Math practice

Twice 4 is what?

8 *twice/double = ×2 so 4×2=8

7 is approximately what percent of 5? a. 130% b. 192% c. 140%

Answer: C Steps: in your calculator multiply 5 by the choices so 5×130%= 6.5 Wrong because is not 7 5×192%= 9.6 wrong bc is not 7 5×140%=7 Correct because it equals 7

5 less than what is 6

answer is 11 *less than = subtract *is = equal so the question is asking what number subtract 5 gives a 6 so 11-5=6 so the answer is 11 Or add 5+6=11

60% of 15% of 800 is what? a. 7 b. 120 c. 72 d. 180

the answer is C (72) Steps: plugged in the calculator *percentage sign in calculator: press shift and ( sign Or do 60÷100 "of" in word problem means to multiply so 60% × 15% × 800 = 72 Or 60÷100 × 15÷100 × 800 = 72

If 20 percent of a number N is 36, what is 0.2 percent of N? a. 36.0 b. 7.2 c. 1.8 d. 0.36

the answer is D Steps: 1) "of" means multiple so we don't know what N is but it says that 20% × some number will give you a 36 so start putting random number (Hint: if there are percent and the equal is whole # then start putting # that are greater than 100) so if we tried 20%× 180= 36 Or 20÷100×180=36 2) 180 is not the answer because its not asking about the N value it is asking what is 0.2% × N so if N= 180 then 0.2%× 180= 0.36

solve for inequalities 3x-8<12+5x

the answer is: -10<X ( solve for x ) *if the x was negative then switch the sign Ex: -3x > 9 = x < -3

What is the prime factorization of 16?

16 ^ 4 4 ^ ^ 2 2 2 2

one third of 12 is what?

4 *12×1/3=4 OR. 12÷3=4

Marie lives with her mother, father, one sister, and five brothers. i. what is the ratio of women to men in the family? ii. what is the ratio of kids to parents? iii. how many people are there in the family in total? iv. what fraction of the family is men?

Answers: i. = 1:2 Or 3:6 ii= 7:2. iii. 9. iv. 6/9 or 2/3 Steps for i.: Marie is female she have mother and sister so the question asking what is the ratio (when answering ratio you should answer like this # : #) of women to men in the family. So you will divide 3/6 = 1/2 since the question is asking about ratio you should write it as 1:2 Steps for ii: the question is asking about the ratio of the kids to parents so divide the kids by the parents: 7/2 = 7:2 Steps for iii: the question is not asking about the ratio but it is asking about the total which means you have to add all the family up so we have Marie+ mother+ father+ one sister + five brothers 1+1+1+1+5= 9 Steps for iv: the question is asking for fraction so we will have answer like this (#/#) so is asking fraction of men in the family so we have 6 men and the family total is 9 so 6/9 = 2/3

To find the greatest common factor (GCF) of 24 and 32. Then find the least common factor (LCF) of 24 and 32.

Factor First: 32: 1,2,4,8,16,32 24: 1,2,3,4,6,8,12,24 * 1,2,4, and 8 can be divided by both 32 and 24 GCF: 8 LCF: 1

List the factor of 8 and then list four multiplies of 8.

Factor of 8: 1,2,4,8 Four multiplies of 8: 8, 16, 24, 32

Exponet Rules:

Multiply the base & Add exponents Ex: 2x^4 . 2x^2 = 4x^6 Divide the base & Subtract the exponent Ex: 4x^3 ÷ 2x^2 = 2x or 2x^1 More ex: (2x^2)^3 = 8x^6. *(2^3 =8) & (2×3= 6) 8x^3 ________ = 2x or 2x^1 4x^2 (x^4)^2 = x^8 2x^2 . 6y^3 = 12x^2 y^3

A person's maximum heart rate can be calculated approximately by subtracting the person's age from 220. Using this method, what is the difference between the maximum heart rate of a 15-year-old and that of a 60-year-old ?

