Please help with the following questions on simplifying ratios:

42 : 35 : 63

3.5 kg : 1400 g

350 mm : 2.5 m : 75 cm

Do I need to convert the units to they match before I can solve these? Please explain the whole process. Thanks.
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4 Answers

For the first question you need to find the greatest common factor. Start by trying 2 and work your way up. 2 does not work because it will not go into 35 or 63. 3 does not go evenly into 35. 4 also will not work. 5 does not work. 6 also will not work. . .Then we come to 7. . .if we divide each number by 7 we get the following:

6:5:9

We know this is in lowest simplist form because 5 is a prime number.

Next we need to convert kilograms to grams by multiplying by 1000 to get

35000 g : 1400 g

in this case the greatest common factor is 1400 which if we divide both numbers we get

25 g : 1 g

For the final question we should convert to mm

2.5m=2500mm

75cm=750mm

350 mm : 2500 mm : 750 mm

We know that 50 will go evenly into each of these and we know that 350/50 is 7 which is prime. So 50 must be the greatest common factor.  Divide all 3 terms by 50 and we get

7 mm : 50 mm : 15 mm
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