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Terms in this set (111)
Convert the decimal 0.875 to a percent
To convert from a decimal to a percentage, multiply by 100 (and add a "%" sign).
The easiest way to multiply by 100 is to move the decimal point 2 places to the right
So 0.875 = 87.5% answer
Convert the decimal 3.025 to a percent.
To convert from a decimal to a percentage, multiply by 100 (and add a "%" sign).
The easiest way to multiply by 100 is to move the decimal point 2 places to the right.
So 3.025 = 302.5%. answer
Convert 3.5% to a decimal
To convert from a percent to a decimal, divide by 100 (and remove the "%" sign).
The easiest way to divide by 100 is to move the decimal point 2 places to the left
So 3.5% = 0.035 answer
Convert 18.75% to a decimal
To convert from a percentage to a decimal, divide by 100 (and remove the "%" sign).
The easiest way to divide by 100 is to move the decimal point 2 places to the left
So 18.75% = 0.1875 answer
Convert 3/5 to a decimal
The easiest way to convert a fraction to a decimal is to divide the top number by the bottom number (divide the numerator by the denominator)
3/5=3 divided 5=0.6 answer
convert 11/20 to decimal
The easiest way to convert a fraction to a decimal is to divide the top number by the bottom number (divide the numerator by the denominator)
11/20=11 div 20=0.55 answer
Convert the decimal 0.65 to a fraction in its lowest terms.
First, write down the decimal "over" the number 1:
0.65=frac 0.65/1
Then multiply top and bottom by 100 since there are two numbers after the decimal point:
frac 0.65/1=frac 0.65 times 100} {1 times100}=
frac 65/100
This makes it a correctly formed fraction.
Then simplify the fraction (in this case by dividing top and bottom by 5):
frac{65}{100}= frac{13}{20}
Convert the decimal 0.125 to a fraction
First, write down the decimal "over" the number 1:
0125=\frac{0125}{1}
Then multiply top and bottom by 1,000 since there are three numbers after the decimal point:
\frac{0125}{1}=\frac{0125\times1,000}{1\times1,000}=\frac{125}{1,000}
This makes it a correctly formed fraction.
Then simplify the fraction (in this case by dividing top and bottom by 5):
\frac{125}{1,000}=\frac{25}{200}\\\\\text{Thenby5again}\\\\\frac{25}{200}=\frac{5}{40}\\\\\text{Thenby5again}\\\\\frac{5}{40}=\frac{1}{8}
And that is as far as we can go!
Express frac 5/8 as a percent
The easiest way to convert a fraction to a percentage is first to divide the top number by the bottom number:
frac{5}{8}=5 div 8=5.000 div 8=0.625 answer
Express 17/25 as a percent
The easiest way to convert a fraction to a percentage is first to divide the top number by the bottom number:
frac{17}{25}=17 div 25=17.00 div 25=0.68 answer
Express 5% as a fraction
First convert to a decimal by dividing by 100 (move the decimal point 2 places to the left) and remove the "%" sign:
5% = 0.05
Then use the steps for converting a decimal to a fraction:
0.05=frac 0.05}{1}=frac {0.05 times 100}{1 times100}=frac{5}{100}
Simplify the fraction (by dividing top and bottom by 5):
frac{5}{100}=frac{1}{20}
Express 32% as a fraction
First convert to a decimal by dividing by 100 (move the decimal point 2 places to the left) and remove the "%" sign:
32% = 0.32
Then use the steps for converting a decimal to a fraction:
0.32=frac{0.32}{1}=frac{0.32 times 100}
{1 times100}=frac{32 {100}
{Simplifythefraction(by dividing top and bottom by 4)}
frac{32}{100}=\frac{8}{25}
convert to decimal or %: 1/2
1 div 2= .50 or 50% (by moving decimal point to the right twice)
convert to decimal or %: 1/4
1 div 4= .25 or 25% (by moving decimal point to the right twice)
convert to decimal or %: 3/4
3 div 4= .75 or 75% (by moving decimal point to the right twice)
convert to decimal or %: 1/5
1 div 5= .20 or 20% (by moving decimal point to the right twice)
convert to decimal or %: 3/5
3 div 5= .60 or 60% (by moving decimal point to the right twice)
convert to decimal or %: 4/5
4 div 5= .80 or 80% (by moving decimal point to the right twice)
convert to decimal or %: 1/8
1 div 8= .125 or 12.5% (by moving decimal point to the right twice)
convert to decimal or %: 3/8
3 div 8= .375 or 37.5% (by moving decimal point to the right twice)
convert to decimal or %: 5/8
5 div 8 = .625 or 62.5% (by moving decimal point to the right twice)
convert to decimal or %: 7/8
7 div 8 = .875 or 87.5% (by moving decimal point to the right twice)
convert to decimal or %: 1/3
1 div 3 = .333 or 33.3% (by moving decimal point to the right twice)
convert to decimal or %: 2/3
2 div 3 = .666 or 66.6% (by moving decimal point to the right twice)
Multiplying Fractions
Multiplying Fractions
Top times top and bottom times bottom
Improper Fractions
Improper Fractions
Change an improper fraction into a mixed number by dividing the numerator by the denominator
Dividing Fractions
Dividing Fractions
Inverse the second fraction and multiply
Ratio
Ratio
A relationship between two numbers
Proportion
Proportion
Two ratios that have equal values
Percent
Percent
Per hundred - part per hundred
Military Time
Military Time
Uses numbers 00 through 23 to represent the hour in a 24-hour period. Example: 9:35 AM regular time converts to 0935 hours or 09:35 hours. 9:35 PM regular time would be written as 2135 hours or 21:35 hours.