The answer is 45 Steps: 220-15= 205 220-60= 160 205-160= 45

When 15% of 40 is added to 5% of 260, the resulting number is: a. 19 b. 40 c. 95

The answer is A Steps: 40×15% = 6 260×5%= 13 13+6= 19

The price of a long distance phone call consist of a fixed service charge plus an additional fee for each minute of the call. If the total charge is $3.50 first a 20-minutes call and $5.00 for a 40-minutes call, what is the total charge for a 1-hour (60-minutes) call? a. $4.25 b.$6.50 c. $7.50

The answer is B Steps: If the price increasing every 20 minutes for ex: for 20min= $3.50 and after another 20min (40min) = 5.00 so 5.00- 3.50= 1.5 then 5.00+ 1.5 = 6.50 60min= $6.50

A tray of water is placed in a freezer. Its initial temperature is 23°C after 3 hours. By how much did the temperature fall during that time? a. 8°C b. 31°C c. 23°C

The answer is B Steps: 23--8= 31

Mega Lo Mart increases the cost of a DVD player from $200 to $250. If the store increases the cost of a $350 television by the same percent, what is the new cost of the television? a. $380.50 b. $425.00 c. $437.50

The answer is C Steps: 200 × #%= 250 so if we tried 200 × 125%= 250 so now we know that it increases by 125% so now we want to know the price of the television so 350×125%= 437.5

Louis has a box of 50 fruit-flavored gumdrops. There are 10 cherry-flavored gumdrops, and he eats all of them. Louis eats none of the other gumdrops. What percent of the gumdrops has Louis eaten? a. 2% b. 10% c. 20% d. 100%

The answer is C Steps: the formula of percentage is (value ÷ total value)×100 so if he eats 10 (value) gumdrops and the total is 50 (total) then.... 10÷50×100= 20 so its 20%

What is the difference (to the nearest hundredth) between the largest and smallest of these four fractions: 13/20, 5/8, 1/2, 7/16? a. 0.13 b. 0.19 c. 0.21

The answer is C Steps: the question asking for difference (subtraction) and it is asking for largest to smallest so first find the largest and smallest numbers of the four fraction largest: 13/20 smallest: 7/16 so 13/20 - 7/16 = 0.21

Mathew, Emily, Cynthia, John, and Stephanie are all going for student council. If three equivalent positions are available in this year's election, how many different leadership boards are possible?

The answer is: 10 Steps: 1) count how many names/people are listed (there are 5) 2) how many positions are listed (3 positions) 3) in the calculator press (shift) and (÷) it should give you a C or (nCr) 4) put 5C3

6 is how much greater than 2

answer is 4 *6-2=4

If n is a positive integer, then the product of 14n and 15n is not necessarily dividable by which of the following? a. 10 b. 12 c. 30

correct answer is B Steps: 1) factor 14 and 15 14: 1,2,7,14 15: 1,3,5,15 2) so now we factor and we have 4 numbers for each one so now we will multiply each number by the other number to see if we will get a 14 and 15 ex: lets see firat choice (10) 2 (from 14 factor) × 5 ( from 15 factor) = 10 for choice b (12) we have 3 from 15 factor but we don't have a 4 in the factor of 14 so 12 is the correct answer

(xy)^3 z^0 -------------- = ? x^3 y^4

the answer is 1/y Steps: 1) multiply >> (xy)^3 = x^3 y^3 2) always remember that any #^0 = 1 so z is = 1 3) subtract >> x^3 y^3 1 ----------- = y^-1 and 1 x^3 y^4 4) if there is a negative exponent switch it side so 1/y or 1/y^1

If m is the least prime number and n is the least positive integer multiple of 12, what is the difference between n and m?

the answer is 10 Steps: 1) least prime # is 2 (prime number is numbers that are only multiplied by 1 and it self (1 IS NOT PRIME #)) so m= 2 2) Least POSITIVE integer (integer is any # not fraction) so the least positive # is 1 so n=1 3) the question said that n is multiple of 12 so 1×12= 12 so n=12 4) we want to find the difference between n and m so we will subtract n-m so 12-2 = 10

3 more than 7 is what?

the answer is 10 *more than means adding so 3+7=10

if you add up 5 consecutive odd integers that are each greater than 16, what is the smallest possible sum?

the answer is 105 Steps: 1) First understand the definition: consecutive # are # in order (ex: 1234) and odd are # that can't be multiplied by 2 (1,3,57,9,11) integer numbers that are not fraction 2) the question ask for odd numbers that are greater than 16 3) 17 is odd and greater than 16 so the question also asks for adding up 5 consecutive # so 17+19+21+23+25(they are in order of odd #) = 105

6 more than twice 5 is what?

the answer is 16 Steps: twice= ×2 so twice 5 means 5×2=10 10+6 =16

One-half of the sum of 3 and 9 is what?

