Fractions and math

Question

A contractor mixes 2/9 of a gallon of tan paint with 8/3 gallons of white paint to make a custom color. How many gallons of this custom color does the contractor have?

Answer 1

26/9 = 2 8/9 = 2.888... gallons

2/9 + 8/3 = (2+24)/9 = 26/9

8/3= 8(3)/3(3) = 24/9

to add fractions, convert them so they have the same denominator

then add their new numerators. in this problem just convert 8/3 to 24/9, then add 2+24

or

multiply by the LCD, Least Common Denominator

for 3 and 9, 9 is the LCD. as both 3 and 9 evenly divide into 9

2/9 x 9 = 2, 8/3 x9 = 24. 2+24=26. then divide that by 9 to get 26/9

or if you can't figure out what the LCD use any Common Denominator

such as 9x3 =27, just multiply the 2 denominators together to get a Common Denominator

27x2/9 =54/9=6, 27x8/3=72, 6+72=78, 78/27= 26/9

another method is convert the fractions to decimals. use a calculator if you need to:

2/9 = .222.... (the 2's go on forever)

8/3 = 2.666... (the 6's go on forever)

add them, each 2 and 6 adds to 8:

to get 2.888.... gallons

which = 2 8/9 = 26/9

= about about 2.9 gallons, rounding off, up, to one decimal place

= about 2.89, rounding to two decimals

= about 2.889 rounding to three decimals

most problems that want a decimal answer will require 1,2 or 3 decimals

if this is Pearson, Cengage or some computer program, online problem

pay attention to how they want the answer, otherwise you can type in a correct answer, but if in the wrong form, you get no credit. if they want 2 decimals and you do 3, you get zero credit

if they just say they want the "exact" answer, then they probably want the fraction 26/9 or 2 8/9

possibly they'd take 2.888...

but they wont' accept a rounded answer such as 2.9, 2.89 or 2.889