Order of Operations
Order of Operations
Please Excuse My Dear Aunt Sally
Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction
Percent Formula
Percent Formula
Part / Whole (of) = % / 100
What is 15 out of 75 as a percent?
20%
step 1: 15 divide 75 = 0.20
step 2: change the decimal to % by moving the decimal twice to the right.
step 3: add the % sign
What is 2 out of 50 as a percent?
4%
step 1: 2 divide 50=0.04
step 2: change decimal to % by moving the decimal twice to the right.
step 3: add the % sign
What is 20 out of 100 as a percent?
20%
step 1:
20 divide 100 = 0.20
step 2: change to % by moving decimal twice to the right.
step 3: add % sign
What is 28% of 100?
28
100 x .28%= 28
What is 95% of 20?
19
step:
20 x 0.95 =19
The number 2 is 20% of what number?
10
step 1:
2 divide 20%= 0.1
step 2:
move the decimal twice to the right. = 10
The number 65 is 25% of what number?
260
step 1:
65 divide 25%= 2.6
step 2:
move decimal twice to the right= 260
The number 9 is 20% of what number?
45
step 1:
9 divide 20% = 0.45
step 2:
move the decimal twice to the right= 45
The number 44 is 25% of what number?
176
step 1:
44 divide 25% = 1.76
step 2:
move the decimal twice to the right= 176
Write 4% as a decimal
Answer: 0.04
Explanation: 4% = 4/100 =0.04
or
**the easiest way is to move the decimal to the left twice
Write 15% as a fraction.
= 3/20
*****
short cut explanation
****
15
____
100
15 divide 5= 3
________________ _____
100 divide 5= 20
answer:
3
____
20
________________________________________________
Answer:
The simplified fraction form of 15% is
3
20
.
Explanation:
Percents are always out of 100. In every case, the actual percent you get is the numerator, which is the number on the top of the fraction. The denominator is ALWAYS going to be 100.
To simplify this, you need to find the greatest common factor for both of the numbers.
The factors of 15 are: 1, 3, 5, 15.
The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100
The factors these both numbers share are 1 and 15. The greatest common factor is 5. So, divide both of the numbers by 5.
You will get
3
20
.
Write 33 1/3% as a decimal.
Answer: 0.3333
Explanation:
33 is our whole number, so we won't be doing anything with it, however the fraction 1/3 needs to become a decimal. We can find the decimal by dividing 3 into 1 which goes 0.33 times. So our percentage is 33.33% which when divided by 100, or when we move the decimal place to the left two places we have... 0.3333
Write 2.5 as a percent.
Write 2.5 as a percent.
Correct answer: 250%
Explanation: 250%, any time you are asked to turn a number into a percent, just mulitply that number by 100 and put your percentage sign.
25 is what percent of 40?
25 is what percent of 40?
Answer: 62.5%
easiest way:
step 1: 25 divide 40 = 0.625
step 2: move the decimal twice to the right= 62.5
step 3: add the % sign
_________________________________________
Explanation:
This is a word problem; look at the main operating words.
25 is(=) what (x)40 so we have as our problem
25 = x40, now solve for x by dividing both sides of the equation by 40,
25/40 = x, now reduce your fraction...
5/8 , turn this into a decimal and multiply by 100.
=62.5%
50 is what percent of 300?
easiest way:
step 1: 50 divide 300 = 0.166666666666667
step 2: move the decimal twice to the right=
16.666666666667
step 3: add the % sign
= 16.6666666666667%
---------------------------------
Use again the same percentage formula:
% / 100 = Part / Whole replace
the given values:
% / 100 = 50 / 300
Cross multiply:
% x 300 = 50 x 100
Divide by 300, reduce the fraction and get the percentage:
% = 50 x 100 / 300 = 16.666666666667%
What is 50% of 300?
1) What is 50% of 300?
easiest way:
300 x 50%= 150
________________________________
Always use this formula to find a percentage:
% / 100 = Part / Whole replace the given values:
50 / 100 = Part / 300
Cross multiply:
50 x 300 = 100 x Part, or
15000 = 100 x Part
Now, divide by 100 and get the answer:
Part = 15000 / 100 = 150
12 is what percent of 40?
Correct answer: 30%
easiest way:
step 1: 12 divide 40 = 0.3
step 2: move the decimal twice to the right = 30
step 3: add the % sign = 30%
_______________________________________
Explanation:
12 = x40
divde both sides by 40 and you get..
12/40 which reduces to 3/10, turn this into a decimal..=0.3 and multiply this by 100 to get
30%
What is 30% of 70?
What is 30% of 70?
Answer: 21
Explanation:
When you are given this type of problem be sure to read the operating words,..
x =0.30 (70), this equation is the translation of the above statement. answer
21
0.5% of $1000 is what?
0.5% of $1000 is what?
Answer: 5
Explanation: You must first turn the percentage into a decimal then multiply. so 0.5% implies to divide this by 100 or 0.5/100 = 0.005 (1000) =5
Write 5/8 as a percent
Write 5/8 as a percent
Answer: 62.5%
Explanation: First turn this into a decimal by dividing 8 into 5.= 0.2, then multiply this by 100 = 20
Write 9/11 as a percent.
Write 9/11 as a percent.
Answer: 82%
Explanation: Divide 11 into 9 to get 0.818 and multiply this by 100 to get about 81% or 81.8%
12/13 of 40 is what percent?
12/13 of 40 is what percent?
