Hello, Let's get straight into it!
1. Which fractions are equivalent to 25/45?
A. 5/9, 15/28
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 gallons)
A. 65 quarts
B. 18 quarts
C. 13 quarts
D. 4 quarts
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 the subway station every 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. Use <, =, or >. 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
9. Harry rides his bike 25 3/8 miles. Karen rides her bike 25 2/5 miles. Who rides farther? (Explain).
The answers:
1. C. 5/9, 75/135.
2. B. 5/11
3. C. 10/3
4. C. 13 quarts
5. B. 120
6. B. In 36 minutes
7. B. 3/4 < 33/40
8. D. 3/8 < 2/3 < 19/24
9. (My explanation). Karen rides farther because if you change the fraction to their equivalents with a common denominator, 25 3/8 miles becomes 25 15/40 and 25 2/5 miles becomes 25 16/40, This is how Karen rides farther.
1. The fractions that are equivalent to 25/45 are C. 5/9, 75/135.
To find equivalent fractions, we can simplify the original fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which in this case is 5.
So, 25/45 divided by 5/5 gives us 5/9.
Similarly, when we divide the numerator 25 and denominator 45 by their GCF of 5, we get 5/9.
2. To write 10/22 in simplest form, we need to find the greatest common factor (GCF) of 10 and 22, which in this case is 2.
Dividing both the numerator and denominator by 2 gives us 5/11.
Therefore, the simplest form of 10/22 is B. 5/11.
3. To write 3 1/3 as an improper fraction, we first multiply the whole number (3) by the denominator (3) and add the numerator (1).
3 * 3 + 1 = 9 + 1 = 10.
So, 3 1/3 as an improper fraction is C. 10/3.
4. A quart is equal to 1/4 of a gallon.
To find how many quarts of oil are needed for the truck's engine, we need to convert the given amount of gallons to quarts.
3 1/4 gallons is equal to (3 * 4) + 1 quarts, which is equal to 12 + 1 quarts, or 13 quarts.
Therefore, the answer is C. 13 quarts.
5. To find the least common multiple (LCM) of 30 and 40 using prime factorization, we factorize both numbers into their prime factors.
30 = 2 * 3 * 5
40 = 2 * 2 * 2 * 5
Then, we take the highest power of each prime factor:
2^3 * 3^1 * 5^1 = 120
Therefore, the LCM of 30 and 40 is B. 120.
6. To determine when both trains will leave the station together again, we need to find the least common multiple (LCM) of the two given intervals.
The LCM of 12 minutes and 9 minutes is 36 minutes.
Therefore, both trains will leave the station together again in B. 36 minutes.
7. To compare 3/4 and 33/40, we need to have the same denominator.
To do this, we can multiply the numerator and denominator of 3/4 by 10 to get 30/40.
Since 30/40 is greater than 33/40, we can conclude that 3/4 is greater than 33/40.
Therefore, the answer is A. 3/4 > 33/40.
8. To order the fractions 3/8, 19/24, and 2/3 from least to greatest, we can convert them to equivalent fractions with a common denominator.
The common denominator for these fractions is 24.
3/8 = 9/24
19/24 = 19/24
2/3 = 16/24
So, the fractions in order from least to greatest are:
3/8 < 19/24 < 2/3.
Therefore, the answer is C. 3/8 < 19/24 < 2/3.
9. To determine who rides farther between Harry and Karen, we can compare their distances.
Harry rides 25 3/8 miles, which is equivalent to 25.375 miles.
Karen rides 25 2/5 miles, which is equivalent to 25.4 miles.
Since 25.4 is greater than 25.375, Karen rides farther than Harry.
Therefore, Karen rides farther.