giving us an equation that only has y so we can solve for y. -7y = -21 Since -7 is being multiplied by y, we have to undo the multiplication by using division. Therefore we are going to divide both sides by -7. large (-7y)/(-7) = (-21)/(-7) This simplifies to: 1y = 3 Since 1y and y are the same thing, our answer is: y = 3 Step 3: Find the value of the other term Now that we have the value of the y-term we can substitute it into either of the original equations to find the value of the x -term. 2x + 5y =19 2x + 5(3) = 19 2x + 15 = 19 2x + 15 -15 = 19 -15 2x = 4 Since 2 is being multiplied by x, we have to undo the multiplication by using division. Therefore, we are going to divide both sides by 2. (2x)/(2) = 4/2 This simplifies to: 1x =2 Since 1x and x are the same thing, our answer is: x = 2 So for this system, our solution is x = 2 and y = 3.

154.23 Step 1: Your Rounding Rules Underline the place value you are rounding to. Look to the right of the number you have underlined. If you see a 5-9, the underlined digit goes up by 1. If you see a 0-4, the underlined digit stays the same. Anything to the right of the underlined digit turns to 0. Anything to the left of the underlined digit usually stays the same (unless a 9 was rounded up) Step 2: Check Out Each Answer Choice To Determine Which Was Rounded Correctly and is the largest number Answer choice: 153.62 Underline 3 to round the number to the nearest whole number. 153.62 Since the number to the right of 3 is 6, 3 goes up to 4. Any number to the right of 4 turns to 0 and any number to the left stays the same. 154.00 153.62 does round to 154 but must be compared to the other answer choices to see if it is the largest number that rounds to 154. Answer choice: 154.52 Underline 4 to round the number to the nearest whole number. 154.52 Since the number to the right of 4 is 5, 4 goes up to 5. Any number to the right of 5 turns to 0 and any number to the left stays the same. 155.00 To the nearest whole number, 154.52 rounds to 155 not 154 so, this answer choice is not Answer choice: 153.61 Underline 3 to round the number to the nearest whole number. 153.61 Since the number to the right of 3 is 6, 3 goes up to 4. Any number to the right of 4 turns to 0 and any number to the left stays the same. 154.00 153.61 does round to 154 but must be compared to the other answer choices to see if it is the largest number that rounds to 154. Answer choice: 154.23 Underline 4 to round the number to the nearest whole number. 154.23 Since the number to the right of 4 is 2, 4 stays the same. Any number to the right of 4 turns to 0 and any number to the left stays the same. 154.00 154.23 does round to 154 but must be compared to the other answer choices to see if it is the largest number that rounds to 154. Step 3: Compare the numbers in the answer choices that round to 154 to see which is the largest. Comparing answers, we have 153.61 < 153.62 < 154.23, Therefore, 154.23.

Step 1: Interpret the question To find the average in this scenario, we need to take the ratio of the total cost of the fruits and vegetables to the total number of pounds of them. Therefore, we have a division between the total cost and the total number of pounds. The total cost of the fruits and vegetables will be the sum of their costs. Total cost: 5.85 + 9 The total number of pounds of fruits and vegetables will be the sum of their weights. Total number of pounds: 3 + 2.7 To get the average cost per pound for the fruits and vegetables, we divide the 2 totals. Average cost per pound = (Total cost) ÷ (Total number of pounds) Step 2: Round our numbers Since the question asks “approximate total cost…” we have to round some of these numbers before we add them together. The numbers $5.85 and 2.7 will need to be rounded. $ 5.85 will be rounded to the nearest ones place. Let’s round $ 5.85 We underline the place value we are rounding to: 5.85 When we look to the right of the 5 we see an 8, which tells us the underlined digit goes up by one. So, 5 goes to 6. Everything to the right of 6 turns to 0. 6.00 Since the zero after the decimal has no value, we can eliminate it. 5.85 rounds to 6. 2.7 will also be rounded to the nearest ones place. Let’s round 2.7. We underline the place value we are rounding to: 2.7 When we look to the right of the 2 we see a 7, which tells us the underlined digit goes up by one. So, 2 goes to 3. Everything to the right of 3 turns to 0. 3.0 Since the zero after the decimal has no value, we can eliminate it. 2.7 rounds to 3. Step 3: Solve First, find the total cost of the fruits and vegetables. 6+ 9 = 15 So, the total cost of the fruits and vegetables is $15. Next, find the total weight of the fruits and vegetables. 3 + 3 = 6 So, the total weight of the fruits and vegetables is 6 pounds. Finally, we get the average cost per pound of the fruits and vegetables by dividing the total cost by the number of pounds. 15 ÷ 6 = 2.5 So, the average cost per pound for fruits and vegetables is $2.50