Answer: 36.9%
Explanation:
The word, "of" idicates the operation of multiplication., therefore change 12/13 into a decimal and multiply,,, 0.92 (40) = 36.9 , now if we divide this by 40 and multiply by 100 we get 92.3%
25 % of 200
fraction is/of=fraction %/100 or
fraction part/whole=fraction %/100
Formula for percentage
We will take examples to illustrate.Let us start with the formula on the left
An important thing to remember: Cross multiply
It means to multiply the numerator of one fraction by the denominator of the other fraction
Examples #1:
25 % of 200 is____
In this problem, of = 200, is = ?, and % = 25
We get:
is/200 = 25/100
Since is in an unknown, you can replace it by y to make the problem more familiar
y/200 = 25/100
Cross multiply to get y × 100 = 200 × 25
y × 100 = 5000
Divide 5000 by 100 to get y
Since 5000/100 = 50, y = 50
So, 25 % of 200 is 50
What number is 2% of 50 ?
fraction is/of=fraction %/100 or
fraction part/whole=fraction %/100
Formula for percentage
What number is 2% of 50 ?
This is just another way of saying 2% of 50 is___
So, set up the proportion as example #1:
is/50 = 2/100
Replace is by y and cross multiply to get:
y × 100 = 50 × 2
y × 100 = 100
Since 1 × 100 = 100, y = 1
Therefore, 1 is 2 % of 50
24% of ___ is 36
fraction is/of=fraction %/100 or
fraction part/whole=fraction %/100
Formula for percentage
24% of___ is 36
This time, notice that is = 36, but of is missing
After you set up the formula, you get:
36/of = 24/100
Replace of by y and cross multiply to get:
36/y = 24/100
y × 24 = 36 × 100
y × 24 = 3600
Divide 3600 by 24 to get y
3600/24 = 150, y = 150
Therefore, 24 % of 150 is 36
Now, we will take examples to illustrate how to use the formula for percentage on the right
25% of ____ is 60
fraction is/of=fraction %/100 or
fraction part/whole=fraction %/100
Formula for percentage
To use the other formula that says part and whole, just remember the following:
The number after of is always the whole
The number after is is always the part
If I say 25 % of___ is 60, we know that the whole is missing and part = 60
Your proportion will will like this:
60/whole = 25/100
After cross multiplying, we get:
whole × 25 = 60 × 100
whole × 25 = 6000
Divide 6000 by 25 to get whole
6000/25 = 240, so whole = 240
Therefore, 25 % of 240 is 60
___% of 45 is 9
fraction is/of=fraction %/100 or
fraction part/whole=fraction %/100
Formula for percentage
___% of 45 is 9
Here whole = 45 and part = 9, but % is missing
We get:
9/45 = %/100
Replacing % by x and cross multiplying gives:
9 × 100 = 45 × x
900 = 45 × x
Divide 900 by 45 to get x
900/45 = 20, so x = 20
Here we go!. I hope these formula for percentage were helpful.
13% of $900.00 is what ?
Answer: 117
Explanation:
$900.00 x 0.13 %
= 117
Sarah traveled 2/7 of her total trip of 400 miles. How far did Sarah travel?
Sarah traveled 2/7 of her total trip of 400 miles. How far did Sarah travel?
Answer: 114.3miles
Explanation: The operating word is the word "of", so turn 2/7 into a decimal which is 0.285 and multiply this times the number of miles she traveled. 0.285 (400)=114.2, the answer on the test will probably be rounded to the nearest mile which would make it =114 miles
Write 65 5/8 as a decimal
Write 65 5/8 as a decimal.
Answer: 65.625
Explanation:
A decimal is always a number smaller than one, so we can leave 65 as it is and just turn the fraction into a decimal., so our decimal becomes = 65.625
Write 2 1/5 as a percent
= 220.00%
explanation:
step 1: change the number to decimal first.
a) don't do anything with the whole number "2".
b) change 1/5 to decimal by dividing it first: 1 div 5= 0.2
step 2: add them: 2 + 0.2 =2.02
step 3: move the decimal to the right twice (=202. ),
then add the % sign= 220.00 %
85% of all the students have B's.
What is the percentage that do not have B's, if the total number of students is 160.
85% of all the students have B's.
What is the percentage that do not have B's, if the total number of students is 160.
Correct answer: 15%
Explanation:
This is a trick question. All you have to know is that everything is out of 100%, so if 85% is given, the balance is simply = 15%
Your stock current costs is $34.56 dollars per share. At the closing of the Dow, your stock went up 1/8%. How much is your stock worth now?
Your stock current costs is $34.56 dollars per share. At the closing of the Dow, your stock went up 1/8%. How much is your stock worth now?
Correct answer: $34.60
Explanation:
1/8% is equal to 0.125/100 = 0.00125, now if we mulitply this times the stock value, we get 0.00432 and then we add this to our stock amount =0.0423 + 34.56 = $34.60.
If 15% of all Americans are millionaires, how many Americans are not millionaires, if there are 245,000,000 Americans?
If 15% of all Americans are millionaires, how many Americans are not millionaires, if there are 245,000,000 Americans?
Correct answer: 208,250,000
Explanation:
Remember 15% is the balance of 85%, which are the percentage of Americans that are not millionares. So just take 0.85 times the population.
=280,250,000
According to the diet clinic Angie was diagnosed as being 15 pounds overweight for her body size. If Angie weighs 150 pounds, what percentage her weight needs to be lost?
According to the diet clinic Angie was diagnosed as being 15 pounds overweight for her body size. If Angie weighs 150 pounds, what percentage her weight needs to be lost?
