1.8.1: Preparation 1.8

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    From LibreTexts, under CC BY-NC 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    (1) Which of the following calculations solves this problem according to the order of operations?

    8 + 6 × (3 + 6) ÷ 2 – 4

    (i) 8 + 6 × (3 + 6) ÷ 2 – 4
    → 8 + 6 × (3 + 6) ÷ 2
    → 8 + 6 × (3 + 3)
    → 8 + (18 + 3)
    → 8 + 21
    → 29

    (ii) 8 + 6 × (3 + 6) ÷ 2 – 4
    → 8 + 6 × 9 ÷ 2 – 4
    → 8 + 54 ÷ 2 – 4
    → 8 + 27 – 4
    → 35 – 4
    → 31

    (iii) 8 + 6 × (3 + 6) ÷ 2 – 4
    → 8 + (18 + 6) ÷ 2 – 4
    → 8 + (18 + 3) – 4
    → 8 + 21 – 4
    → 29 – 4
    → 25

    (iv) 8 + 6 × (3 + 6) ÷ 2 – 4
    → 8 + 6 × (3 + 3) – 4
    → 8 + (18 + 3) – 4
    → 8 + 21 – 4
    → 29 – 4
    → 25

    (v) 8 + 6 × (3 + 6) ÷ 2 – 4
    → 14 × (9) ÷ 2 – 4
    → 14 × (9) ÷ 2
    → (126) ÷ 2
    → (63)
    → 63

    (2) Miguel has a coupon for 20% off any purchase in a furniture store. He decides to purchase a desk originally priced at $80. Excluding tax, how much does Miguel save on his purchase?

    (i) $2

    (ii) $4

    (iii) $16

    (iv) $40

    (3) Sylvia is charged 8% tax for her $2 cheeseburger. How much does Sylvia owe the cashier?

    (i) $1.84

    (ii) $2.08

    (iii) $2.16

    (iv) $2.80

    Profit, Loss, and Revenue

    The following terms will be used in the next class. Make sure you understand what they mean.

    • Revenue: This is the amount of money that a business receives when it sells a product or service.
    • Net profit: The net profit is the actual amount of money a business makes after expenses. Expenses are something a person or people spend money on. The expression for this is:

    Net profit = Revenue − Expenses

    Example: A restaurant might charge a customer $10 for a meal, but it cost the restaurant $4 for the food, $1 for the waiter’s paycheck, and $1 for the building. You need to add up all the restaurant’s expenses ($4 + $1 + $1 = $6). Then you subtract it from the total amount they make ($10) to figure out the net profit. The expression would be 10 – (4 + 1 + 1) = 4. The restaurant’s net profit is $4.

    • Net loss: A net loss is similar to net profit, but a business has a net loss if the net profit is a negative number.

    Example: If the restaurant’s expenses were higher than the revenue, they would have a net loss. They could pay the waiter more ($5) and the building could cost more ($3). The expression would be 10 – (4 + 5 + 3) = −2. The restaurant’s net loss is $2.

    In Collaboration 1.7, you are going to be working through a tax form like the one shown below. This is a Schedule SE tax form. People who are self employed use this form to calculate how much tax they owe. Please take a few minutes to read it in preparation for Collaboration 1.7.

    IllustrationIllustrationScreenshot of Self-Employment tax form. At the top, it notes: If your only income subject to self-employment tax is church employee income, see instructions for how to report your income and the definition of church employee income. Part A: If you are a minister, member of a religious order, or Christian science practitioner and you filed Form 4361, but you had $400 or more other net earnings from self-employment, check here and continue with Part I. Skip lines 1a and 1b if you use the farm optional method in part II. See instructions. 1a: Net farm profit or (loss) from Schedule F, line 34, and farm partnerships, Schedule K-1 (Form 1065), box 14, code A. b: If you received social security retirement or disability benefits. enter the mount of conservation Reserve program payment included on Schedule F, line 4b, or listed on Schedule K-1 (Form 1065), box 20, code AH. Skip line 2 if you use the non farm optional method in Part II. See instructions. 2: Net profit or (loss) from Schedule C, line 31, and Schedule K (Form 1065), box 14, code A (other than farming). See instructions for other income to report or if you are a minister or member of a religious order. 3: Combine lines 1a a, 1b, and 2. 4a: If line 3 is more than zero, multiply line 3 by 92.35% (0.9235). Otherwise, enter amount from line 3. Note: If line 4a is less than $400 due to Conservation Reserve Program payments on line 1b, see instructions. b: If you elect one or both of the optional methods, enter the total of line 15 and 17 here. c: Combine lines 4a and 4b. If less than $400, stop. You don;t ow self-employment tax. Exception: if less than $400 and you had church employee income, enter 0 and continue. 5a: Enter your church employee income from Form W-2. See instructions. 5b: Multiply line 5a by 92.35% (0.9235). If less than $100, enter 0. 6: Add line 4c and 4b. 7: Max amount of combined wages and self-employment earnings subject to social security tax or the 6.2% portion of the 7.56% railroad retirement (tier 1) for 2021. 8a: Total social security wages and tips (total of boxes 3 and 7 on Form W-2) and railroad retirement (tier 1) compensation. If $142,800 or more, skip lines 8b through 10, and go to line 11. b: Unreported tips subject to social security tax from Form 4137, line 10. c: Wages subject to social security tax from Form 89191, line 10. d: Add lines 8a, 8b, and 8c. 9: Subtract line 8d from line 7. If zero or less, enter 0 here and on line 10 and go to line 11.10: Multiply the smaller number of line 6 or line 9 by 12.4%. 11: multiply line 6 by 2.9%. 12: Self-employment tax. Add lines 10 and 11. Enter here and Schedule 2 (Form 1040), line 4. 13: Deduction for one-half of self-employment tax. Multiply line 12 by 50% (0.50). Enter here and on Schedule 1 (Form 1040), line 15.

    After Preparation 1.7 (survey)

    You should be able to do the following things for the next class. Rate how confident you are on a scale of 1–5 (1 = not confident and 5 = very confident).

    Before beginning Collaboration 1.7, you should understand the concepts and demonstrate the skills listed below.

    Skill or Concept: I can …

    Rating from 1 to 5

    follow the order of operations.

    		 

    find a percent of a number.

    		  

    estimate 1% of a number.

    		  

    If your confidence ratings are below 3 for any of these skills/concepts, what are three things you might do to increase your confidence in these areas? If your confidence ratings are all 3 or above for these skills/concepts, what are three things your classmates might do to increase their confidence in these areas?

    This page titled 1.8.1: Preparation 1.8 was last modified on Wed, 15 May 2024 07:37:43 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Carnegie Math Pathways (WestEd) .