7th grade math number systems study guide...microsoft word - 7th grade math number systems study...
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7th Grade Math Number Systems Study Guide Use the number line below to answer questions 1-4:
1.) Name two pairs of points that could be combined to have a sum of zero:
Point ______ & _______ and Point _____ & ______
2.) Find the distance between point C and E: _________ Name one pair of points that are the same distance apart as points C and E: ______ & ______
3.) Find the value of each using the values on the number line above: C + G = _______ E + B = _______ E -‐ H = ________ D + B = _______ C -‐ B = ______
4.) Which of the following has the greatest value? Justify your answer. a. B -‐ F b. F -‐ B c. F(B) d. F + B Answer: _______ Justification: _____________________________________________________________________ _______________________________________________________________________________________________________
5.) Write a number sentence for each number line:
________________________________
_________________________________
________________________________
A B C D E F G H
6.) Find the value of each expression, and use arrows to represent each number sentence on the number-‐line:
7.) Match each situation with the corresponding expression, then find the value of the expression: Letter Answer a. Malik owes his mom $10, then pays her back $5 _____ -‐10 -‐ 5 = _______ b. The temperature was -‐10°, then decreased by 5° _____ 10 -‐ 5 = ________ c. Pat is 10 feet above sea level, then descends 5 feet _____ -‐10 + 5 = _______
8.) Match the equivalent expressions: 9.) Match the equivalent expressions:
a. -‐8 + 5 _____ 8 + (-‐5) a. -‐4 -‐ 7 _____ -‐7 + (-‐4) b. -‐8 -‐ 5 _____ -‐8 + (-‐5) b. -‐4 + 7 _____ -‐7 -‐ (-‐4) c. 8 -‐ 5 _____ -‐8 -‐ (-‐5) c. 4 -‐ 7 _____ 7 + (-‐4)
10.) Match the equivalent expressions 11.) Match the equivalent expressions: a. -‐2 (5 + 3) _____ 10 + 6 a. -‐4 (y -‐ z) _____ 4y + (-‐4z) b. -‐2 (-‐5 -‐ 3) _____ -‐10 -‐ 6 b. 4 (-‐y -‐ z) _____ -‐4y -‐ (-‐4z) c. 2 (5 -‐ 3) _____ 10 -‐ 6 c. -‐4 (-‐y + z) _____ -‐4y + (-‐4z)
12.) Decide whether each pair of terms are equal (=) or not equal (≠), then place the correct symbol above the line between the two terms.
a. b. c. d. −
e. − f. g.
a.) 4 -‐ 9 = ____________
b.) -‐3 -‐ (-‐7) = _________
c.) -‐2 + (-‐4) = ____________
13.) Decide whether each pair of expressions are equal (=) or not equal (≠), then place the correct symbol between the terms.
a. b. c.
d. e. f.
14.) Decide whether each product is positive or negative:
a. (-‐y)(-‐y)(-‐y) b. -‐1(x)(x) c. d. -‐(-‐p × -‐p)
__________________ __________________ __________________ __________________
15.) Find the sum, difference, product, or quotient:
a. -‐6 -‐ 11 = ________ b. -‐3 × 6 = ________ c. 7 + (-‐15) = ________ d. = _________
e. -‐9 -‐ (-‐20) = ________ f. (-‐4)(-‐3)(-‐2) = ________ g. 25 -‐ 38 = ________ h. -‐21 + (-‐11) = _________
i. -‐5 × -‐6 × -‐2 × -‐1 = _________ j. ¾ ÷ -‐⅙ = ______ k. -‐⅜ × -‐⅚ = ________ l. 3⅖ ÷ 4⅓ = ___________
16.) Convert each fraction to a decimal, then determine whether the decimal terminates in zeros(t), or repeats(r). If the decimal is repeating, place the line over the appropriate digits.
a. =_______ b. =_____ c. =_____ d. =_____ e. =_____ f. =_____
17.) The temperature in Anchorage Alaska at 6am was -‐18°. A scientist recorded the change in temperature over the next 5 hours. The increases and decreases in temperature can be represented as: -‐3°, +7°, +11°, -‐5°, +2°. What was the temperature in Anchorage Alaska after 5 hours? Show your work.
18.) The temperature in Chicago is -‐11.8°F. The temperature in New York is 8.3°F. How much warmer is it in New York, than in Chicago? Show your work.
19.) Vernon has a bank account balance of -‐$24.70, and then deposits $30 into his account. What is his new balance after the deposit? Show your work.
20.) A bakery uses ⅗ of a cup of sugar for each batch of cookies. How many batches of cookies can they bake with 9 cups of sugar? Show your work.
21.) The floor of a canyon has an elevation of -‐6.5 ft. Erosion causes the elevation to change by -‐0.25 feet per year. How many years will it take for the canyon floor to have an elevation of -‐20 feet? Show your work.
22.) Ariel is making bracelets. She bought a 15⅙ foot long string, and a 12⅓ foot long string. If each bracelet requires ½ of a foot of string, how many bracelets can Ariel make?
23.) Chloroform freezes at about -‐63.5°C. Fresh water freezes at 0∘C. Ethanol freezes at about -‐114.7°C.
Imagine that the temperature has dropped to the freezing point for Chloroform. How many degrees more must the temperature drop for Ethanol to turn solid?
Answer Key: Page One:
1.) A & H and C & F 2.) 8, A & D 3.) 2, -‐4, -‐6, -‐8. 2
4.) b. F – B has a value of +12 because 5 –(-‐7) = 12. All other options have negative values.
5.) F. -‐2 + 5 = 3 G. -‐5 + 2 = -‐3 H. -‐5 – 2 = -‐7
Page Two:
6.) a.) -‐5
b.) 4
c.) -‐6
7.) b: -‐15
c: 5
a: -‐5
8.) c 9.) a 10.) b 11.) c b c a a a b c b
12.) a. = b. = c. ≠ d. = e. ≠ f. = g. ≠
Page 3:
13.) a. ≠ b. = c. = d. ≠ e. = f. ≠
14.) a.) negative b.) negative c.) positive d.) negative
15.) a.) -‐17 b.) -‐18 c.) -‐8 d.) 6 e.) 11 f.) -‐24 g.) -‐13 h.) -‐32 i.) 60 j.) -‐18/4 = -‐4 ½ k.) 15/48 = 5/6 l.) 51/65
16) a. 0.6 (t) b. (r) c. 0.375 (t) d. 4.3 (t) e. f.
17.) -‐6° 18.) 20.1°F
Page 4:
19.) $5.30 20.) 15 batches 21.) 54 years 22.) 55 bracelets 23.) 51.2°C