Math Question: Who received the best grade? (Percentage) Mark who got 23/30 Joey who got 53/70 Bob who got 7/11 Bobby-Joe who got 42/60

If you can use a calculator for this, you can convert everything to decimal one at a time, or put them in a spreadsheet and sort them from least to greatest or greatest to least. If you do this and your tool treats 7/11 as a date, just make it 14/22. There are other "tricks" to sort fractions with different denominators. Mark got 23/30 and Bobby-Joe got 42/60. There's 2 quick ways to compare Mark and Joe: 23/30=46/60>42/60 or 42/60=21/30<23/30, so Mark did better than Bobby-Joe. You can do long division on each fraction. You don't need to, Mark did better than Bobby-Joe, so Bobby-Joe definitely didn't receive the best grade, which is what you're being asked to find. I think you'd be better off finding the LCD (Least Common Denominator) and going from there. Your fractions are: 23/30, 53/70, 7/11, 42/60 You can reduce 42/60 to 21/30 if you like, but it's not necessary. The denominators are: 30,70,11,60 30 divides into 60, so you want the Least Common Multiple of the other 3: LCM(70,11,60)= The answer should be LCM = 4620 (I used an online tool), but we can work it by hand. 70,11,60 factor each number: 70=7*10=7*2*5 11 is prime 60=6*10=2*3*2*5 2*5 (or 10) shows up in 60 and 70, but everything else shows up only once. 7*2*5*11*2*3*2*5 has that 2*5 twice, and is not the LEAST common multiple, though it will work as a common demoninator 7*2*5*11*2*3 that 2*5 once, and is the LCM. that equals 4620, but by hand: 7*2*5*11*2*3= 7*10*11*6= 70*11+6= 70*6*11= 420*11= 420*(10+1)= 420(10+1)= 420(10)+420(1)= 4200+420= 4200+(400+20)= (4200+400)+20= 4600+20= 4620 Your fractions are: 23/30, 53/70, 7/11, 42/60 With denominators: 30,70,11,60 We now convert: 23/30 --> ?/4620 53/70 --> ?/4620 7/11 --> ?/4620 42/60 --> ?/4620 23/30 --> ?/4620 23/30 = x/4620 (23*4620)/30 = x 3542 = x 53/70 --> ?/4620 53/70 = x/4620 (4620*53)/70 = x x=3498 7/11 --> ?/4620 7/11 = x/4620 (4620* 7)/11 = x x=2940 42/60 --> ?/4620 42/60 = x/4620 (4620*42)/60 = x x=3234 Bobby-Joe got 42/60=3234/4620 Bob got 7/11=2940/4620 Joey got 53/70=3498/4620 Mark got 23/30=3542/4620 3542>3498>3234>2940 So Mark got the highest score. There's a way to eliminate two people quickly, so you only have to do LCM on two people: Mark got 23/30 and Bobby-Joe got 42/60=21/30. 23>21 so Mark did better than Bobby-Joe. Mark got 23/30. 23/30 is greater than 20/30. 20/30=2/3. 7/11 is less than 2/3. Bear with me. 8/12=2/3. 8/12=2/3. 7/11<8/12 because... 7/11=1-(4/11) and 8/12=1-(4/12). 4/12 is less than 4/11 because... 1/11 > 1/12 This is obvious from how fractions work. if you 11 people sharing 1 tent they have more room each than if there's 12 people in that same tent. if 1/11 > 1/12 then 4*(1/11) > 4*(1/12) 4/11 > 4 /12 Subtracting a bigger number from 10 leaves a smaller number (10-7<10-2, since 3<8). The same applies with fractions--1-(2/3) is smaller than 1-(1/100000) which is pretty close to 1. So 7/11 is less than 8/12 because 1-(4/11) < 1-(4/12). And since 1-(4/12)=2/3 we know that 7/11<2/3. So then we only need to find the GCD (greatest common denominator) between Mark and Joey. 23/30, 53/70: LCM(30,70)= 3*7*10=210 23/30=x/210 23/30=x/(30*7) 23/30=(7*23)/210 23/30=(161)/210 compared to: 53/70=x/210 53/70=(3*53)/(3*70) 53/70=159/210 And again it's Mark, but you only have to compare 2 scores using LCM methods in this instance. Sometimes they'll turn around and ask you who had the lowest score, so calculating all four might be necessary. One more thing: You can say 7/11=x/4620 and solve, or you can look at the factors: 2*2*3*5*7*11 and multiply the numerator by every factor that's not in the denominator. In this example, 7/11 is 7 times (2*2*3*5*7*11)/4620 but without the 11... so it's (7*4620)/(11*4620) which is (7/11)(4620/4620). which is just the same as (7/11)*(66/66) or (7/11)*(37/37) or any other fraction that =1. But instead of multiplying 7* 4620 and 11* 4620 and then dividing 11 out of both top and bottom, we use the factorized version we already have from when we calculated the LCM. 7/11 is (7/11)(4620/4620). 4620=(). We can use the factorized version: 7/11=(7/11)(1)=(7/11)(4620/4620)=(7/11)(2*2*3*5*7*11/4620) and then cancel the 11s: (7/11)(2*2*3*5*7*11/4620)= 7*(1/11)*(2*2*3*5*7)*(11)*(1/4620)= 7*(11)*(1/11)*(2*2*3*5*7)*(1/4620)= 7*(11/11)*(2*2*3*5*7)*(1/4620) 11/11=1, so: 7*(11/11)*(2*2*3*5*7)*(1/4620)= 7*(1)*(2*2*3*5*7)*(1/4620)= 7*(2*2*3*5*7)*(1/4620)= 7*(2*2*3*5*7)/(4620) Or with another score, 23/30: 23/30=(23/30)*1=(23/30)(1/1)=(23/30)(4620/4620)= (23*4620)/(30*4620)= [23*(2*2*3*5*7*11)]/(30*4620) You probably know what to do from here^^. [23*(2*2*3*5*7*11)]/(30*4620)= [23*(2*2*3*5*7*11)]/[(2*3*5)*4620] Which is just 30 factorized. [23*(2*2*3*5*7*11)]/[(2*3*5)*4620]= [23*(2*3*5*2*7*11)]/[(2*3*5)*4620]= [23*(((2*3*5))*2*7*11)]/[(2*3*5)*4620 (2*3*5) can be canceled, simplifying to: [23*(((2*3*5))*2*7*11)]/[(2*3*5)*4620= (23*2*7*11)/4620 One technique is to circle every factor of the GCD (4620) that is not a factor of the denominator of the fraction you are converting (7/11, 23/30) to a common base. Another is to erase or cross out every factor that is. Once you're familiar with the technique, it can be faster than solving 23/30=x/4620 etc.
Answered On 05/27/2020 13:31