1. Which fraction are equivalent to 25/45?
A. 5/9, 15/45
B. 30/48, 75/135
C. 5/9, 75/135
D. 35/54, 40/108
2. Write the fraction in simplest form.
10/22
A. 2/5
B. 5/11
C. 6/11
D. 5/12
3. Write 3 1/3 as an improper fraction.
A. 11/3
B.9/3
C.10/3
D. 7/3
4. A truck's engine needs 3 1/4 gallons of oil for an oil change. How many quarts of oil are needed?
(Hint: 1 quart= 1/4 gallon)
A. 65 quart
B. 18 quart
C. 13 quart
D. 4 quart
5. Use prime factorization to find the LCM of 30 and 40
A. 90
B. 120
C. 150
D. 200
6. An "A" train leaves a subway station 12 minutes. An "E" train leaves every 9 minutes. If both trains just left the station on parallel tracks, when will both leave the station together again?
A. in 108 minutes
B. in 36 minutes
C. in 72 minutes
D. in 24 minutes
7. Compare the pair of numbers.
3/4___ 33/40
A. 3/4 > 33/40
B. 3/4 < 33/40
C. 3/4 = 33/40
8. Order the numbers from least to greatest.
3/8, 19/24, 2/3
A. 2/3< 19/24< 3/8
B. 2/3< 3/8< 19/24
C. 3/8< 19/24< 2/3
D. 3/8< 2/3< 19/24
Please some one answer me !
1. To find fractions that are equivalent to 25/45, we need to simplify the fraction to its lowest terms. We can do this by finding the greatest common divisor (GCD) of the numerator (25) and the denominator (45) and dividing both by the GCD. Let's calculate the GCD of 25 and 45:
GCD(25, 45) = 5
Now divide both the numerator and the denominator by 5:
25/5 = 5
45/5 = 9
Therefore, the fraction 25/45 is equivalent to 5/9.
Now let's check the answer choices:
A. 5/9, 15/45: Yes, 5/9 is equivalent to 25/45.
B. 30/48, 75/135: None of these fractions are equivalent to 25/45.
C. 5/9, 75/135: Yes, 5/9 is equivalent to 25/45, but 75/135 is not.
D. 35/54, 40/108: None of these fractions are equivalent to 25/45.
So the correct answer is A. 5/9, 15/45.
2. To write the fraction 10/22 in simplest form, we need to simplify it by finding the GCD of the numerator (10) and the denominator (22) and dividing both by the GCD. Let's calculate the GCD of 10 and 22:
GCD(10, 22) = 2
Now divide both the numerator and the denominator by 2:
10/2 = 5
22/2 = 11
Therefore, the simplified form of 10/22 is 5/11.
So the correct answer is B. 5/11.
3. To write 3 1/3 as an improper fraction, we need to convert the mixed number (3 1/3) to an improper fraction. We can do this by multiplying the whole number (3) by the denominator of the fraction (3) and adding the numerator (1). The result becomes the new numerator, while the denominator remains the same. Let's calculate:
3 * 3 + 1 = 10
So 3 1/3 is equivalent to the improper fraction 10/3.
The correct answer is A. 11/3.
4. To find out how many quarts of oil are needed when the truck's engine needs 3 1/4 gallons of oil, we can multiply the gallons by the conversion factor of 1 quart/1/4 gallon. Let's calculate:
3 1/4 * 1 quart/1/4 gallon
First, convert the mixed number (3 1/4) to an improper fraction:
3 * 4 + 1 = 13
So 3 1/4 is equivalent to the improper fraction 13/4.
Now multiply:
13/4 * 1 quart/1/4 gallon
Multiply the numerators and denominators:
(13 * 1) / (4 * 1/4) = 13/1 = 13
Therefore, 13 quarts of oil are needed.
The correct answer is C. 13 quart.
5. To find the least common multiple (LCM) of 30 and 40 using prime factorization, we need to find the prime factors of both numbers and then multiply the highest power of each prime factor.
Prime factorization of 30: 2 * 3 * 5
Prime factorization of 40: 2^3 * 5
Now multiply the highest power of each prime factor:
2^3 * 3 * 5 = 8 * 3 * 5 = 120
So the LCM of 30 and 40 is 120.
The correct answer is B. 120.
6. To find out when the "A" train and "E" train will leave the station together again, we need to find the least common multiple (LCM) of 12 and 9, which represents the time it takes for both trains to leave simultaneously.
The LCM of 12 and 9 is 36.
Therefore, both trains will leave the station together again after 36 minutes.
The correct answer is B. in 36 minutes.
7. To compare the fractions 3/4 and 33/40, we need to find a common denominator. The least common multiple (LCM) of 4 and 40 is 40.
Now let's convert both fractions to have the common denominator of 40:
3/4 * 10/10 = 30/40
33/40
Now we can compare the two fractions:
30/40 < 33/40
30 is less than 33.
Therefore, the correct answer is B. 3/4 < 33/40.
8. To order the fractions 3/8, 19/24, and 2/3 from least to greatest, we can compare them using a common denominator. The least common multiple (LCM) of 8, 24, and 3 is 24.
Now let's convert all the fractions to have the common denominator of 24:
3/8 * 3/3 = 9/24
19/24
2/3 * 8/8 = 16/24
Now we can order the fractions:
9/24 < 16/24 < 19/24
Therefore, the correct answer is C. 3/8 < 19/24 < 2/3.
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