Answer:
Part 1) \(3/7,18/42\)
Part 2) \(60/100\)
Part 3) \(5/8=15/24\)
Step-by-step explanation:
we know that
If two ratios form a proportion, then the two ratios in simplest form are equal
Part 1
Which ratios form a proportion?
case A) \(4/9,12/25\)
equate the ratios
\(4/9=12/25\\4*25=12*9\)
\(100
eq 108\) ------> is not true
therefore
the ratios case A does not form a proportion
case B) \(3/7,18/42\)
equate the ratios
\(3/7=18/42\\3*42=7*18\)
\(126=126\) ------> is true
therefore
the ratios case B form a proportion
case C) \(5/11,20/45\)
equate the ratios
\(5/11=20/45\\5*45=20*11\)
\(225
eq220\) ------> is not true
therefore
the ratios case C does not form a proportion
case D) \(5/8,15/25\)
equate the ratios
\(5/8=15/25\\5*25=15*8\)
\(125
eq120\) ------> is not true
therefore
the ratios case D does not form a proportion
Part 2
Which ratio forms a proportion with 18 over 30?
case A) \(20/35\)
equate the ratio to \(18/30\)
\(20/35=18/30\\20*30=35*18\)
\(600
eq 630\) ------> is not true
therefore
the ratio case A does not form a proportion with \(18/30\)
case B) \(50/90\)
equate the ratio to \(18/30\)
\(50/90=18/30\\50*30=90*18\)
\(1,500
eq 1,620\) ------> is not true
therefore
the ratio case B does not form a proportion with \(18/30\)
case C) \(36/48\)
equate the ratio to \(18/30\)
\(36/48=18/30\\36*30=48*18\)
\(1,080
eq 864\) ------> is not true
therefore
the ratio case C does not form a proportion with \(18/30\)
case D) \(60/100\)
equate the ratio to \(18/30\)
\(60/100=18/30\\60*30=100*18\)
\(1,800=1,800\) ------> is true
therefore
the ratio case D form a proportion with \(18/30\)
Part 3
Which proportion has cross products of 5 × 24 and 8 × 15?
case A) \(5/8=15/24\)
the cross product is equal to
\(5*24=8*15\)
therefore
the proportion case A is a solution
case B) \(5/24=8/15\)
the cross product is equal to
\(5*15=24*8\)
therefore
the proportion case B is not a solution
case C) \(8/24=15/5\)
the cross product is equal to
\(8*5=24*15\)
therefore
the proportion case C is not a solution
case D) \(15/8=5/24\)
the cross product is equal to
\(15*24=8*5\)
therefore
the proportion case D is not a solution
