a. 9/10
explanation:
• the denominators (bottom number) are the same so there is no need to change to a common factor
• because the fractions have common factors, you add the top numbers (3+6) to get 9
• then you put the top number over the 10 (9/10) and it’s simplified as much as possible
b. 3/4
explanation:
• each denominator (bottom term) is a factor of 12 so you have to change each fraction to #/12
• to change 1/3, you multiply the top and bottom numbers by 4 (1x4 & 3x4 = 4/12)
• to change 1/4, you multiply the top and bottom numbers by 3 (1x3 & 4x3 = 3/12)
• to change 1/6, you multiple the top and bottom numbers by 2 (1x2 & 6x2 = 2/12)
• then you add each of the top numbers (4+3+2) and put it over the common denominator (12) to get 9/12
- both 9 & 12 are divisible by 3, so you simply by dividing both by 3 to get 3/4
c. 1/3
explanation:
•the denominators are the same, so you subtract 5-3 without changing the denominator & you get 2/6
• then, because both numbers are divisible by 2, you divide both by 2 and get 1/3
Set up a ratio. 1 1/8 gallons is to 13 1/2 miles as 1 gallon is to x miles.
x= unknown number of miles
(1 1/8) / (13 1/2)= 1 / x
cross multiply top left by bottom right and bottom left by top right
1 1/8 * x= 13 1/2 * 1
1 1/8x= 13 1/2
convert each mixed number to improper fractions
9/8x= 27/2
divide both sides by 9/8
x= 27/2 ÷ 9/8
to divide fractions, multiply by the reciprocal/inverse of 9/8
x= 27/2 * 8/9
multiply numerators together; multiply denominators together
x= (27*8)/(2*9)
x= 216/18
x= 12 miles
ANSWER: A car can travel 12 miles for each 1 gallon of gas.
Hope this helps! :)
GCF, Greatest Common Factor.
-9(3d-2)=-29
-27d+18=-29
-27d=-29-18
-27d=-47
d=-47/-27
d=47/27