the answer is 6 Steps: "the sum of" means adding so 3+9=12 "one half" is ×1/2 or ÷2 so 12÷2=6

Solve: 1 3/4

the answer is 7/4 Steps: 1) leave the denominator 2) multiply the denominator by the outside number so 4 × 1= 4 3) add the number you got by the numerator so 4+3 = 7 Or in calculator write 1+3/4= 7/4

A pair of boots costs $50 and a certain coat costs $150. If the cost of the boots is increased by 20% and the cost of the coat is decreased by 30%, what is the sum of their new costs? a. $165 b. $200 c. $330

the answer is A Steps: 1) let start by the first item which is boots: so if the boots cost $50 and it increased (multiply then add) by 20% So: 50×20%= 10 then we will add 50+10= 60 so the coat cost $60 2) lets do the second item which is coat: the coat costs $150 and decreased (multiply then subtract) by 30% so: 150×30%= 45 then we will subtract so 150-45= 105 3) the question is asking for the sum of the new price of the both items so 105+60= 165

which of the following is not a real number? a. -√-36 b. √36 c. -√36

the answer is A *to answer this really quick plug these # in calculator and see which one gives an error Or remember the definition and rule (real number is when negative is inside the square root) ex √-#

what rational number is halfway between 1/5 and 1/8 ? a. 26/80 b. 13/80 c. 1/6 d. 13/40

the answer is B Steps: 1) make them have the same denominator ----> 1/5 × 8 & 1/8 × 5 2) Add them 5/40 + 8/40 = 13/40 3) the question asks for half (1/2) so 13/40 × 1/2 = 13/80

Erin is baking cookies and needs 6 2/3 cups of flour to make two batches. If she has 4 2/7 cups of flour in her pantry, then how many more cups of flour does she need for he recipe? a. 2 1/21 b. 2 8/21 c. 2 13/21 d. 2 2/8

the answer is B Steps: 1) the question asking for "how many more cups of flour she need) so to find that we have to subtract. 2) We will subtract the outside number first so 6-4=2 3) now we will subtract the 2/3 by 2/7 4) make the denominator equal so 2/3 × 7 and 2/7 ×3 5) subtract (leave the denominator) 14/21 - 6/21 = 8/21 6) put the outside number with them 2 8/21

If the product of six difference integers is negative, what is the greatest number of them that can be negative? a. 6 b. 5 c. 3 d. 0

the answer is B Steps: 1) the question asks for greatest # out of all the choices (which are 6,5,3, and 0) 6 is the greatest but if we multiply a six negative numbers we will get a positive: ex -1×-1×-1×-1×-1×-1= 1 so we have 5 as the greatest out of the choice and if we multiply a five negative numbers we will get a negative number ex: -1×-1×-1×-1×-1= -1

system of equations -x -y = -2 and 2x -y = -11

the answer is: y= 5. x=-3 Steps: 1) out them in parenthesis (-x -y = -2) (2x -y = -11) 2) Multiply and change only one sign (positive to negative) or (negative to positive) 2(-x-y=-2) 1(2x-y=-11) 3) Add them -2x +2y =-4 + 2x -y = -11 = -3y=-15 4) Solve for y y= 5 5) plug in y number into the equation (chose either -x -y = -2 Or 2x -y = -11) -x -5=-2 6) solve for x x= -3 ​

which of the following is equivalent to (7-i) (7+i) ? Note: i^2 = -1 a. 49-2i b. 14-i c. 50 d. 48

the correct answer is C Steps: 1) multiply them (7-i) × (7+i) 7×7 = 49 7×i=7i. -i× 7= -7i -i×i= -i^2 so 49+ 7i- 7i- i^2 2) add or/and subtract ----> 49- i^2 3) the question said that i^2= -1 so 49- (-1) = 50 ​

The diagnoal of a rectangle is 16. How wide is the rectangle if the length is 6? a. 10 b. 11 c. 4√10 d. 2√55

the correct answer is D Steps: 1) diagonal of rectangle formula is: d^2 = L^2 + W^2 2) plug the numbers into the formula: d= diagonal L= length. w= width so the question said that the diagonal is 16 and the length is 6 and is asking for the width so 16^2= 6^2 + w^2 3) solve for w 16^2= 6^2 + w^2 256= 36= w^2 4) subtract 256-36 = 220 5) square root 220

Solve for x 3x+15= 24

x= 3

solve for y 2y-10=20

y=15