Operations & Algebraic Thinking
Number & Operations in Base Ten
Number & Operations - Fractions
Measurement & Data
Geometry
100

Which is the equivalent to 72 divided by 9?

A. 72/9

B. 9/72

C. 74/9

D. 9/74

equivalent means equal 

72 comes before 9 

72 divided (/) by 9

A. 72/9

100

How many zeros will be added to the end of the number 931 when multiplied by 1,000?

A. 5 zeros

B. 3 zeros

C. 6 zeros

D. 20 zeros

How many means you're counting

What are you counting? 0's 

How many 0's are in 1000? 3

B. 3 zeros

NOTE: Some questions try to misguide you with giving you irrelevant information notice the words in italics (How many zeros and 1,000) you did not need that other information so make sure YOU READ the QUESTION & Ask yourself what is the question asking me. DONT FORGET TO HIGHLIGHT, UNDERLINE (CTRL+U) (shortcut) or ITALICS (CTRL+I) (shortcut)

100

Four students are asked to write the expression 32 ÷ 8 as a fraction. The table shows each student's response.

Student 1     8/32

Student 2     2/32

Student 3     16/4

Student 4     32/8

Select TWO students with the correct answer.

A. Student 1

B. Student 2

C. Student 3

D. Student 4

write 32 ÷ 8 as a fraction (/)

32 is first so it goes on top 32

8 is second so it goes on bottom 8

32/8 

Solve. 32/8 = 4, what other answer is equal to 4?

A. 8/32 = 1/4 (8÷8 = 1 and whatever you do to the top, you do to the bottom, 8 can go into 32 four times) 

B. 2/32 = 1/16 (2÷2= 1 and whatever you do to the top, you do to the bottom, 2 can go into 32 sixteen times)

C. 16/4 = 4 

D. 32/8 = 4

Student C and Student D

100

A large bucket for Takis has a capacity of 15,000 milliliters. If there are 1,000 milliliters in 1 liter, what is the capacity of the large bucket, in liters?

Converting 

Formula 1000 milliliters = 1 liter 

15000 milliliters = ? liters

Cross out zeros method.

How many 0's are in 1000? 3

Cross out three 0's in 15000

15000 milliliters = 15 liters

100

Consider the right rectangular prism 


3 inches           7 inches         1 inch

What is the volume of the prism?

A. 32 cubic inches

B. 25 cubic inches

C. 21 cubic inches

D. 10 cubic inches

Volume = Length x Width x Height

Volume = 7 inches x 3 inches x 1 inch

Volume = 7 x 3 = 21 x 1 = 21

Volume = 21 cubic inches 

C. 21 cubic inches

200

In which number does the digit 3 have a value that is 1/10 the value of the digit 3 in the number 623.5?

A. 102.63

B. 247.35

C. 31.76

D. 5.13

digit 3 value = 1/10 value of (x-multiply) digit 3 in 623.5?

HTO.T

3 is in ones column = 3 

1/10 of (x - multiply) 3 = 3/10 =0.3 

B. 247.35

200

If you have 120 apples and you give away 1/3 of them, then buy 40 more, how many apples do you have now?

Calculate 1/3 of 120 (multiply)

120 ÷ 3 =40 

120 - 40 =80 

then you buy 40 more (add)

80 + 40 =120 

120 apples

200

What is the value of 4/3 + 5/12 ?

Find the Least Common Denominator (LCD)

The denominators are 3 and 12. The LCD is 12.

For 4/3 you have to convert the denominator to equal 12. What times 3 gives you 12? 4

What you do to the bottom, you do to the top. 

Multiply 4 by 4 = 16

Multiply 3 by 4 = 12 therefore 4   =   16​

                                            3         12

Now we can add the numerators since the denominator is now the same. 

16/12 + 5/12 = 21/12

16/12 + 5/12 

​​​


200

All squares have 4 sides equal in length. What is another shape that always has 4 sides equal in length?

A. triangle

B. rhombuses

C. quadrilateral

D. parallelogram 

B. rhombuses

200

|Option:      |Length:     |Width:      |Height:        |

        A            4 feet          4 feet          4 feet

        B            8 feet          3 feet          3 feet

        C            2 feet          4 feet          8 feet

        D            1 foot          8 feet          7 feet

        E            4 feet          2 feet          10 feet

A) Length: 4 ft, Width: 4 ft, Height: 4 ft

  • Calculation:
    4×4×4=64 cubic feet
  • This set of dimensions is valid because the product of the length, width, and height equals the volume of the prism (64 cubic feet).

