# Fraction Multiplication And Division

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| By Joel Dodd
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Joel Dodd
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Quizzes Created: 26 | Total Attempts: 168,251
Questions: 15 | Attempts: 628

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Assesses and reinforces the student's understanding and skill with fraction arithmetic.

• 1.

### The denominator (bottom) of a fraction tells you

• A.

How many fractions you have

• B.

If it is a decimal or not

• C.

How big the fraction is

• D.

How many equal parts each whole unit is divided into

D. How many equal parts each whole unit is divided into
Explanation
The denominator of a fraction tells you how many equal parts each whole unit is divided into. This means that the denominator represents the number of equal parts that make up the whole. For example, in the fraction 1/4, the denominator is 4, indicating that the whole is divided into 4 equal parts. The denominator helps determine the size and magnitude of the fraction, but its primary purpose is to indicate the number of equal parts the whole unit is divided into.

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• 2.

### A fraction can be considered to be a division operation on its own

• A.

True

• B.

False

A. True
Explanation
A fraction can be considered as a division operation on its own because it represents the division of one number (the numerator) by another number (the denominator). For example, the fraction 1/2 can be interpreted as the division of 1 by 2, which equals 0.5. Therefore, it is true that a fraction can be seen as a division operation.

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• 3.

### A whole number can always be thought of as

• A.

A fraction if divided by one

• B.

A prime number, indivisible by anything but itself

• C.

An irrational number, like pi

A. A fraction if divided by one
Explanation
A whole number can always be thought of as a fraction if divided by one because any number divided by one is equal to itself. Therefore, if we divide a whole number by one, we get the same whole number as the quotient.

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• 4.

### To multiply two fractions together you multiply across, ie the numerators together and the denominators together.

• A.

True

• B.

False

A. True
Explanation
When multiplying two fractions, you multiply the numerators together and the denominators together. This is because when you multiply fractions, you are essentially multiplying the values of the numerators and denominators separately. Therefore, the correct answer is true.

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• 5.

### To divide two fractions together you multiply across, ie the numerators together and the denominators together.

• A.

True

• B.

False

B. False
Explanation
When dividing two fractions, you actually multiply the first fraction by the reciprocal of the second fraction. This means you multiply the numerator of the first fraction by the denominator of the second fraction, and the denominator of the first fraction by the numerator of the second fraction. Therefore, the correct answer is false.

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• 6.

### A reciprocal is

• A.

Any number written upside down

• B.

What you multiply any number by for a product equal to one.

• C.

A fancy name for a decimal

• D.

An irrational number, like pi

B. What you multiply any number by for a product equal to one.
Explanation
The correct answer is "what you multiply any number by for a product equal to one." A reciprocal is the multiplicative inverse of a number, meaning that when you multiply a number by its reciprocal, the product is always equal to one. For example, the reciprocal of 2 is 1/2, and when you multiply 2 by 1/2, the result is 1. Reciprocals are useful in various mathematical operations, such as dividing fractions or solving equations involving fractions.

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• 7.

### The reciprocal of a fraction is a fraction with the top and bottom swapped around.

• A.

True

• B.

False

A. True
Explanation
The statement is true because when we find the reciprocal of a fraction, we simply swap the numerator and denominator. This is because the reciprocal represents the multiplicative inverse of a fraction, which means that when multiplied together, the original fraction and its reciprocal will equal 1. Swapping the top and bottom of the fraction ensures that the resulting fraction is indeed the reciprocal.

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• 8.

### ⅖  x ³/₇ =

• A.

6/35

• B.

6/12

• C.

5/12

• D.

5/35

A. 6/35
Explanation
To solve this question, we need to multiply the fraction ⅖ by the cube of the reciprocal of ₇. The reciprocal of ₇ is 1/₇, and its cube is (1/₇)³ = 1/343. Multiplying ⅖ by 1/343 gives us (⅖) x (1/343) = 2/1715. Simplifying this fraction, we get 6/35. Therefore, the correct answer is 6/35.

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• 9.

### ¾ x 4 =

• A.

3/16

• B.

7/4

• C.

12/4

• D.

3/8

C. 12/4
Explanation
The expression ¾ x 4 can be simplified by multiplying the numerator and denominator of ¾ by 4. This gives us (3 x 4) / (4 x 1) = 12/4.

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• 10.

### 5 x ⅓ =

• A.

6/3

• B.

6/3

• C.

1/15

• D.

5/3

D. 5/3
Explanation
When multiplying a whole number by a fraction, we multiply the whole number by the numerator of the fraction and keep the denominator the same. In this case, 5 multiplied by 1/3 is equal to 5/3.

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• 11.

### ²³/₃ x ⅔ =

• A.

25/9

• B.

46/9

• C.

25/6

• D.

46/6

B. 46/9
Explanation
To multiply fractions, multiply the numerators together and multiply the denominators together. In this case, the numerator is 2/3 and the denominator is 2/3. When we multiply them, we get 4/9. Therefore, the correct answer is 4/9.

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• 12.

### ⅞ ÷ ⅖ =

• A.

14/40

• B.

7/10

• C.

3.5/1.6

• D.

35/16

D. 35/16
Explanation
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we have ⅞ divided by ⅖. The reciprocal of ⅖ is 5/2. Multiplying ⅞ by 5/2 gives us (8*5)/(7*2) = 40/14 = 20/7. Simplifying this fraction further, we get 35/16, which is the same as the given answer.

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• 13.

### ⅚ ÷ 4 =

• A.

5/24

• B.

20/6

• C.

1.25/1.3

• D.

5/10

A. 5/24
Explanation
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we have ⅚ divided by 4, which can be written as ⅚ multiplied by 1/4. Multiplying the numerators gives us 5, and multiplying the denominators gives us 24. Therefore, the correct answer is 5/24.

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• 14.

### 7 ÷ ¾ =

• A.

21/4

• B.

11/3

• C.

10/4

• D.

28/3

D. 28/3
Explanation
When we divide 7 by 3/4, we can think of it as multiplying 7 by the reciprocal of 3/4. The reciprocal of 3/4 is 4/3. So, 7 divided by 3/4 is equal to 7 multiplied by 4/3, which simplifies to 28/3.

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• 15.

### ⁴¹/₃ ÷ ⅖ =

• A.

6/205

• B.

205/6

• C.

82/15

• D.

46/5

B. 205/6
Explanation
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we have ⁴¹/₃ divided by ⅖. The reciprocal of ⅖ is 5/2. Multiplying ⁴¹/₃ by 5/2 gives us (4 + 1/3) * (5/2) = (13/3) * (5/2) = (65/6). Therefore, the correct answer is 65/6, which is equivalent to 205/6.

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