Quantitative Reasoning

Question 1

When multiplying a decimal by a power of 10, you move the decimal point over by the _____ of 10

Example: .029 x 10^3 =29

Answer 1

Integer

Question 2

What is the answer to:

.0344 x 10^4 =?

Answer 2

344

Question 3

What is the answer:

.029 x 10^6 =?

Answer 3

29,000

Question 4

When dividing by powers of 10, you move the decimal point over by the corresponding number of places to the ____. Add a ____ as a placeholder if necessary

Answer 4

Left
Zero

Question 5

Solve:

Divide 416 by 10,000 = ?
- how many times to the left must you place the decimal?

Answer 5

.0416
4. Because there’s 4 zeros

Question 6

Every positive number has 2 square roots, one _____ and one _____

Answer 6

Positive and negative

Question 7

Only _____ radicals can be added or subtracted together

Answer 7

Like (same)

Question 8

Solve:

2 √3 + 4 √2 - √2 - 3 √3 = ?

Answer 8

3 √2 - √3

Question 9

To multiply or divide one radical by another, multiply or divide the numbers _____ the radical signs, then the numbers ____ the radical signs

Answer 9

Inside
Outside

Question 10

Solve:

(6 √5)2 √3 = ?

Answer 10

12 √15

Question 11

Solve:

(12 √15) / (2 √5) = ?

Answer 11

6 √3

Question 12

Solve:

√72

= √36 √2
= ?

Answer 12

6 √2

Question 13

What do you do when a question tells you to find the reciprocal of a fraction?

What is the reciprocal of 1/25?

Answer 13

You invert the fraction to get the reciprocal.

1/25 = 25

Question 14

When dividing fractions, what’s something you can do to make things easier?

Example:
(4/3) / (4/9) = ?

Answer 14

Multiply the inverses.

(4/3)(9/4) = 36/12 = 3

Question 15

When comparing fractions, what a neat way to find out which is greater?
Solve:

Which is greater, 3/8 or 6/13?

Answer 15

Cross multiply!

3x13=39
8x6=48

Therefore, 6/13 is greater

Question 16

When turning a mixed number to a fraction, what do?

Solve:

Concert 2 3/7 into a fraction

Answer 16

Multiply the denominator to the first variable and add it to the numerator.

(7x2)+3/7. = 17/7

Question 17

The reciprocal of a fraction between 0 and 1 is ______ than both the original fraction and 1

Example:

What is the reciprocal of 2/3?
-is it greater than or less than 1 and the original fraction?

Answer 17

Greater

3/2, greater than 1 and original fraction

Question 18

The reciprocal of a fraction between -1 and 0 is _____ than both the original fraction and -1.

Example:

What is the reciprocal of -2/3?
- is it greater than or less than -1 and its original fraction

Answer 18

-3/2 or -1 1/2, which is less than both -1 and original fraction (-2/3)

Question 19

The square of a fraction between 0 and 1 is _______ than the original fraction

Example:

Solve, (1/2)^2

Answer 19

Less

(1/2)^2 = 1/4

Question 20

The square of any number between 0 and -1 is ______ than the original fraction

Answer 20

Greater

Question 21

Multiplying an positive number by a fraction between 0 and 1 gives a product ______ than the original number

Example:

6(1/4) = ?

Answer 21

Smaller

6(1/4) = 6/4 = 3/2

Question 22

Multiplying any negative number by a fraction between 0 and 1 gives a product _____ than the original number

Example:

(-3)(1/2) = ?

Answer 22

Greater

= -3/2

Question 23

When converting a decimal between 0 and 1 to a fraction, determine the place value of the _____ non zero digit and set that to the denominator

Example:
Convert 0.875 to a fraction in lowest terms

Answer 23

Last

.875 = 875/1,000
Reduce the fraction
7/8

Question 24

What is the decimal equivalent of 4/5?

Answer 24

4 / 5 =0.8

Question 25

When comparing decimals, convert them into fractions with their respective denominators (make sure to make them equal, if one has a denominator of 1,000, multiply by 10 to the numerator to make it equal) Example: Which is greater, .254 or .3?

Answer 25

254/ 1000 Or 300 / 1000 (correct) .3 > .254

Question 26

Arrange in order from smallest to greatest: (remember, convert into fraction of equal denominator first) 0.7, 0.77, 0.07, 0.707, 0.077

Answer 26

.07, .077, .7, .707, .77

Question 27

What is the percent equivalent of .17?

Answer 27

17% Just multiply by 100.

Question 28

What is the common fraction equivalent of 32%?

Answer 28

32/100 = 8/25

Question 29

What is the decimal equivalent of 32%?

Answer 29

32/100 =0.32

Question 30

When you divide two percents, do they cancel out?

Answer 30

Yes

Question 31

When you divide a percent by a regular number, does the percent sign stay or cancel out?

Answer 31

Percent sign stays

Question 32

Problem: Ben spends $30 of his annual gardening budget on seed. If his total annual gardening budget is $150, what percentage of his budget is spend on seed?

Answer 32

30/150 x 100 = 1/5 x 100 = 100/5 = 20%

Question 33

What is the formula for percent increase and decrease? Percent increase = ? Percent decrease = ?

Answer 33

Increase(100%)/original Decrease(100%)/original

Question 34

Problem: Two years ago, 450 seniors graduated from Inman high school. Last year, 600 seniors graduated. By what percent did the number of graduating seniors increase?

Answer 34

600 - 450 =150 So 150/450 x 100% = 33 1/3% or .33%

Question 35

Problem: If the price of a $120 dress is increased by 25%, what is the new selling price?

Answer 35

25% = x/120 • 100% 25/100 = x/120 1/4 = x/120 120/4 = x X = 30 New selling price = 120+30=150