Correct answer: 10%
Explanation:
The question here is,,,,,, 15 pounds is what % of 150 or....
15 = x 150,, so we divide both sides of the equation by 150 to get 30 percent. Did you remember to multiply by 100 to get your percent?
John walked ¾ the distance of Bob. If Bob walked 3 ¼ miles, how far did John walk?
John walked ¾ the distance of Bob. If Bob walked 3 ¼ miles, how far did John walk?
Correct answer: 2 and 7/16 of a mile
Explanation:
1. 2 and 7/16 of a mile
2. 3 miles
3. 2.5 miles
Solution;
Take ¾ of 3 ¼. The word "of" means to multiply.
¾(3 ¼)
¾ (13/4)
Numerator multiples numerator and denominator multiples denominator. 39/16
This is an improper fraction which needs to be made into a mixed numeral.
John walked 2 and 7/16 of a mile
Place in order of greatest to least.
3/4, 7/8, 9/11
Place in order of greatest to least.
3/4, 7/8, 9/11
Correct answer: 7/8, 9/11, ¾
Explanation:
First try to reduce any to lowest terms.
Then find a common denominator for all and convert each fraction to an equivalent fraction.
The common denominator is 352.
264/352, 308/352, 288/352 these would then be ordered from greatest to least.
= 7/8>9/11>3/4
0.00078/0.00002
0.00078/ 0.00002
Correct answer: 39
Explanation:
Turn the numerator and denominator into a factor of 10.
78 x 10 -5 ÷ 2.0 x10-5
Divide 2 into 78 = 39
Convert to a percent; 0.0087
Convert to a percent; 0.0087
Correct answer: 0.87%
Explanation: Any time you are asked to change a number to a percent, simply multiply that numberr by 100 or find the decimal and move it two places to the right.
Convert to a percent; 1.25
Convert to a percent; 1.25
Answer: 125%
Explanation:
Move the decimal point two places to the right, which is the same as multiplying by 100.
=125%
convert to decimal or %: 2/5
2 divide 5 = 0.40 answer
to convert to %:
move decimal point twice to the right & add the % sign.
conver 0.75 to fraction
answer: 3/4
To convert a Decimal to a Fraction follow these steps:
Step 1: Write down the decimal divided by 1, like this: decimal1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
Step 3: Simplify (or reduce) the fraction
Example: Convert 0.75 to a fraction
Step 1: Write down 0.75 divided by 1:
0.751
Step 2: Multiply both top and bottom by 100 (there are 2 digits after the decimal point so that is 10×10=100):
× 100
right over arrow
0.751 = 75100
right under arrow
× 100
(Do you see how it turns the top number
into a whole number?)
Step 3: Simplify the fraction (this took me two steps):
÷5 ÷ 5
right over arrow right over arrow
75100 = 1520 = 34
right under arrow right under arrow
÷5 ÷ 5
Answer = 34
Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction !
convert 0.625 to a fraction
answer: 5/8
Step 1: write down:
0.6251
Step 2: multiply both top and bottom by 1,000 (there are 3 digits after the decimal point so that is 10×10×10=1,000)
6251000
Step 3: Simplify the fraction (it took me two steps here):
÷ 25 ÷ 5
right over arrow right over arrow
6251000 = 2540 = 58
right under arrow right under arrow
÷ 25 ÷ 5
Answer = 58
convert 2.35 to a fraction
answer: 2 7/20
When there is a whole number part, put the whole number aside and bring it back at the end:
Example: Convert 2.35 to a fraction
Put the 2 aside and just work on 0.35
Step 1: write down:
0.35
Step 2: multiply both top and bottom by 100 (there are 2 digits after the decimal point so that is 10×10=100):
35/100
Step 3: Simplify the fraction:
35 ÷ 5 = 7
____ ___ ___
100 ÷ 5= 20
right over arrow
= 7/20
Bring back the 2 (to make a mixed fraction):
Answer = 2 7/20
convert 0.333 to a fraction
answer: 333/1000
Example: Convert 0.333 to a fraction
Step 1: Write down:
0.333
Step 2: Multiply both top and bottom by 1,000 (there are 3 digits after the decimal point so that is 10×10×10=1,000)
333/1000
Step 3: Simplify Fraction:
Can't get any simpler!
Answer = 333/1000
But a Special Note:
If you really meant 0.333... (in other words 3s repeating forever which is called 3 recurring) then we need to follow a special argument. In that case we write down:
0.333...1
Then multiply both top and bottom by 3:
× 3
right over arrow
0.333...1 = 0.999...3
right under arrow
× 3
And 0.999... = 1 (Does it? - see the 9 Recurring discussion for more if you are interested), so:
Answer = 13
Express 0.85 as a fraction in its lowest terms.
answer: 17/20
Step 1:
\text{Writedown}\frac{085}{1}
Step 2:
Multiply both top and bottom by 100 (because there were 2 digits after the decimal point):
\frac{085}{1}=\frac{085\times100}{1\times100}=\frac{85}{100}
Step 3:
Simplify the fraction:
85 and 100 have a common factor 5, so divide top and bottom by 5:
\frac{85}{100}=\frac{17}{20}
Express 0.64 as a fraction in its lowest terms.
