6th Grade Math - Algebra

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http://www.greenazibo.com/Problem 1.What value of x makes the equation below true?

7 + x = 84

A. 12

B. 77

C. 83

D. 91

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How To SolveThere are 2 basic rules to a problem like this.Isolate the unknown on one side of the equal sign.Whatever action you perform must be performed on both sides of the equal sign.

7 + x = 84Subtract 7 from both sides to isolate x7 + x – 7 = 84 – 7x = 77The correct answer is B, 77

http://www.greenazibo.com/Solve simple proportions within context

Problem 2. Guafi selects 15 pieces of fruit. If 3 out of 5 of these fruit are bananas, b, how many bananas does Guafi select?

A. 3

B. 9

C. 13

D. 25

http://www.greenazibo.com/How To SolveFacts provided;There are 15 total pieces of fruitThere are 3 bananas for every 5 pieces of fruitWrite a formula that expresses those two statements;15 pieces of fruit (3 out of every 5 pieces of fruit) is a banana.G-Zibo Tip – In a word problem, the word “is” means equals in the formula15 (3/5) = bThere are 2 basic rules to a problem like this.Isolate the unknown on one side of the equal sign.Whatever you do to one side of the problem you must do to the other side of the problem.15 (3/5) = bSimplify the left sideMultiply 15 times 3/5

Then you have

9 = bB is the correct answer

http://www.greenazibo.com/Translate two-step verbal sentences into algebraic equations

Problem 3.What algebraic equation represents “three times the difference of a number, x, and nine equals fifteen”?

A. 9x -3 = 15

B. 3(9) – x = 15

C. 9 – 3x = 15

D. 3(x – 9) = 15

http://www.greenazibo.com/How To Solve

The statement gives 3 times the difference of xand 9

3(x – 9) equals 15

The word equals determines where the equal sign goes,

15 on one side,

Everything else on the other

3(x -9) = 15

Choice D is the correct answer

http://www.greenazibo.com/Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc.Problem 4. A circle has a radius of 18 inches. What is the circumference of the circle in terms of π?G-Zibo Tip- C = 2πrC = circumferencer = radiusπ = pi = 3.14

A. 36πB. 20πC. 18πD. 9π

http://www.greenazibo.com/How To Solve

The problem states “in terms of π”, that means that π must be part of the answer.

Substitute 18 for the radius (r) in the formula provided in the tip

C = 2 x π x 18

C (circumference) = 36π

The correct answer is A

http://www.greenazibo.com/Translate two-step verbal sentences into algebraic equationsProblem 5.The number of solar panels, s, installed along Oak Street is 3 less than 4 times the number of solar panels, installed along Poplar Street. Which expression can be used to determine the number of solar panels on Oak Street?

A. = 7sB. = 12sC. = 3-4sD. = 4s-3

http://www.greenazibo.com/How To SolveAnalyzing the statement it showsOak Street is (equals) 3 less (negative) than 4 times (multiply) Poplar street solar panels, s,

In this case, 3 is a negative number because of the statement, "3 less than". 4 is a positive number and then it is multiplied by the variable s because of the statement, "4 times Poplar street solar panels, s". = -3 + 4s

Now rearrange the formula to look like one of the answers above; Choice D is the correct answer.

G-Zibo Tip: Many times word problems such as these can be very frustrating and confusing. It is important that if you are feeling frustrated by this type of problem try again after when you are feeling refreshed and have a clear mind. As the concept sinks in by repeating the problem (practice, practice, practice) try substituting the solar panels for another object and the street names for another location. Make up your own word problem and solve (practice, practice, practice).

http://www.greenazibo.com/Solve and explain simple one step equations using inverse operations involving whole numbers

Problem 6.What is the value of n in the equation below?

66 + n = 226

Show your work

Answer_________________

http://www.greenazibo.com/How To Solve

There are 2 basic rules to a problem like this.

