Number Sense and Operations
Algebraic Reasoning
Percentages
100
Which integer has the greater value?
-11 or -13?
-11
REMEMBER: If the number is negative, the larger number is CLOSER to zero.
100
What expression represents "three times n decreased by 8"?
3n - 8
REMEMBER KEY WORDS HERE!
Decreased means subtract. decreased by means - that number.
Times means to multiply. We write variables right next to numbers to multiply instead of a symbol! Mathematicians are LAZY!!!
100
What is 25% of 120?
30
200
A regular piece of ice has a temperature of 32oF. A piece of dry ice has a temperature of -109oF.
What do you know about the ice?
A. the regular ice is colder than the dry ice.
B. The temperature of the dry ice is closer to 0oF.
C. The dry ice is colder than the regular ice.
D. The dry ice has a greater temperature.
C. The dry ice is colder than the regular ice.
REMEMBER: Colder temperatures are smaller numbers. Since the dry ice is a much smaller number of -109, we can assume it is much colder than regular ice.
200
A sign at an amusement park states riders must be AT LEAST 54 inches tall to ride the roller coaster. Which inequality represents that statement?
A. h > 54
B. h >= 54
C. h < 54
D. h <= 54
B
REMEMBER!
At least, means that number OR more. so we can be 54 inches tall, OR taller.
200
Find 35% of 260
91
300
Select all values that are less than 16.
A. abs(-15)
B. -abs(-16)
C. -abs(15)
D. abs(-16)
E. abs(-17)
A, B, and C
REMEMBER: Absolute value is the distance from zero and distance is always POSITIVE!
B is correct as well because it is -16, as we had a negative in front of the absolute value. Thus it makes our original answer negative.
300
Evaluate the expression when a = 11
3 xx((a-1)div5)
6
Substitute 11 for a and solve with order of operations!
300
A store offers a 15% discount on a $75 jacket. How much is the discount?
$11.25
400
Find the value of
1.2xx0.03
0.036
REMEMBER: You can use a calculator to find these basic operation answers! USE YOUR RESOURCES!
You can also do 12 * 3 to get 36 and then move the decimal over 3 places to re-insert the decimal.
400
Simplify:
-3(x+6)
-3x-18
Multiply -3 to both x and 6. -3 * x=-3x and -3 * 6= -18
400
A class has 40 students, and 60% of them are girls. How many girls are in the class?
24 girls
500
Evaluate
3/5 xx6/25
18/125
REMEMBER: To multiply fractions we just multiply across. Multiply the numerators 3 and 6 to get 18 and the denominators 5 and 25 to get 125!
500
which value is a solution of the equation c +14=20
6
REMEMBER: you need to "undo" the operations being done to c. So... I need to subtract 14 from 20 to find out what c equals!
500
A watermelon weighs 8 kg, and 20% of its weight is water. How much water does it contain?
1.6 kg of water
600
What is the quotient of 7/8div21/24 ?
HINT: REMEMBER Keep, Change, Flip!
1
To divide fractions, we multiply by the reciprocal. KEEP 7/8 the same, CHANGE division to multiplication and then FLIP 21/24 into it's reciprocal 24/21. Now multiply across!
600
A number minus 12 equals 9. What is the number?
21
Something -12 is 9. SO... 12+9 is my number! 12 + 9 is 21!
600
What percent of 250 is 50?
20%
700
Brin has 6 pairs of white socks and 4 pairs of black socks. After doing laundry, Brin lost 1 white sock and 2 black socks. How many TOTAL socks is Brin left with?
A. 7
B. 13
C. 17
D. 23
C. 17
6*2 is 12 and 4*2 is 8. She had 20 individual socks total, then lost 3. 20-3=17!
700
Solve
c/8=-20
A. 12
B. -12
C. 160
D. -160
D. -160
REMEMBER: you need to "undo" the operations being done to c. So... I need to multiply 8 by -20 to find out what c equals!
700
A school has 900 students, and 360 are in the band. What percentage of the students are in the band?
40%
800
Find the Least common Multiple of 8 and 12.
A. 4
B. 24
C. 48
D. 96
B. 24
LCM is the first number that 8 and 12 fit perfectly into.
I count by 8s and 12s until I find the smallest common number in my lists.
8, 16, 24
12, 24
800
Which answer makes the equation true?
4.75 + x = 11.65
A. 5.9
B. 6.8
C. 6.9
D. 7.1
C. 6.9
SIMPLY SUBSTITUTE!
Plug in the numbers for x until you get your solution! OR you can do 11.65 - 4.75 to find it quicker :)
800
In a survey, 180 people out of 450 prefer watching movies at home. What percent prefer movies at home?
40%
900
Find the greatest common factor of 16, 32, and 96.
A. 4
B. 6
C. 12
A. 4
GCF is the largest number that fits into 16, 32 and 96. With multiple choice just divide all of these options into the 3 numbers and find the largest that fits into ALL.
IF NOT MULTIPLE CHOICE: list out the factors of all of these numbers and circle the largest they have in common!
900
The ratio of Sally's rent to her other monthly expenses is 2 to 3. What is the ratio of her rent to her total expenses for the month?
2 to 5
REMEMBER: Total will equal all ratio parts added together. So the total is 2 + 3 which is 5.
900
A company produces 1,200 laptops, and 144 of them are defective. What percentage of the laptops are defective?
12%
1000
Which expression is equivalent to 45 + 75?
A. 15(3 + 4)
B. 15(3 + 5)
C. 5(8 + 12)
D. 5(9 + 10)
B. 15(3 + 5)
YOU HAVE TO DISTRIBUTE 15 to 3 and 5. Multiply 15 by both numbers.
15*3 is 45 and 15*5 is 75
1000
Andrew drove 456 miles in 8 hours. What is the unit rate in miles per hour?
HINT: Divide the distance by time!
57mph
The hint says it all guys!
1000
25% of what number is 75?
300
1100
Evaluate:
(7+1)^2+2
66
REMEMBER: PEMDAS
Parenthesis: 7+1 is 8
Exponents: 8 squared is 64
Addition: 64+2 is 66
1100
NO
Simplify the ratios to find out if they are equivalent!
REMEMBER: Simplifying ratios is the same as fractions! Divide both parts until you can't anymore!
1100
40% of what number is 200?
500
1200
Select all equivalent forms of 6.25.
A. 625%
B. 62.5%
C. 6 1/8
D. 6 1/4
E. 625/100
A, D, and E
REMEMBER: 1.00 is 100% so 6.25 is 625%
0.25 is equal to 1/4 so 6.25 is equal to 6 and 1/4
and 625/100 in your calculator would result in 6.25
1200
Jasper planted 20 plants in his garden bed. 8 of the plants are tomato plants. What percentage of the plants are tomatoes?
A. 14%
B. 15%
C. 40%
D. 180%
C. 40%
REMEMBER: Percent (as a decimal) = amount/total.
So I did 8/20 and got 0.4 which = 40%
1200
15% of a number is 90. What is the number?
600
1300
Evaluate: 3+ (-2)(-5)
13
REMEMBER: a negative * a negative = a positive! Using PEMDAS, -2 * -5 is POSITIVE 10, plus 3 is 13
1300
Caitlyn can run 11 miles in 90 minutes while Marjorie can run 6 miles in 50 minutes. Who is the faster runner?
Caitlyn because his pace is .122 miles per min which is faster than Marjorie's pace is 0.12 miles per min.
UNIT RATE: Divide distance by time to get their miles per minute and the larger number is faster because it was a larger distance in 1 minute.
1300
60% of a number is 420. Find the number.
700