Step 1:
\text{Writedown}\frac{064}{1}
Step 2:
Multiply both top and bottom by 100 (because there were 2 digits after the decimal point):
\frac{064}{1}=\frac{064\times100}{1\times100}=\frac{64}{100}
Step 3:
Simplify the fraction:
64 and 100 have a common factor 4, so divide top and bottom by 4:
\frac{64}{100}=\frac{16}{25}
Express 0.375 as a fraction
answer: 3/8
Step 1:
\text{Writedown}\frac{0375}{1}
Step 2:
Multiply both top and bottom by 1,000 (because there were 3 digits after the decimal point):
\frac{0375}{1}=\frac{0375\times1,000}{1\times1,000}=\frac{375}{1,000}
Step 3:
Simplify the fraction:
375 and 1,000 have a common factor 5, so divide top and bottom by 5:
\frac{375}{1,000}=\frac{75}{200}
75 and 200 have a common factor 5, so divide top and bottom by 5 again:
\frac{75}{200}=\frac{15}{40}
15 and 40 have a common factor 5, so divide top and bottom by 5 yet again:
\frac{15}{40}=\frac{3}{8}
Express 0.425 as a fraction
answer: 17/40
Step 1:
\text{Writedown}\frac{0425}{1}
Step 2:
Multiply both top and bottom by 1,000 (because there were 3 digits after the decimal point):
\frac{0425}{1}=\frac{0425\times1,000}{1\times1,000}=\frac{425}{1,000}
Step 3:
Simplify the fraction:
425 and 1,000 have a common factor 5, so divide top and bottom by 5:
\frac{425}{1,000}=\frac{85}{200}
85 and 200 have a common factor 5, so divide top and bottom by 5 again:
\frac{85}{200}=\frac{17}{40}
Express 0.9875 as a fraction
answer: 79/80
Step 1:
\text{Writedown}\frac{09875}{1}
Step 2:
Multiply both top and bottom by 10,000 (because there were 4 digits after the decimal point):
\frac{09875}{1}=\frac{09875\times10,000}{1\times10,000}=\frac{9,875}{10,000}
Step 3:
Simplify the fraction:
9,875 and 10,000 have a common factor 5, so divide top and bottom by 5:
\frac{9,875}{10,000}=\frac{1,975}{2,000}
1,975 and 2,000 have a common factor 5, so divide top and bottom by 5 again:
\frac{1,975}{2,000}=\frac{395}{400}
395 and 400 have a common factor 5, so divide top and bottom by 5 again:
\frac{395}{400}=\frac{79}{80}
The sum 0.25 + 0.375 = 0.625 can be expressed using fractions as:
answer: 1/4 + 3/8 = 5/8
Express each of the decimals as fractions:
025=\frac{025}{1}=\frac{025\times100}{1\times100}=\frac{25}{100}=\frac{5}{20}=\frac{1}{4}
\\\\\\0375=\frac{0375}{1}=\frac{0375\times1,000}{1\times1,000}=\frac{375}{1,000}=\frac{75}{200}=\frac{15}{40}=\frac{3}{8}
\\\\\\0625=\frac{0625}{1}=\frac{0625\times1,000}{1\times1,000}=\frac{625}{1,000}=\frac{125}{200}=\frac{25}{40}=\frac{5}{8}
\\\\\\\text{Sothecorrectwaytoexpressthesumusingfractionsis}\frac{1}{4}+\frac{3}{8}=\frac{5}{8}
The sum 0.35 + 0.125 = 0.475 can be expressed using fractions
answer: 7/20 + 1/8 = 19/40
Express each of the decimals as fractions:
035=\frac{035}{1}=\frac{035\times100}{1\times100}=\frac{35}{100}=\frac{7}{20}
0125=\frac{0125}{1}=\frac{0125\times1,000}{1\times1,000}=\frac{125}{1,000}=\frac{25}{200}=\frac{5}{40}=\frac{1}{8}
0475=\frac{0475}{1}=\frac{0475\times1,000}{1\times1,000}=\frac{475}{1,000}=\frac{95}{200}=\frac{19}{40}
So the correct way to express the sum using fractions is:
\frac{7}{20}+\frac{1}{8}=\frac{19}{40}
Express 0.555... as a fraction
(in other words 5s repeating forever which is called 0 point 5 recurring)
answer: 0.555...= 5/9
Method 1
Step 1:
\text{Writedown}\frac{0555}{1}
Step 2:
Multiply both top and bottom by 9 (why 9? only because experience tells me it works for this particular question):
\frac{0555}{1}=\frac{0555\times9}{1\times9}=\frac{4999}{9}
And 4.999... = 5 , so:
\text{Answer}=\frac{5}{9}
Method 2
Let x = 0.555...
Multiply by 10, which means move the decimal point one place to the right:
10x = 5.555...
x and 10x have exactly the same decimal part, so if we subtract, it will disappear:
10x - x = 5.555... - 0.555...
Simplify: 9x = 5
\text{Dividebothsidesby9}x=\frac{5}{9}
So there's our answer:
0555=\frac{5}{9}
Express 0.636363... as a fraction
(in other words 63s repeating forever which is called 0 point 63 recurring)
answer: 7/ 11
Step 1:
\text{Writedown}\frac{0636363}{1}
Step 2:
Try multiplying both top and bottom by 9:
\frac{0636363}{1}=\frac{0636363\times9}{1\times9}=\frac{5727272}{9}
This method doesn't seem to work for this example. What we have now is no better than what we started with!
Let's try a different method:
Let x = 0.636363...
Multiply by 100, which means move the decimal point two places to the right:
100x = 63.636363...
x and 100x have exactly the same decimal part, so if we subtract, it will disappear:
100x - x = 63.636363... - 0.636363...