B) Length: 8 ft, Width: 3 ft, Height: 3 ft

  • Calculation:
    8×3×3=72 cubic feet
  • This set of dimensions is not valid because the product exceeds the volume of 64 cubic feet.

C) Length: 2 ft, Width: 4 ft, Height: 8 ft

  • Calculation:
    2×4×8=64 cubic feet
  • This set of dimensions is valid because the product of the dimensions equals the volume of the prism (64 cubic feet).

D) Length: 1 ft, Width: 8 ft, Height: 7 ft

  • Calculation:
    1×8×7=56 cubic feet
  • This set of dimensions is not valid because the product is less than the volume of 64 cubic feet.

E) Length: 4 ft, Width: 2 ft, Height: 10 ft

  • Calculation:
    4×2×10=80 cubic feet
  • This set of dimensions is not valid because the product exceeds the required volume of 64 cubic feet.

Select answers A and C

300

Which represents 24 divided by the sum of 6 and 3?

A. (6 + 3) ➗ 24

B. 24 ➗ (6 + 3)

C. 6 ➗ (3 + 24)

D. (24 ➗ 6) + 3

24 divided means ➗ = 

24 ➗ by the sum of 6 and 3 =

sum of 6 and 3 means they go (together), sum means add + 

B. 24 ➗ (6 + 3) 

300

Compare: 0.0808 _ 0.080
A) >
B) <
C) =
D) Cannot be determined

Answer: A) >
Explanation: 

When comparing decimals, write in expanded form:
0.0808= 8 hundredths + 8 ten-thousandths
0.080= 8 hundredths
Since 0.0808 has additional ten-thousandths, it is greater than 0.080

300

Maria is making sandwiches for a school event. She needs 2/3 of a loaf of bread for each sandwich. If she has 4 loaves of bread, how many complete sandwiches can she make?

a) 4
b) 5
c) 6
d) 8

Answer: C) 6 sandwiches


Explanation: To solve this, we divide 4 (loaves) by 2/3 (loaf per sandwich).


4 ÷ 2/3=  to divide by a fraction we need to flip the fraction and multiply 4 by 3/2.

4 × 3/2= 6 

=(4 x 3=12) / 2

=12/2

=6

4 ÷ 3/2= 6


This means Maria can make 6 complete sandwiches.

300

Ms.B has 2,500 milliliters of juice. How many liters of juice does she have, if there are 1,000 milliliters in 1 liter?

A) 0.25 liters
B) 2.5 liters
C) 25 liters
D) 250 liters

1 liter = 1,000 milliliters

2,500÷1,000=2.5

Move decimal place to the left when dividing. 

How many 0's are in 1,000? 3

Move decimal place to the left 3 times

2500 = 2500.0 = 2.5

B. 2.5 Liters


300

Which of the following is a quadrilateral?

  • A) Triangle
  • B) Circle
  • C) Square
  • D) Pentagon

Quad means 4 

Triangle has 3 sides

Circle is round

Square has 4 sides

Pentagon has 5 sides

C. Square

400

The table shows the number of back flips and push ups Chris Brown does in each dance rehearsal session:

|Session:     |Back Flips:     |Push Ups:     |

        1                  8                  6

        2                 11                10

        3                 14                14

        4                 17                18

If the pattern continues, which statement is true?

A. Chris Brown adds 2 back flips and 3 push ups to each session.

B. Chris Brown adds 1 back flip and 2 push ups to each session.

C. Chris Brown adds 4 back flips and 5 push ups to each session.

D. Chris Brown adds 3 back flips and 4 push ups to each session.


Which pattern:

Look at each column 

Back flips: 8, 11, 14, 17 - ask yourself how did 8 get to 11, how did 11 get to 14, how did 14 get to 17

The numbers are increasing so that means we are adding. You can check the answers given with process of elimination. TEST TAKING STRATEGY

8 + __ = 11, 11 + __ = 14, 14 + __ = 17

11 - 8 = 3, 14 - 11 =3, 17 - 14 = 3 

So, Chris Brown is adding 3 back flips to each session. There is only one answer with "add 3 back flips" 

D. Chris Brown adds 3 back flips and 4 push ups to each session.

 

400

A rectangular garden has an area of 28.12 square meters and a width of 4.3 meters. What is its length?
A) 6.45 meters
B) 6.54 meters
C) 6.35 meters
D) 6.53 meters

What is the question giving us?

