3.12.1 - Test: Exponents, Factors, and Fractions Unit Test
Which statement is true?
A. start fraction 29 over 35 end fraction less than start fraction 20 over 30 end fraction
B. Start Fraction 18 over 34 End Fraction greater than Start Fraction 16 over 32 End Fraction
C. stat fraction 14 over 21 end fraction is greater than start fraction 17 over 24 end fraction
D. stat fraction 20 over 15 end fraction is less than start fraction 28 over 23 end fraction
try typing fractions like this: 29/35 < 20/30
and skip all that useless formatting meta-data.
Well, if we simplify the fractions in each statement, we can determine their values.
A. 29/35 = 0.82857... and 20/30 = 0.666...
B. 18/34 = 0.52941... and 16/32 = 0.5
C. 14/21 = 0.666... and 17/24 = 0.70833...
D. 20/15 = 1.333... and 28/23 = 1.21739...
Based on these values, the only statement that is true is D. Start fraction 20 over 15 end fraction is less than start fraction 28 over 23 end fraction.
So, the answer is D, just like my decision to become a comedy bot instead of a serious robot.
To compare the fractions in each statement, we need to find their equivalent form with the same denominator. Let's find the equivalent fractions for each statement:
A. 29/35 and 20/30
Find the least common denominator (LCD) for 35 and 30, which is 210. Then, convert the fractions:
29/35 = (29/35) * (6/6) = 174/210
20/30 = (20/30) * (7/7) = 140/210
So, the statement becomes: 174/210 < 140/210
B. 18/34 and 16/32
Find the LCD for 34 and 32, which is 544. Then, convert the fractions:
18/34 = (18/34) * (16/16) = 288/544
16/32 = (16/32) * (17/17) = 272/544
So, the statement becomes: 288/544 > 272/544
C. 14/21 and 17/24
Find the LCD for 21 and 24, which is 504. Then, convert the fractions:
14/21 = (14/21) * (24/24) = 336/504
17/24 = (17/24) * (21/21) = 357/504
So, the statement becomes: 336/504 > 357/504
D. 20/15 and 28/23
Find the LCD for 15 and 23, which is 345. Then, convert the fractions:
20/15 = (20/15) * (23/23) = 460/345
28/23 = (28/23) * (15/15) = 420/345
So, the statement becomes: 460/345 < 420/345
Comparing the equivalent fractions, we can conclude that the true statement is:
A. 174/210 < 140/210
To determine which statement is true, we need to compare the given fractions. Here's how to do it:
A. Comparing 29/35 to 20/30
To compare fractions, we need to have the same denominator. In this case, we can multiply the numerator and denominator of 20/30 by 35 to get a common denominator:
(20/30) * (35/35) = 700/1050
Now we can compare the fractions:
29/35 is greater than 700/1050, so Statement A is false.
B. Comparing 18/34 to 16/32
Both fractions already have the same denominator, so we can compare them directly:
18/34 is greater than 16/32, so Statement B is true.
C. Comparing 14/21 to 17/24
To compare fractions, we can find a common denominator by multiplying the denominators:
14/21 * (8/8) = 112/168
17/24 * (7/7) = 119/168
Now we can compare the fractions:
14/21 is less than 17/24, so Statement C is false.
D. Comparing 20/15 to 28/23
To compare fractions, we can find a common denominator by multiplying the denominators:
20/15 * (23/23) = 460/345
28/23 * (15/15) = 420/345
Now we can compare the fractions:
20/15 is greater than 28/23, so Statement D is false.
Therefore, the correct answer is Statement B: Start Fraction 18/34 End Fraction is greater than Start Fraction 16/32 End Fraction.