Respuesta :
Answer:
1) A, 2) A, 3) B, 4) D, 5) A, 6) proportion, 7) 4 : 3, 8) a) The simplest ratio of 14 : 42 is 1 : 3, b) The simplest ratio of 56 : 80 is 7 : 10, 9) a) The series 4, 6, 8, 12 is in proportion, since each element after the first one is equal to the sum of the previous element and 2 units, b) The series 15, 45, 5, 25 is not in proportion, since it is an alternating series, 10) 4 cans of juice cost 140, 11) a) 3 : 2, b) 3 : 1, 12) The ratio of 15 centimeters to 2 meters is 3 : 40.
Step-by-step explanation:
1) The ratio is determined by following operation:
[tex]x = \frac{300}{100}[/tex]
[tex]x = \frac{3}{1}[/tex]
3 : 1 is the ratio of 300 to 100. (Answer: A)
2) The weight of 1 book is found by the total weight of books divided by the total amount of books, that is:
[tex]x = \frac{80\,kg}{20}[/tex]
[tex]x = 4\,kg[/tex]
The weight of 1 book is 4 kilograms. (Answer: A)
3) The equivalent ratio of 3 : 2 is found by multiplicating both numerator and denominator by a given positive number:
[tex]x = \frac{3\times 2}{2\times 2}[/tex]
[tex]x = \frac{9}{4}[/tex]
An equivalent ratio of 3 : 2 is 6 : 4. (Answer: B)
4) The middle terms of ratio correspond with the denominator of the ratio on the left and the numerator of the ratio on the right. Hence, the middle terms of 3 : 15 = 21 : 105 are 15 and 21. (Answer: D)
5) 8 : 4 is not proportional to 8 : 16, since both numerators and denominators are not multiplied by the same number. That is:
[tex]x = \frac{8\times 1}{4\times 4}[/tex]
[tex]x = \frac{8}{16}[/tex]
8 : 4 :: 8 : 16 is not proportional. (Answer: A)
6) If two ratios are equal, then they are in proportion. That is:
[tex]a \,:\,b \,::c\,:\,d[/tex], where [tex]r = \frac{c}{a} = \frac{d}{b}[/tex], [tex]\forall\,r > 0[/tex].
If two ratios are equal, then they are in proportion. (Answer: proportion)
7) The ratio of 20 boys to 15 girls is derived of 20 divided by 15 until a denominator of the least integer is found by simplifying the fraction:
[tex]\frac{20}{15} = \frac{4}{3}[/tex]
The ratio of 20 boys to 15 girls is 4 : 3. (Answer: 4 : 3)
8) Express the following ratios in the simplest form:
a) [tex]\frac{14}{42} = \frac{7}{21} = \frac{1}{3}[/tex].
The simplest ratio of 14 : 42 is 1 : 3.
b) [tex]\frac{56}{80} = \frac{28}{40} = \frac{14}{20} = \frac{7}{10}[/tex]
The simplest ratio of 56 : 80 is 7 : 10.
9) When a series is in proportion, it must be in increasing or decreasing order at constant rate.
a) The series 4, 6, 8, 12 is in proportion, since each element after the first one is equal to the sum of the previous element and 2 units.
b) The series 15, 45, 5, 25 is not in proportion, since it is an alternating series.
10) We determine the cost of 4 cans of juice by simple rule of three:
[tex]x = \frac{4\,cans}{6\,cans}\times 210[/tex]
[tex]x = 140[/tex]
4 cans of juice cost 140.
11) a) The ratio of her earning to her expenditure is:
[tex]x = \frac{150000}{150000-50000}[/tex]
[tex]x = \frac{3}{2}[/tex]
The earning to expenditure ratio is 3 : 2.
b) The ratio of her earning to her savings is:
[tex]x = \frac{150000}{50000}[/tex]
[tex]x = 3[/tex]
The earning to savings ratio is 3 : 1.
12) 1 meter equals 100 centimeters. Then, the given ratio is:
[tex]x = \frac{15\,cm}{200\,cm}[/tex]
[tex]x = \frac{3}{40}[/tex]
The ratio of 15 centimeters to 2 meters is 3 : 40.