Which is: 99x = 63
\Rightarrowx=\frac{63}{99}
63 and 99 have a common factor 9, so divide top and bottom by 9:
\frac{63}{99}=\frac{7}{11}\\\\\text{Sotheresouranswer}\\\\0636363=\frac{7}{11}
Express 0.825 as a fraction
answer : 33/40
Step 1:
\text{Writedown}\frac{0825}{1}
Step 2:
Multiply both top and bottom by 1,000 (because there were 3 digits after the decimal point):
\frac{0825}{1}=\frac{0825\times1,000}{1\times1,000}=\frac{825}{1,000}
Step 3:
Simplify the fraction:
825 and 1,000 have a common factor 5, so divide top and bottom by 5:
\frac{825}{1,000}=\frac{165}{200}
165 and 200 have a common factor 5, so divide top and bottom by 5 again:
\frac{165}{200}=\frac{33}{40}
which is larger 3/8 or 5/12
answer: 5/12
for UNLIKE DENOMINATORS, MAKE THEM THE SAME
steps
FIND THE LEAST COMMON DENOMINATORS FOR BOTH FRACTIONS
list multiples of 8: 8x1=8, 8x2=16, 8x3=24
list multiples of 12: 12x1=12, 12x2=24
so the least common denominators for both numbers is 24.
now, change the denominators to 24: so 3/8 and 5/12 is now 3/24 and 5/24.
FIND THE LEAST COMMON NUMERATORS FOR BOTH FRACTIONS
for 3/8, 3 was multiplied with 8 to get the LCD;therefore, use 3 to multiple with numerator 3; 3x 3=9, so 3/8 is now 9/24.
for 5/12, 2 was multiplied with 12 to get the LCD, therefore, use 2 to multiply with numerator 5: 2x5=10, so 5/12 is now 10/24.
so the 3/8 and 5/12 are now 9/24 and 10/24.
NOW COMPARE
we can now see that 9/24 is smaller than 10/24 (because 9 is smaller than 10),
so the answer =5/12 is larger fraction than 3/8.
which is larger 5/6 or 11/15
answer: 5/6
for UNLIKE DENOMINATORS, MAKE THEM THE SAME
steps
FIND THE LEAST COMMON DENOMINATORS FOR BOTH FRACTIONS
LCD for 6: 6X15=90
LCD for 15: 15X6=90
the new denominators for both is 90
FIND THE LEAST COMMON NUMERATORS FOR BOTH FRACTIONS
LCM for 5: 15, so 5x15=75
LCM for 11: 6, so 11x6=66
so the 5/6 is now 75/90 and the
11/15 is now 66/90
NOW COMPARE
we can see that 75/90 is the larger fraction (because 75 is more than 66)
so 5/6 is the larger fraction .
which one is larger: 6/8 or 7/8
answer: 7/8
which one is larger 4/6 or 5/6
answer: 5/6
which one is smaller 2/8 or 6/8
answer: 2/8
which one is larger: 2/3 or 1/5
answer:
2 is larger than 1 but the denominators are not the same.
CHANGE THE DENOMINATORS, SO THEY BOTH OF THE SAME
LCD for 3:
LCD for 5:
DO THE SAME FOR NUMERATORS
LCM for 2:
LCM for 1:
NOW COMPARE
which one is larger 5/8 or 4/6
answer: 4/6
proper steps:
1. before comparing them, change both fractions so they have the same denominators or bottom numbers.
2. first, find the smallest denominators called lowest common denominators (lcd).
2a. CHANGE THE DENOMINATORS, SO THEY BOTH HAVE THE SAME DENOMINATORS.
find the numbers than can be divided evenly by 8 for first denominator.
IST DENOMINATOR 8: 8, 16, 24, 32, 40, 48, 56, 64
(8x1=8; 8x2=16, 8x3=24, and so on)
2ND DENOMINATOR 6: 6, 12, 18, 24, 30, 36, 42, 48
(6x1=6; 6x2=12; 6x3=18; 6x4=24 and so on)
it looks like 24 and 48 can be divided evenly by both 8 and 6.
24 is the smallest number that appear on both rows, so it's the lowest common denominators-lcd.
2b. change both denominators to 24, so they both have the same denominators.
now: 5/24, 4/24
3. CHANGE THE NUMERATORS THE SAME WAY WE CHANGE THE DENOMINATORS.
1ST NUMERATOR 5:
we got the LCD 24 for original denominator 8 by multiplying 8x3=24
therefore, we are going to use #3 to multiply with the original numerator 5. 5x3=15
5 x 3= 15
_______ ____
8 x 3= 24
, so we change 5/8 to 15/24.
3b. 2ND NUMERATOR 4
(for fraction 4/6):
we got the LCD 24 for the original denominator 6 by multiplying 6x4=24
therefore, we are going to use #4 to multiply with the original numerator 4. 4x4= 16
, so we change 4/6 to 16/24
the NEW FRACTIONS ARE NOW:
15/24 and 16/24
4. NOW COMPARE THE TWO: 15/24 AND 16/24.
16/24 is larger than 15/24, so 4/6 is larger than 5/8
Which one of the following fractions is the largest?
a. 29/36 b. 7/9 c. 5/6 d. 3/4
answer: 5/6
To compare the fractions, we need to write each of them as an equivalent fraction with a common denominator i.e. we must find the least common multiple of 36, 9, 6 and 4.