Isolate the unknown on one side of the equal sign.

Whatever you do to one side of the problem you must do to the other side of the problem.

66 + n = 226

Subtract 66 from each side

66 + n - 66 = 226 – 66

n = 160

http://www.greenazibo.com/Solve and explain simple one step equations using inverse operations involving whole numbersProblem 7. At a recycling center there are 16 pallets of used car batteries to recycle. The manager places 8 batteries per pallet for shipping to the factory. He uses the equation below to calculate the total number of batteries, b, to recycle.

b/8 = 16What is the total number of batteries to ship to the factory?Show your workAnswer_________________

http://www.greenazibo.com/How To Solve

There are 2 basic rules to a problem like this.

Isolate the unknown on one side of the equal sign.

Whatever action you perform must be performed on both sides of the equal sign.

b/8 = 16

Multiply both sides by 8 to cancel out the 8 in b/8

b/8 x 8 = 16 x 8

b = 128

http://www.greenazibo.com/Solve and explain simple one-step equations using inverse operations involving whole numbers

Problem 8. The tide on the island of Tonga changes from 4.7 feet at high tide to 1.3 feet at low tide. Write an equation that shows the change in tide when x represents the number of feet the tide increased.

Equation_________________

How many feet did the tide increase?

Show your work

Answer_________________

http://www.greenazibo.com/How To Solve

Set up a formula that will look for the difference between the high tide and low tide.

High tide equaled 4.7 feet

Low tide equaled 1.3 feet

The equation would be

4.7 feet – 1.3 feet = x

3.4 feet = x

The tide increased by 3.4 feet

http://www.greenazibo.com/Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc.)Problem 9. Rio measures one side of a solar panel. The length is 8 feet and the width is one half of the length. What is the area, in square feet, of the solar panel?G-Zibo Tip, A = lwA = Areal = lengthw = width

A. 4B. 16C. 32D. 108

http://www.greenazibo.com/How To Solve

The length is 8 feet

The width is given as ½ the length (8 feet) = 1/2 x 8 = 4

A = lw

Substitute the numbers for length and width;

A = 8 x ½(8)

A = 8 x 4

A = 32

C is correct

http://www.greenazibo.com/Translate simple verbal expressions into algebraic expressionsProblem 10. Demi brought 8 bottles of water to a picnic. Of those bottles of water, she and her friends opened a certain number of bottles, b. What expression can be used to determine the number of unopened bottles at the picnic?

A. 8 + bB. b + 8C. 8 – bD. b - 8

http://www.greenazibo.com/How To SolveDemi started with 8 bottles and she and her friends drank some of the water. The number of bottles that were drunk is then subtracted from the total.

Original total = 8 bottlesBottles she and her friends opened = b

The number of bottles they drank is then subtracted from the original number.

Choice C states that 8 – b is the answer, that is the correct choice.

http://www.greenazibo.com/Solve simple one-step equations using basic whole-number factsProblem 11. Kennet brought 6 bags of cans to the recycling center. He received a total of $12. He used the equation below to determine the price per bag, b, which he received.

6b = $12.00How much money did Kennet receive for each bag?A. $72.00B. $18.00C. $6.00D. $2.00

http://www.greenazibo.com/How To Solve

Isolate the unknown on one side of the equal sign. Then whatever action you perform must be performed on both sides of the equal sign.

6b = $12.00

Divide both sides by 6

6b ÷ 6 = $12.00 ÷ 6

b = $2.00

Answer D is the correct choice.

http://www.greenazibo.com/Substitute assigned values into variable expressions and evaluate using order of operations

Problem 12. What is the value of the expression below when r = 2?