Step 1: Interpret the Problem and Set Up a Proportion In this problem, we know that 14 devices were collected in 3 shifts. We are trying to find the number of devices that were collected over 18 shifts. When we set up the proportion, the units must match. Since we are dealing with devices per shift, the number of devices will be in the numerator and shifts will be in the denominator. What is missing is the number of devices. So we have: (14 devices)/(3 shifts) = (x devices)/(18 shifts) 14/3 = (x)/(18) Step 2: Cross-multiply and Solve the Equation To find the x, we multiply one denominator by the opposite numerator. 14 × 18 = 3 × x This gets simplified to: 252 = 3x Now we can solve for x: 252/3 = (3x)/(3) 252 ÷ 3 = 84 x = 84 There were 84 devices in the batch.

Step 1: Interpret the Problem and Set Up a Proportion In this problem, we know that $17 is equivalent to 266 Egyptian Pounds. We are trying to find the number of pounds that could be obtained with $121 at the same exchange rate. When we set up the proportion, the units must match. Since we are dealing with dollars per pound, dollars will be in the numerator and pounds will be in the denominator. Let x be the number of pounds that is equivalent to 121 dollars. So we have: ($17)/(266 pounds) = ($121)/(x pounds) 17/266 = (121)/(x) Step 2: Cross-multiply and Solve the Equation To find the x, we multiply one denominator by the opposite numerator. 17 × x = 121 × 266 This gets simplified to: 17x = 32,186 Now we can solve for x: (17x)/(17) = (32,186)/(17) 32,186 ÷ 17 = 1,893.3 x = 1,893.3 $121 can buy 1,893.3 Egyptian Pounds.

Step 1: Translate Given Information into Algebra Expression For this question, we are looking to write an expression to represent a certain total. The starting amount will be an unknown amount and every other amount will be written in terms of the initial amount. In the given prompt, we know that Orlando drove an unknown number of miles during his first week, so the number of miles he drove that week will be assigned a variable x. Number of miles driven first week → x We are also given that Orlando drove fifteen more miles in his second week in comparison to the number he drove in the first week. This means, Number of miles driven in the second week → x + 15 Finally, we are told that he drove twenty-five fewer miles in his third week when compared to the first week. Since he drove fewer miles, this means we will be subtracting 25 miles from the amount he drove the first week which is represented by x. Number of miles driven in third week → x, 25 Step 2: Determine Total Now that we have all the individual expressions, we can find the final sum. We are asked to write an expression that represents the total number of miles that Orlando drove in the 3-week road trip. To find the total, we need to find the expression that adds all the expressions and simplify. x + x +15 + x, 25 We can now rearrange the expression to group like terms together. to include the sign IN FRONT of a term. { x}+{x}+ {15} +{x} -{25} Now becomes: {x}+{x}+{x}+{15}-{25} The expression becomes: 3x, 10

the following inequalities: <, less than >, greater than ≤, less than or equal to ≥, greater than or equal to Step 1: Interpret the Prompt In this type of scenario, you are given the items and the price of each one. The first step is to define the variables that will represent the number for each item. s = number of shirts bought p = number of pants bought The cost of a shirt is $6.50, therefore, the expression that represents the total Thomas will spend on the shirts = 6.50 s The cost of pants is $12, therefore, the expression that represents the total Thomas will spend on pants = 12 p Step 1: Write Your Inequality In this case, we are told he has $64, which means he can spend at most $64. This means he can spend less than or equal to $64 so we know the symbol “<” will be involved. Knowing that the total he will spend is the sum of what he spends on shirts (6.50s) and the total he will spend on pants ( 12p ), now we can construct our inequality: 6.50s + 12p < 64

