Operations With Fractions - Unit Quiz

1. Which of the following fractions is equivalent to 6/9?

12/16

12/18

18/12

To find an equivalent fraction to 6/9, we need to simplify it. Both 6 and 9 are divisible by 3, so we can divide both the numerator and denominator by 3. This gives us 2/3. Looking at the answer choices, the only fraction that is equivalent to 6/9 is 12/18.

Explanation

To find an equivalent fraction to 6/9, we need to simplify it. Both 6 and 9 are divisible by 3, so we can divide both the numerator and denominator by 3. This gives us 2/3. Looking at the answer choices, the only fraction that is equivalent to 6/9 is 12/18.

2. Find the LEAST common denominator for 3/4 and 4/5.

9

20

40

The least common denominator is the smallest number that both 4 and 5 can divide evenly into. In this case, the least common denominator for 3/4 and 4/5 is 20, because both 4 and 5 can evenly divide into 20. Therefore, 20 is the correct answer.

Explanation

The least common denominator is the smallest number that both 4 and 5 can divide evenly into. In this case, the least common denominator for 3/4 and 4/5 is 20, because both 4 and 5 can evenly divide into 20. Therefore, 20 is the correct answer.

3. Matthew is saving his allowance to buy a game system for $200. He has saved 3/5 of the money he needs to purchase the system. How much money has he saved?

$40

$120

$160

Matthew has saved 3/5 of the money he needs to purchase the game system. Since the total cost of the game system is $200, 3/5 of $200 is equal to (3/5) * $200 = $120. Therefore, Matthew has saved $120.

Explanation

Matthew has saved 3/5 of the money he needs to purchase the game system. Since the total cost of the game system is $200, 3/5 of $200 is equal to (3/5) * $200 = $120. Therefore, Matthew has saved $120.

4. 2- 4/5 =

Write your answer as a MIXED NUMBER.

1/5

1 and 1/5

6/5

The given fraction 4/5 can be written as a mixed number by dividing the numerator (4) by the denominator (5). The quotient is 0 with a remainder of 4. The whole number part is 0 and the fractional part is 4/5. Therefore, the mixed number representation of 4/5 is 0 and 4/5 which can be simplified to 1 and 1/5.

Explanation

The given fraction 4/5 can be written as a mixed number by dividing the numerator (4) by the denominator (5). The quotient is 0 with a remainder of 4. The whole number part is 0 and the fractional part is 4/5. Therefore, the mixed number representation of 4/5 is 0 and 4/5 which can be simplified to 1 and 1/5.

5. What is the reciprocal of 9/17?

19/17

17/9

17/19

9/17

Explanation

6. Find half of 4/6.

4/12

1/3

5/8

To find half of 4/6, you multiply 4/6 by 1/2:

(4/6) × (1/2) = 4/12.

Next, simplify 4/12 by dividing both the numerator and denominator by 4:

4/12 = 1/3.

Thus, half of 4/6 is 1/3.

Explanation

To find half of 4/6, you multiply 4/6 by 1/2:

(4/6) × (1/2) = 4/12.

Next, simplify 4/12 by dividing both the numerator and denominator by 4:

4/12 = 1/3.

Thus, half of 4/6 is 1/3.

7. 3/8 ÷ 3/4

1/2

9/32

12/24

When dividing fractions, we invert the second fraction and multiply it with the first fraction. In this case, we have (3/8) ÷ (3/4). Inverting the second fraction, we get (3/8) * (4/3). Simplifying the multiplication, we get (3 * 4) / (8 * 3), which equals 12/24. Simplifying further by dividing both the numerator and denominator by their greatest common divisor, which is 12, we get 1/2. Therefore, the correct answer is 1/2.

Explanation

When dividing fractions, we invert the second fraction and multiply it with the first fraction. In this case, we have (3/8) ÷ (3/4). Inverting the second fraction, we get (3/8) * (4/3). Simplifying the multiplication, we get (3 * 4) / (8 * 3), which equals 12/24. Simplifying further by dividing both the numerator and denominator by their greatest common divisor, which is 12, we get 1/2. Therefore, the correct answer is 1/2.

8. 1 and 1/8 + 2 and 3/4

3 and 7/8

24/12

3 and 4/12

The given expression represents the addition of two mixed numbers. To add mixed numbers, we first add the whole numbers together, which gives us 3. Then, we add the fractions together. The fractions have the same denominator, so we simply add the numerators together to get 7. The denominator remains the same, which is 8. Therefore, the sum of 1 and 1/8 and 2 and 3/4 is 3 and 7/8.

Explanation

The given expression represents the addition of two mixed numbers. To add mixed numbers, we first add the whole numbers together, which gives us 3. Then, we add the fractions together. The fractions have the same denominator, so we simply add the numerators together to get 7. The denominator remains the same, which is 8. Therefore, the sum of 1 and 1/8 and 2 and 3/4 is 3 and 7/8.

9. 5 ÷ 2/5

10/5

2

12 and 1/2

The given expression is 5 ÷ (2/5). To divide by a fraction, we can multiply by its reciprocal. So, we can rewrite the expression as 5 × (5/2). Multiplying 5 by 5 gives us 25, and dividing by 2 gives us 12 and a remainder of 1. Therefore, the answer is 12 and 1/2.

Explanation

The given expression is 5 ÷ (2/5). To divide by a fraction, we can multiply by its reciprocal. So, we can rewrite the expression as 5 × (5/2). Multiplying 5 by 5 gives us 25, and dividing by 2 gives us 12 and a remainder of 1. Therefore, the answer is 12 and 1/2.

10. Betty has 3/10 of a pie left over from dinner last night. She and her brother want to split the left over pie equally. What fraction of the pie will each one get?

3/20

6/10

3/5

Betty has 3/10 of a pie left over from dinner last night. She and her brother want to split the leftover pie equally. To find out what fraction of the pie each one will get, we need to divide the leftover pie equally between two people. Since there are two people, we divide the pie into two equal parts. Dividing 3/10 by 2 gives us 3/20. Therefore, each person will get 3/20 of the pie.

Explanation

Betty has 3/10 of a pie left over from dinner last night. She and her brother want to split the leftover pie equally. To find out what fraction of the pie each one will get, we need to divide the leftover pie equally between two people. Since there are two people, we divide the pie into two equal parts. Dividing 3/10 by 2 gives us 3/20. Therefore, each person will get 3/20 of the pie.