9 -3r =

A. 0

B. 3

C. 6

D. 12

http://www.greenazibo.com/How To SolveThe formula provided is 9 – 3r =r was given a value of 2r = 2Substitute 2 for r in the formula9 – 3(2) = Multiply the -3 times 2, which will equal -6The problem now becomes 9 – 6 = 3Choice B is the answer.

http://www.greenazibo.com/Translate simple verbal expressions into algebraic expressions

Problem 12. An aquarium has 30 kinds of salt-water fish. If f represents the number of tropical salt-water fish, which expression can be used to determine the total number of fish that are nottropical salt-water fish?

A. 30f

B. 30/f

B. 30 – f

D. 30 + f

http://www.greenazibo.com/How To Solve

The aquarium has 30 kinds of fish

f is the unknown number of tropical salt-water fish

Whatever is not f would have to be the remaining kinds of fish

30 – f =

Choice C has the correct formula.

http://www.greenazibo.com/Use substitution to evaluate algebraic expressions (may include exponents of one, two and three)

Problem 13. What is the value of the expression 6m + 33 when m equals 7?

Show your work

http://www.greenazibo.com/How To SolveThe formula given6m + 33

The value of m is 7. Substitute 7 for m in the formula6(7) + 33

Solve the exponent first. 33 = 3 x 3 x 3 = 276(7) + 27

Solve the multiplication of 6 times 742 + 27Add the result69 is the answer

http://www.greenazibo.com/Solve and explain simple one-step equations using inverse operations involving whole numbers

Problem 14. Urie is planting a garden. He has a total of 320 seedlings to plant. He has planted 14 so far. The equation below can be used to determine the number of seedlings, s, Urie still needs to plant.

14 + s = 320

What is the number of seedlings that Urie still needs to plant?

Show your work

http://www.greenazibo.com/How To Solve

There are 2 basic rules to a problem like this.

Isolate the unknown on one side of the equal sign.

Whatever action you perform must be performed on both sides of the equal sign.

14 + s = 320

Subtract 14 from both sides

14 + s - 14 = 320 – 14

s = 306

Urie has to plant 306 more seedlings

http://www.greenazibo.com/Solve simple one-step equations using basic whole-number facts

Problem 15. If 8n = 96, what value of n makes the equation true?

A. 12

B. 88

C. 104

D. 768

http://www.greenazibo.com/How To Solve

There are 2 basic rules to a problem like this.

Isolate the unknown on one side of the equal sign.

Whatever action you perform must be performed on both sides of the equal sign.

8n = 96

Divide both sides by 8 to isolate the n

8n ÷ 8 = 96 ÷ 8

n = 12

http://www.greenazibo.com/Substitute assigned values into variable expressions and evaluate using order of operationsProblem 16. Gabija has been growing 5 containers of avocado seeds in his windows at home. Once they started to sprout he added 3 more avocado seeds. The expression below shows the total number of avocado seeds in Gabija’s window when a represents the number of avocado seeds in each container.Let a represent the number of avocado seeds per container.3 + (a x 5)If each container holds 8 seeds, how many total avocado seeds are in Gabijo’s windows

A. 18B. 28C. 43D. 55

http://www.greenazibo.com/How To SolveThere are 2 basic rules to a problem like this.Isolate the unknown on one side of the equal sign.Whatever action you perform must be performed on both sides of the equal sign.

3 + (a x 5) = The number of avocado seeds per container is 8, represented as aa = 8Substitute 8 for a in the formula3 + (8 x 5) =Perform the multiplication first8 x 5 = 40Then the addition3 + 40 = 43The answer is C

http://www.greenazibo.com/Use substitution to evaluate algebraic expressions (may include exponents of one, two, and three)Problem 17. Arlen wrote the expression below for 3 of his classmates to calculate the age of his tortoise.

n2 x 7 - 4If n represents the number of classmates, what is the age of Arlen’s tortoise?

