decimal, percentage and fractions
What is 95% of 20?
19 step: 20 x 0.95 =19
convert to decimal or %: 2/3
2 div 3 = .666 or 66.6% (by moving decimal point to the right twice)
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%
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
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
13% of $900.00 is what ?
Answer: 117 Explanation: $900.00 x 0.13 % = 117
Proportion
Proportion Two ratios that have equal values
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
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
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}
increase 97 by 23%
answer: 119.31 97 x 23%= 22.31 + 97 = 119.31
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}
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
___% 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.
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%
Improper Fractions
Improper Fractions Change an improper fraction into a mixed number by dividing the numerator by the denominator
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
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
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
convert to decimal or %: 7/8
7 div 8 = .875 or 87.5% (by moving decimal point to the right twice)
What is 28% of 100?
28 100 x .28%= 28
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
Percent Per hundred - part per hundred
Percent Formula
Percent Formula Part / Whole (of) = % / 100
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%
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
convert to decimal or %: 1/3
1 div 3 = .333 or 33.3% (by moving decimal point to the right twice)
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
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%
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
convert to decimal or %: 3/4
3 div 4= .75 or 75% (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 %: 3/8
3 div 8= .375 or 37.5% (by moving decimal point to the right twice)
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
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
convert to decimal or %: 5/8
5 div 8 = .625 or 62.5% (by moving decimal point to the right twice)
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%
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 %
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
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.
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%
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}
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}
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!
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
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
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
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}
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 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
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.
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
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.
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}
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}
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}
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}
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
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 !
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}
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
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 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 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}
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
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}
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}
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 0.9875 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}
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}
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 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 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
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}
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 .
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. 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 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
identify the digit in the tenths place: 42. 168 a. 1. b. 4 c. 6 d. 8
answer: a. 1
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
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
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?
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
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.
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 decimal or %: 1/2
1 div 2= .50 or 50% (by moving decimal point to the right twice)
which one is smaller 2/8 or 6/8
answer: 2/8
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
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}
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 44 is 25% of what number?
176 step 1: 44 divide 25% = 1.76 step 2: move the decimal twice to the right= 176
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
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
Multiplying Fractions
Multiplying Fractions Top times top and bottom times bottom
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
convert to decimal or %: 1/4
1 div 4= .25 or 25% (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 %: 1/8
1 div 8= .125 or 12.5% (by moving decimal point to the right twice)
Dividing Fractions
Dividing Fractions Inverse the second fraction and multiply
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
which one is larger 4/6 or 5/6
answer: 5/6
convert to decimal or %: 4/5
4 div 5= .80 or 80% (by moving decimal point to the right twice)
Ratio
Ratio A relationship between two numbers
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