When solving inequalities remember to use: Inverse Operations, operations that undo one another. So if subtraction is present, we use addition, etc. What we do to one side we MUST do to the other Our goal is to ISOLATE the variable which means to have JUST one of the variables. Step 1: Get all x -terms to one side of the inequality In this inequality, we notice that there are x -terms on both sides of the inequality symbol so we can start by applying the inverse of one of the x -terms on both sides of the inequality. We see that there is a 6x on the right side of the inequality, so we can apply the additive inverse of 6x on both sides so that we only have x -terms on the left side of the equation. Therefore we are going to subtract 6x from both sides. 4x, 12, 6x ≥ 6x + 2, 6x Which then becomes: -2x, 12 ≥ 2 Step 2: Solve the Inequality When we solve inequalities, we can start by applying the inverse of the constant term on both sides of the equation. The constant is the term with no variable attached to it. We see that 12 is being subtracted from the -2x, the -12 is the constant term because there is no x attached, so we have to undo the subtraction by using addition. Therefore we are going to add 12 to both sides. -2x, 12 + 12 ≥ 2 + 12 Which then becomes: -2x ≥ 14 Now we can solve: Since -2 is being multiplied by x, we have to undo the multiplication by using division. Therefore we are going to divide both sides by -2. (-2x)/(-2) ≥ (14)/(-2) There is an important rule to remember when we divide inequalities by a negative number. When an inequality is divided by a negative number the inequality symbol switches direction as shown below: 1x ≤ -7 Since 1x and x are the same thing, our final answer is: x ≤ -7

The Rules of Simplifying Expressions: You are only able to combine like terms, which means you can combine the coefficients of terms that have the same variable with the same exponent. If the expression includes parentheses, the first step is to apply the distributive property. The distributive property allows you to multiply the coefficient outside the parentheses to every term inside of the parentheses. After you distribute, there will be no more parentheses and you will be able to combine like terms. Step 1: Apply the Distributive Property There is a -5 outside of the parentheses, which we will multiply with both terms inside the parentheses. -4 -5 (x, 3) + 5 Note, -5 × x equals -5x and -5x, 3 equals +15. -4, 5x + 15 + 5 Step 2: Group-like Terms We can now rearrange the expression where we combine our like terms. -4 - 5x + 15 + 5 Now we rearrange group-like terms together: -5x, 4 + 15 + 5 you MUST include the sign that comes in front of each term. If there is no sign, assume it’s a positive sign. Step 3: Combine Like Terms Combine the x -terms. There is only one in this expression, so there is no need to combine. -5x Combine the constants: , 4 + 15 + 5 = +16 Step 4: Put All Sets of Simplified Terms Together -5x + 16

254.34 in² the formula for the area of a circle: π r² = area Or: π × r × r = area Which stands for: π (pi = 3.14) × radius × radius Step 1: Substitute Our Numbers Into the Equation So let’s look at our equation: π × r × r The problem has told us to use 3.14 for π and we can see that our radius is 9 inches. Now our equation looks like this: 3.14 × 9 in × 9 in Step 2: Solve Now that we have substituted in our numbers, we can solve it. with decimals, we pretend as if the decimals are not there. We do not line up numbers by their decimal point. {cccccccccc} {1} {3} 3 1. 4 × 9 2 8 2 6 Since there are a total of 2 numbers to the right of the two decimal points in the problem, there will be 2 numbers that are behind the decimal in the product. Therefore, the decimal point goes between the number 8 and the second number 2. 28.26 in Now we multiply the 28. 26 and the 9. We do not line up numbers by their decimal point. {cccccccccc} {7} {2} {5} 2 8. 2 6 × 9 2 5 4 3 4 Since there are a total of 2 numbers to the right of the two decimal points in the problem, there will be 2 numbers that are behind the decimal in the product. Therefore, the decimal point goes between the first number 4 and the 3. 254.34 in² So, the area is 254. 34 in²

When we have an irregular shape, we need to break down the irregular shape into basic shapes for which we know their area formulas. Step 1: Split the Irregular Shape Into Two or More Basic Shapes In this case, we can see that we have three rectangles combined that form an irregular shape. We can draw a horizontal line (↔) to make a rectangle on top, a rectangle on the lower left, and a rectangle on the lower right, or we can draw 2 vertical lines (↕) to make a rectangle on the left, a rectangle in the middle, and a rectangle on the right. With this shape, if we draw a horizontal line (↔), we are missing the total width of the rectangle on the top. If we draw 2 vertical lines (↕), we are missing the width of the rectangle in the middle. We will draw a horizontal line to find the area of the shape. Step 2: Find the Width of the Rectangle on the Top. The width of the left and right sides of the rectangle on the lower left is 4 cm since the opposite sides of a rectangle are equal. To find the left width of the rectangle on the top, we can subtract this width from the total width of the left side of the shape. 6 - 4 = 2 cm So, the width of the rectangle on the top of the shape is 2 cm. Step 3: Find the Area of Each Shape After the Split Let’s look at the dimensions for the three rectangles we have formed. Rectangle on the Lower Left: Here we can see the length of the rectangle is 2 cm and the width of the rectangle is 4 cm. To find the area of a rectangle we use the formula: Length × Width = Area Therefore: 2× 4 = 8 cm² The area of this rectangle is 8 cm². Rectangle on the Top: Here we can see the length of the rectangle is 7 cm and the width of the rectangle is 2 cm. To find the area of a rectangle we use the formula: Length × Width = Area Therefore: 7×2 = 14 cm² The area of this rectangle is 14 cm² Rectangle on the Lower Right: Here we can see the length of the rectangle is 2 cm and the width of the rectangle is 3 cm. To find the area of a rectangle we use the formula: Length × Width = Area Therefore: 2 × 3 = 6 cm² The area of this rectangle is 6 cm² Step 4: Add the Areas of Each Shape Once you have found the area of each basic shape within the irregular shape, we can add the areas together. 8 cm² + 14 cm² + 6 cm² = 28 cm² The area of this irregular shape is 28 cm².