Area = 28.12 Width = 4.3 

Answer: B) 6.54 meters
Explanation:
Area = Length × Width

28.12 =    ?     x   4.3

Therefore, Length = Area ÷ Width


28.12 ÷ 4.3 =6.54 


Move decimal in divisor and dividend right:
2812.0 ÷ 43.0 =654.0 

Then move decimal left twice because you have two digits placed behind the decimal

28.12 ÷ 4.30=6.54

400

A recipe calls for 3/4 cup of flour. If you want to make 1/2 of the recipe, how much flour will you need?

a) 1/4 cup
b) 3/8 cup
c) 1/2 cup
d) 6/8 cup

Answer: B) 3/8 cup
Explanation:

  • Half of 3/4 means multiply by 1/2
  • 3/4 × 1/2=3/8
400

The table shows the number of books read by students in a month:

   1-2 books: 8 students
   3-4 books: 12 students
   5-6 books: 5 students
   7-8 books: 3 students

How many students read more than 4 books?

A) 8 students
B) 12 students
C) 20 students
D) 28 students

A) 8 students

  • Students reading 5-6 books: 5
  • Students reading 7-8 books: 3
  • Total: 5+3=8 students
400

If a point is located at (3,4) on the coordinate plane, what is the value of the x-coordinate?

  • A) 4
  • B) 3
  • C) 7
  • D) 0

Point on coordinate plane is (x,y) 

(3, 4)

(x, y)

B. 3

500

Which equation is true?

A. 4321÷21 = 212

B. 3456÷12 = 364

C. 3450÷15 = 230 

D. 5678÷34 = 301

True means correct: 

Check each equation with division or multiplication

A.

4321÷21=212

  • Step 1: Calculate how many times 21 goes into 43.
  • It goes in 2 times (since 21×2=42).
  • Step 2: Subtract 42 from 43:
    43−42=1
  • Step 3: Bring down the next digit (2) to make it 12.
  • Step 4: Calculate how many times 21 goes into 12.
  • It goes in 0 times.
  • We can stop here because in the answer 212 the tens digit is not 0 so it is NOT true.

B.

3456÷12=364

  • Step 1: Calculate how many times 12 goes into the leading part of 3456.
  • 12 goes into 34 two times (since 12×2=24).
  • We can stop here because in our answer it begins with a 3 NOT a 2, so this equation is NOT true.

C.

3450÷15=230 

  • Step 1: Calculate how many times 15 goes into 34.
  • It goes in 2 times (since 15×2=30).
  • Step 2: Subtract 30 from 34:
    34−30=4
  • Step 3: Bring down the next digit (5) to make it 45.
  • Step 4: Calculate how many times 15 goes into 45.
  • It goes in 3 times (since 15×3=45).
  • Step 5: Subtract 45 from 45:
    45−45=0
  • Step 6: Bring down the last digit (0) to make it 0.
  • Since there are no more digits, the final answer is:
    3450÷15=230

D. 5678÷34=301

  • Step 1: Calculate how many times 34 goes into 5656.
  • It goes in 1 time (since 34×1=34).
  • We can stop here since in our answer it begins with a 3 instead of a 1, so this equation is NOT true.


  

500

Calculate: (3.45 × 2.1) ÷0.5
A) 14.49
B) 14.59
C) 14.69
D) 14.79

Answer: A) 14.49


Explanation:


Follow order of operations:
First: 3.45×2.1=7.245
Then: 7.245÷0.5=14.49
(To divide by 0.5, multiply by 2)

7.245 x 2 =14.49 

500

A garden plot is divided into equal sections. If 2/5 of the garden is planted with tomatoes, and 1/5 is planted with peppers, what fraction of the garden is still available for other vegetables?

a) 1/5
b) 2/5
c) 3/5
d) 4/5

Answer: B) 2/5
Explanation:

  • Tomatoes take 2/5
  • Peppers take 1/5
  • Total used = 2/5 + 1/5= 3/5
  • Space left = 1−3/5=
  • 1 =5/5
  • 5/5 - 3/5 = 2/5
500

A rectangular prism has a length of 6 feet, width of 4 feet, and height of 3 feet. What is its volume?

Volume = L x W x H

L = 6 feet, W = 4 feet, H = 3 feet

6 x 4 x 3 =72 

(6 x 4) x 3=24 x 3 =72 

or

6 x (4 x 3) =6 x 12 =72 

500

A parallelogram must have which of the following properties?

  • A) Opposite sides are parallel and equal in length
  • B) All sides are equal
  • C) All angles are right angles
  • D) Only one pair of parallel sides

A. Opposite sides are parallel and equal in length. 

Remember the hint parallel

 

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