A. 12B. 18C. 36D. 59

http://www.greenazibo.com/How To SolveThe formula givenn2 x 7 – 4The number of classmates, n, is given as 3Substitute the number 3 for the n in the formulaThat gives32 x 7 – 432 is the same as 3 x 3, which equals 9The formula now reads as9 x 7 – 4Perform the multiplication operation first63 – 4Then the subtraction63 – 4 = 59Choice D is correct; the tortoise is 59 years old

http://www.greenazibo.com/Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc..Problem 18. Geena walks at a rate, r, of 4 miles per hour. What is the distance, d that she walks in the time, t, of 3 hours?

G-Zibo Tip, d = rtd = distancer = rate of speedt = time

A. 1 mileB. 7 milesC. 12 milesD. 43 miles

http://www.greenazibo.com/How To SolveThe formula for calculating distance is providedd = rtThe rate of speed, r, was provided, 4 miles per hourThe time, t, was provided, 3 hoursSubstitute the provided numbers for the letter symbols

Multiply the numbers; the “hours” cancel each other leaving just the unit of milesd = 12 milesChoice D is the correct answer

http://www.greenazibo.com/Solve simple one-step equations using basic whole-number factsProblem 19. A sixth grade class is wants to raise money to have an aquarium so they decide to have a bake sale. The students earn $6 for each cake they sell. To determine how many cakes they need to sell to reach their goal of $144, the class uses the equation below where c represents the unknown number of cakes the students need to sell.

6c = 144Part A What is the value of c in the equation?Show your workAnswer_________

http://www.greenazibo.com/How To SolveThere are 2 basic rules to a problem like this.Isolate the unknown on one side of the equal sign.Whatever action you perform must be performed on both sides of the equal sign.The formula provided6c = 144Divide both sides by 6 to isolate the c6c ÷ 6 = 144 ÷ 6On the left side 6 divided by 6 equals 1 leaving C alone on that sideAnd on the right side there is, 144 ÷ 6 = 24c = 2424 cakes must be sold to earn $144Part BThe teacher wrote the equation shown below for her students to solve to find the number of angel fish, a, they could buy to add to the fish tank in their classroom using the $144, if each angel fish costs $9144/a = 9

http://www.greenazibo.com/How To SolveThere are 2 basic rules to a problem like this.Isolate the unknown on one side of the equal sign.Whatever action you perform must be performed on both sides of the equal sign.The formula provided6c = 144Divide both sides by 6 to isolate the c6c ÷ 6 = 144 ÷ 6On the left side 6 divided by 6 equals 1 leaving C alone on that sideAnd on the right side there is, 144 ÷ 6 = 24c = 2424 cakes must be sold to earn $144

http://www.greenazibo.com/Part B

The teacher wrote the equation shown below for her students to solve to find the number of angel fish, a, they could buy to add to the fish tank in their classroom using the $144, if each angel fish costs $9

144/a = 9

http://www.greenazibo.com/How To SolveThere are 2 basic rules to a problem like this.Isolate the unknown on one side of the equal sign.Whatever action you perform must be performed on both sides of the equal sign.144/a = 9a is the denominator on the left sideMultiply both sides by a to remove it from the denominator144/a x a = 9aThe a’s on the left cancel each other out144 = 9aDivide both sides by 9 to isolate the a144 ÷ 9 = 9a ÷ 9The 9’s on the right of the equal sign cancel each other16 = aThe class can buy 16 angelfish with their $144

http://www.greenazibo.com/Use substitution to evaluate algebraic expressions (may include exponents of one, two, and three)

Problem 20. Jorja’s teacher asked the students to evaluate the expression 43 + 2y, when y = 8.

Three of the students wrote their answer on the board

Which student evaluated the expression correctly?

Show your work

http://www.greenazibo.com/How To SolveThe formula provided is43 + 2yThe value of y is given as 8Substitute the 8 for y in the formula43 + 2(8)Perform the action required by the exponent first43 + 2(8) = (4 x 4 x 4) + 2(8) = 64 + 2(8) =Now perform the multiplication of 2 x 864 + 2(8) =64 + 16 = 80 Govad had the correct answer with 80

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