Since 9, 6 and 4 are all factors of 36, the least common multiple is 36
So change them all to equivalent fractions with denominator 36:
\frac{29}{36}=\frac{29}{36}\\\\\frac{7}{9}=\frac{7\times4}{9\times4}=\frac{28}{36}\\\\\frac{5}{6}=\frac{5\times6}{6\times6}=\frac{30}{36}\\\\\frac{3}{4}=\frac{3\times9}{4\times9}=\frac{27}{36}
Now they all have the same denominator, we just need to find the one with the largest numerator, which is 30
\text{Therefore}\frac{5}{6}\text{isthelargestfraction}
Which one of the following fractions is the largest?
a. 1/3 b. 5/12 c. 2/5 d. 13/30
answer; 13/30
To compare the fractions they should have the same denominator (bottom number).
So let's do that.
The first step is to find the least common multiple of 3, 12, 5 and 30 (all the denominators).
Since 3, 12, 5 and 30 are all factors of 60, the least common multiple is 60
So change them all to equivalent fractions with denominator 60:
\frac{1}{3}=\frac{1\times20}{3\times20}=\frac{20}{60}\\\\\\\frac{5}{12}=\frac{5\times5}{12\times5}=\frac{25}{60}\\\\\\\frac{2}{5}=\frac{2\times12}{5\times12}=\frac{24}{60}\\\\\\\frac{13}{30}=\frac{13\times2}{30\times2}=\frac{26}{60}
Now they all have the same denominator, we just need to find the one with the largest numerator, which is 26
\text{Therefore}\frac{13}{30}\text{isthelargestfraction}
Which one of the following fractions is the largest?
a. 3/8 b. 11/24 c. 7/16 d. 5/12
answer: 11/24
To compare the fractions, we need to write each of them as an equivalent fraction with a common denominator i.e. we must find the least common multiple of 8, 24, 16 and 12.
Since 8, 24, 16 and 12 are all factors of 48, the least common multiple is 48
So change them all to equivalent fractions with denominator 48:
\frac{3}{8}=\frac{3\times6}{8\times6}=\frac{18}{48}\\\\\frac{11}{24}=\frac{11\times2}{24\times2}=\frac{22}{48}\\\\\frac{7}{16}=\frac{7\times3}{16\times3}=\frac{21}{48}\\\\\frac{5}{12}=\frac{5\times4}{12\times4}=\frac{20}{48}
Now they all have the same denominator, we just need to find the one with the largest numerator, which is 22
\text{Therefore}\frac{11}{24}\text{isthelargestfraction}
Which one of the following fractions is the smallest?
a. 11/8 b. 5/9 c. 3/5 d. 26/45
answer: 5/9
To compare the fractions let's give them the same denominator.
So we must find the least common multiple of 18, 9, 5 and 45.
Since 18, 9, 5 and 45 are all factors of 90, the least common multiple is 90
So change them all to equivalent fractions with denominator 90:
\frac{11}{18}=\frac{11\times5}{18\times5}=\frac{55}{90}\\\\\frac{5}{9}=\frac{5\times10}{9\times10}=\frac{50}{90}\\\\\frac{3}{5}=\frac{3\times18}{5\times18}=\frac{54}{90}\\\\\frac{26}{45}=\frac{26\times2}{45\times2}=\frac{52}{90}
Now they all have the same denominator, we just need to find the one with the smallest numerator, which is 50
\text{Therefore}\frac{5}{9}\text{isthesmallestfraction}
Which one of the following fractions is the smallest?
a. 1/10 b. 6/70 c. 1/15 d. 2/21
answer: 1/15
To compare the fractions, we need to write each of them as an equivalent fraction with a common denominator i.e. we must find the least common multiple of 10, 70, 15 and 21.
Since 10, 70, 15 and 21 are all factors of 210, the least common multiple is 210
So change them all to equivalent fractions with denominator 210:
\frac{1}{10}=\frac{1\times21}{10\times21}=\frac{21}{210}\\\\\frac{6}{70}=\frac{6\times3}{70\times3}=\frac{18}{210}\\\\\frac{1}{15}=\frac{1\times14}{15\times14}=\frac{14}{210}\\\\\frac{2}{21}=\frac{2\times10}{21\times10}=\frac{20}{210}
Now they all have the same denominator, we just need to find the one with the smallest numerator, which is 14
\text{Therefore}\frac{1}{15}\text{isthesmallestfraction}
Which one of the following fractions is the smallest?
a. 2/7 b. 8/21 c. 1/3 d. 20/63
answer: 2/7
To compare the fractions, we need to write each of them as an equivalent fraction with a common denominator i.e. we must find the least common multiple of 7, 21, 3 and 63.
Since 7, 21, 3 and 63 are all factors of 63, the least common multiple is 63
So change them all to equivalent fractions with denominator 63:
\frac{2}{7}=\frac{2\times9}{7\times9}=\frac{18}{63}\\\\\frac{8}{21}=\frac{8\times3}{21\times3}=\frac{24}{63}\\\\\frac{1}{3}=\frac{1\times21}{3\times21}=\frac{21}{63}\\\\\frac{20}{63}=\frac{20}{63}
Now they all have the same denominator, we just need to find the one with the smallest numerator, which is 18
\text{Therefore}\frac{2}{7}\text{isthesmallestfraction}
Which one of the following fractions is the largest?
answer: 3/10
To compare the fractions, they should have the same denominator (bottom number).
So first let us find the least common multiple of 25, 5, 10 and 50.
