Fractions, Decimals, Percents Flashcards

1
Q
A

For adding & subtracting fractions, first find a common denominator (Least Common Multiple of 3 and 5)

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2
Q
A
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3
Q
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4
Q
A
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5
Q
A

Multiply horizontally:

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6
Q
A

Dividing fractions: Flip the 2nd fraction and multiply

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7
Q
A
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8
Q
A

When we take the RECIPROCAL, we flip the fraction

This is the same as 1 divided by the fraction.

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9
Q

Write “z is x percent of y” as an equation

A

Percent means “divide by 100”

“of” means “multiply”

“is” means =

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10
Q

Write “x is 20% greater than y” as an equation

A
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11
Q

Write “x is 15% less than y” as an equation,

a) write using a decimal
b) convert to a fraction

A
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12
Q

Write “x is n percent greater than y” as an equation

A
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13
Q

A bike was $50, and is now on sale for $32. What is the percent change in price?

A
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14
Q

Distribute:

-3(x-7)

A

= -3*x + -3*-7

= -3x + 27

Be careful with your SIGNS! Double negative turns into a positive

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15
Q

Factor out the Common Factor:

4x + 4y =7

A

Both terms have “4” as a factor.

So, we can factor it out (this is the inverse process to “distribution”)

4(x+y) = 7

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16
Q

Factor out the Common Factor:

3x + 6y + 15z = 7

A

Factor out the Common Factor:

The common factor between 3, 6, and 15 is 3.

(we can prove this by writing the prime factorization: 6=2*3, 15=5*3)

We factor out 3 from each “term”.

3(x + 2y + 5z)

17
Q

Multiplying Exponents:

What is 23 * 24 ?

A

27

When we multiply exponents with the same bases, we add the powers

ab * ac = ab+c

18
Q

What is 2 * x3 * y2 * 3 * y4 * x ?

A

We match up what can be simplified:

2*3 = 6

x3 * x = x4

y2 * y4 = y6

6x4y6

19
Q

Distribute: -2x(-3x + 5)

A
  • 2x * -3x = 6x2
  • 2x * 5 = -10x

6x2 - 10x

20
Q

Factor out the Common Factor:

15x2 - 10x

A

This time, we can factor out both a number and a variable:

The common prime factor of 15 and 10 is 5.

The common variable is x

So, we factor out 5x:

5x(3x-2)

21
Q

Scientific Notation:

Write out as a number: 2.3 * 107 = ?

A

23,000,000

* 107 is like multiplying by 10, 7 times. This moves the decimal point 7 places to the right.

22
Q

What is the units digit, tens digit, and hundreds digit of the number 5318?

A

units: 8
tens: 1
hundreds: 3

23
Q

What is the units digit of 3219 ?

A

We need to find the pattern.

3219 will have the same units digit as 219

21 = 2

22 = 4

23 = 8

24 = 16

25 = 32

26 = 64

The pattern repeats for every 4 numbers in the pattern: {2, 4, 8, 6}

Every 4th power will have a units digit of 6: 24, 28, 212, 216

So, 217 ends in 2, 218 ends in 4, 219 ends in 8.

24
Q

What is units digit of 714

A

71 =7

72 = 49

Only the units digit will affect the next power: so we can do 9*7 =63 –> 73 ends with 3

3*7 =21 –> 74 ends with 1

1*7 = 7 –>75 ends with 7.

So, the pattern repeats for every 4 numbers in the pattern: {7, 9, 3, 1}

So, the 4th, 8th, and 12th powers would have units digit of 1.

713 has units digit of 7

714 has units digit of 9

25
If x and y are integers, with y \> 1, how do we determine whether the fraction x/y is a repeating decimal (for example, 1/3 = .33333333... repeating), versus a "Terminating Decimal" with a finite number of digits (example: 1/40 = 0.025)?
The numerator doesn't matter. If the denominator only includes the prime factors 2 and/or 5, it is not repeating. Example: 1/200 = ? 200 = 2\*2\*2\*5\*5 ---\> so it will be a "Terminating Decimal" 1/200 = 0.005 1/60= 3\*2\*2\*5 = .01666666...... ---\> "Repeating Decimal"
26
For every 5 men, there are 3 women. Express the above ratio in 3 different ways
27
If there are 25% more women than men, what is the ratio of men to women?
28
If the ratio of men to women is 5:7, what fraction of the total are women?
32
If the ratio of men to women is 3:4, which of the following could NOT be the total number of men and women combined? A) 35 B) 72 C) 49 D) 21 E) 280
We can't have a fraction of a person. Therefore, the total must be a multiple of 7. (3+4) 7, 14, 21, 28, etc. Only B is not a multiple of 7. (we might notice that 70 is a multiple of 7, so 72 isn't) 35= 5\*7 49=7\*7 21= 3\*7 280= 40\*7
33
If the ratio of flour to water in a recipe is 3:2, how many cups of flour would we need for 7 cups of water?
Unlike for people, We CAN have fractions of units. We can use the *Unknown Multiplier* method: The ratio of flour to water is 3x : 2x, with x as our unknown multiplier. We know the amount of water, 7, so 2x=7. Solve for x: x=3.5 Now plug in x=3.5 and find the flour: 3x = 3\*3.5 = **10.5 cups of flour**
34
If the ratio of dogs to cats to birds is 2:3:5, and there are 24 cats, how many total animals are there?
We can use the unknown multiplier: 2x:3x:5x 3x represents cats. 3x=24 x=8 So, our multiplier is 8. Counting all 3 animals, we have 2x+3x+5x = 10x So, 10x = 10\*8 = **80**
35
There are 3x for every 2y. There are 3z for every 5x What is the ratio of y to z?
ratio 1) 3x:2y ratio 2) 3z:5x We use a similar process to finding a common denominator with fractions: What is the common factor between 3x and 5x? 15x Multiply the 1st ratio by 5: 15x:10y Multiply the 2nd ratio by 3: 9z:15x So, for every 15x there is 10y, and 9z Therefore the ratio of y to z is 10:9
36
What is the definition of "directly proportional"?
When 2 quantites vary by a constant ratio. It is a linear relationship: y = mx, where m is the slope or constant ratio The graph would start at 0,0 examples: someone earns $20 per hour, with no other payments.