Tell whether the ratios are proportions: 4/7,24/35

1 answer:

7 0

To find whether or not the ratios are proportional, simplify. The first ratio is already simplified, so simplify the second one. to do this, find what factors 24 and 35 have in common.

Factors of 24: 1, 2, 3 ,4, 6, 8, 12, 24

Factors of 35: 1, 5, 7, 35

It looks like there are now common factors between 24 and 35. For the ratios to be proportional, they have to have the same value. If 24/35 can't be simplified to 4/7, the factors are not proportional.

So, to answer the question: No, the ratios are NOT proportions. I hope this helps and have a great rest of your day!

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PLZ HELP ME ASAP PLZ PLZ PLZ!!!!! I NEED LOTS OF HELP!!! I USED 40 POINTS

cupoosta [38]

First, some defintions
reciprocals are like a/b and b/a or 5/1 and 1/5

remember, $\frac{\frac{a}{b}}{\frac{c}{d}}=(\frac{a}{b})(\frac{d}{c})=\frac{ad}{bc}$

john's fraction is reciprocal of sarah's
john=a/b
sarah=b/a

david multiplies his by sarah and gets 12/35
(b/a)(david)=12/35

multplies his number by john and gets 12/35
(a/b)(david)=15/7

hmmm

(b/a)(david)=12/35 and
(a/b)(david)=15/7

if we divide them then we do
$\frac{(\frac{b}{a})(david)}{(\frac{a}{b})(david)}=\frac{\frac{12}{35}}{\frac{15}{7}}=$
$\frac{\frac{b}{a}}{\frac{a}{b}}=\frac{\frac{12}{35}}{\frac{15}{7}}=$
$(\frac{b}{a})(\frac{b}{a})=(\frac{12}{35})(\frac{7}{15})=$
$\frac{b^2}{a^2}=\frac{84}{525}=$
$\frac{b^2}{a^2}=\frac{4}{25}$
square root both sides
$\frac{b}{a}=\frac{2}{5}$

therefor
b=2 and a=5

john's number is a/b=5/2
sarah's number is 2/5

david, hmm

sarah times david=12/35
2/5 times david=12/35
times both sides by 5/2
david=60/70
david=6/7

check other

john times david=15/7
5/2 times 6/7=15/7
30/14=15/7
15/7=15/7
true

sarah's favorite number is 2/5
john's favorite number is 5/2
david's favorite number is 6/7

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