Since 25, 5, 10 and 50 are all factors of 50, the least common multiple is 50
So change them all to equivalent fractions with denominator 50:
\frac{6}{25}=\frac{6\times2}{25\times2}=\frac{12}{50}\\\\\frac{1}{5}=\frac{1\times10}{5\times10}=\frac{10}{50}\\\\\frac{3}{10}=\frac{3\times5}{10\times5}=\frac{15}{50}\\\\\frac{11}{50}=\frac{11}{50}
Now they all have the same denominator, we just need to find the one with the largest numerator (the top number), which is 15
\text{Therefore}\frac{3}{10}\text{isthelargestfraction}
Which one of the following fractions is the largest?
a. 4/9 b. 5/18 c. 1/3 d. 9/24
answer a. 4/9
To compare the fractions, they should have the same denominator (bottom number).
So first let us find the least common multiple of 9, 18, 3 and 24:
The factors are:
3: 3, 6, 9, ..., 69, 72, 75, ...
9: 9, 18, 27, ..., 63, 72, 81, ...
18: 18, 36, 54, 72, 90, ...
24: 24, 48, 72, 96, ...
So the least common multiple is 72
Now change them all to equivalent fractions with denominator 72:
\frac{4}{9}=\frac{4\times8}{9\times8}=\frac{32}{72}\\\\\frac{5}{18}=\frac{5\times4}{18\times4}=\frac{20}{72}\\\\\frac{1}{3}=\frac{1\times24}{3\times24}=\frac{24}{72}\\\\\frac{9}{24}=\frac{9\times3}{24\times3}=\frac{27}{72}
Now they all have the same denominator, we just need to find the one with the largest numerator (the top number), which is 32
\text{Therefore}\frac{4}{9}\text{isthelargestfraction}
Which one of the following fractions is the smallest?
a. 3/10 b. 3/8 c. 7/20 d. 1/4
answer: 1/4
To compare the fractions, they should have the same denominator (bottom number).
So first let us find the least common multiple of 10, 8, 20 and 4:
The factors are:
4: 4, 8, 12, ..., 36, 40, 44, ...
8: 8, 16, 32, 40, 48, ...
10: 10, 20, 30, 40, 50, ...
20: 20, 40, 60, ...
So the least common multiple is 40
So change them all to equivalent fractions with denominator 40:
\frac{3}{10}=\frac{3\times4}{10\times4}=\frac{12}{40}\\\\\frac{3}{8}=\frac{3\times5}{8\times5}=\frac{15}{40}\\\\\frac{7}{20}=\frac{7\times2}{20\times2}=\frac{14}{40}\\\\\frac{1}{4}=\frac{1\times10}{4\times10}=\frac{10}{40}
Now they all have the same denominator, we just need to find the one with the smallest numerator (the top number), which is 10
\text{Therefore}\frac{1}{4}\text{isthesmallestfraction}
Which one of the following fractions is the smallest?
a. 1/2 b. 4/9 c. 14/27 d. 2/3
answer: 4/9
To compare the fractions, they should all have the same denominator (the bottom number).
The first step is to work out what that denominator should be. To do that we find the least common multiple of 2, 9, 27 and 3.
The multiples are:
2: 2, 4, 6, ..., 52, 54, 56, ...
3: 3, 6, 9, ..., 51, 54, 57, ...
9: 9, 18, 27, 36, 45, 54, 63, ...
27: 27, 54, 81, ...
The least common multiple is 54.
Now change them all to equivalent fractions with denominator 54 (remembering to multiply both top and bottom by the same amount in each case):
\frac{1}{2}=\frac{1\times27}{2\times27}=\frac{27}{54}\\\\\frac{4}{9}=\frac{4\times6}{9\times6}=\frac{24}{54}\\\\\frac{14}{27}=\frac{14\times2}{27\times2}=\frac{28}{54}\\\\\frac{2}{3}=\frac{2\times18}{3\times18}=\frac{36}{54}
Now they all have the same denominator, we just need to find the one with the smallest numerator (the top number), which is 24
\text{Therefore}\frac{4}{9}\text{isthesmallestfraction}
Which number is in the hundredths place in 0.5983?
9
8
3
5
answer: 9
5 is what percentage of 40?
a. 10.5%
b. 15 %
c. 25%
d. 12.5%
answer: d. 12.5%
5 divide 40 = 0.125
move the decimal 2x to the right.
add the % sign
What is the decimal equivalent of 3/8?
a. 0.125
b. 0.625
c. 0.375
d. 875
answer: c. 0.375
3 divide 8 = 0.375
Convert .125 into fraction form
a. 1/16
b. 1/8
c. 1/2
d. 1/4
answer. b 1/8
write down 0.125
= .125
_______
1,000
Step 2: Multiply both top and bottom by 1,000 (there are 3 digits after the decimal point so that is 10×10×10=1,000)
= 0.125 x 1000 = 125, a whole number
______ ________
1000 x 1000 = 10,000.00
reduce to the lowest term
125 divide 125 = 1
10,000.00 divide 125= 8000
= 1/8000
_________________________________________________________
Explanation:
To convert 0.125 to its fraction form, think of a number to multiply it with so that it becomes a whole number. That would be 1000, because 0.125 * 1000 = 125, a whole number. Then divide 125 with the same number that you multiplied it with, thus: 1251000
. Now we have a fraction. The next step is to reduce this huge fraction to its lowest form. Factor out the numerator and denominator: 1251000
= 125∗1125∗8
. The 125 in the numerator and denominator cancel out, leaving us the reduced form of the fraction, 18
.
increase 97 by 23%
answer: 119.31
97 x 23%= 22.31 + 97 = 119.31
identify the digit in the tenths place:
42. 168
a. 1. b. 4 c. 6 d. 8
answer: a. 1
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