Step 1: Interpret the Problem First, we must understand what is happening in this situation. We need to know how much gift wrapping paper Jessica needs to wrap the gift. Since the box, she is wrapping it in is a rectangular prism, we need to find the surface area of the box. Step 2: Break Your Shape Down Into Its Net When we break down a rectangular prism into its net, we have six rectangles: a top and a bottom, a front, and a back, and two sides. Step 3: Determine How to Find the Area of Each Part of the Net Let’s first find the area of the top and bottom rectangles of the prism. Since these two shapes are exactly the same, we can find the area of one and then multiply it by two. Here’s how we find the area of a rectangle: Length × Width = Area The length of the top rectangle is 11 inches, and the width is 8 inches. We can plug it into the equation. 11 in × 8 in = 88 in² The area of the top and bottom rectangles is 88 in² each. Now we find the area of the front and back rectangles. Next, let’s find the area of the front and back rectangles of the prism. Since these two shapes are exactly the same, we can find the area of one and then multiply it by two. Here’s how we find the area of a rectangle. Length × Height = Area The length of the front rectangle is 11 inches and the height is 5 inches. We can plug it into the equation. 11 in × 5 in = 55 in² The area of the front and back rectangles is 55 in² each. Lastly, we find the area of the two side rectangles. Finally, let’s find the area of the 2 side rectangles of the prism. Since these two shapes are exactly the same, we can find the area of one and then multiply it by two. Here’s how we find the area of a rectangle. Width × Height = Area The width of a side rectangle is 8 inches and the height is 5 inches. We can plug it into the equation. 8 in × 5 in = 40 in² The area of each of the side rectangles is 40 in². Step 4: Add Up the Areas of Each Part of the Net We have found the area of the top rectangle, front rectangle, and one side rectangle, so now we multiply their areas by two and add them to find the surface area of the rectangular prism. 2 × top area + 2 × bottom area + 2 × side area = surface area Now let’s plug it in. 2 × 88 in² + 2× 55 in² + 2 × 40 in² Now we can solve for the surface area following the order of operations. First, we multiply: 2 × 88 in² + 2 × 55 in² + 2 × 40 in² = 176 in² + 110 in² + 80 in² Now we add to solve by addition: 176 in² + 110 in² + 80 in² = 366 in² So, Jessica needs 366 in² of gift wrap paper.

Step 1: Interpret the Problem First, we must understand what is happening in this situation. We need to find out how much paint is in the paint can. To do this, we find the total volume of the paint can, and then we divide it by 2. Step 2: Substitute the Numbers Into the Equation In this case, we got the formula for the volume from the problem. Volume = π × r² × h The problem has also given us the radius, the height, and the value to use for π which we can substitute as shown below. 3.14 × (4 in)² × 11 in Step 3: Solve Using the Order of Operations Now we can solve for the volume given the formula. 3.14 × (4 in)² × 11 in Using the order of operations, we must square the 4 first. (4 in)² really means 4 in × 4 in = 16 in² Now we can just multiply all three numbers together. 3.14 × 16 in² × 11 in = 552.64 in³ our units are inches cubed (in3) since there were three dimensions involved. Step 4: Divide the Volume by 2 to Find the Amount of Paint To find how much paint is in the paint can, we divide its volume by 2. 552.64 in³ ÷ 2 = 276.32 in³ The volume of paint inside the can, when it is one-half full, is 276.32 in³.