Identify a pair of vertical angles in the figure
2 answers:
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Answer:
a) 3/5 < 4/5
b) In general if two fractions have the same denominator, then whichever fraction has the numerator closer to its denominator will be the largest fraction.
c) <em>or</em>
Step-by-step explanation:
a) 3/5 < 4/5
Flip the sign and the placement of the fraction so 3/5 is less then 4/5.
b) In general if two fractions have the same denominator, then whichever fraction has the numerator closer to its denominator will be the largest fraction.
c) We need to change the denominators to a common denominator to compare the size of the two fractions:
×
=
×
=
The common denominators of the two fractions is 30. Comparing the two fractions:
<em>or</em>
so we get: <em>or</em>
Answer: a.) 72 of each type of animal, for a total of 216
b.) 16 grown cats, 4 kittens
Step-by-step explanation:
part a. It's a distribution (division) problem. The same number of each animal is distributed over some unknown number of troughs, but the total number of troughs adds up to 69. ( I hate to give this all away, as its a brilliant problem! )
Number of troughs for each animal type is How many needed by the number of animals per trough:
h/2 + c/3 + p/8 = 69
Since we are given "the same number of horses, cows and pigs" we can substitute "x" for all.
Get a common denominator. 24 would work, 48 also.
24x + 16x + 6x = 3372
46x = 3372 x = 72
Proof: calculate the number of each kind of trough
Horses 72/2 = 36, Cows 72/3 = 24 Pigs 72/8 = 9 36+24+9 = 69
part b. 5c + 3k = 92, c + k = 20 Rearrange to get a value for c to substitute.
c = 20-k 5(20-k) +3k =92 Distribute and solve
100 - 5k + 3k = 92 becomes -2k = -8 so k = 4 Substitute into the original
c + 4 = 20 becomes c=20-4, so c = 16
Proof: 5c +3k = 92 Substitute values 5(16) + 3(4) = 92 80 + 12 = 92