Improper fractions questions along with detailed solutions are given here to understand the topic very well. As we know, a fraction is a numerical value, which defines the part of a whole. A fraction can be classified into different types, such as proper fraction, improper fraction, mixed fraction and so on. Here, we have provided numerous improper fractions questions, which will help students to differentiate between different types of fractions. Students can practice the problems provided here and they can cross verify their answers with the solutions presented on our page. To get more knowledge about improper fractions, click here.
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What are Improper fractions? In Mathematics, we know that fraction has two parts, such as a numerator and denominator. An improper fraction is one of the types of fractions. The improper fractions are those, whose numerator is larger than the denominator. For example, 15/7 is an improper fraction, where the numerator is bigger than the denominator. (i.e., 15 > 7). Some other examples of improper fractions include 17/9, 11/2, 19/8, and so on. Also, read: Fractions. |
Practice the improper fractions questions provided here to get a thorough understanding of the concept.
Improper fractions Questions with Solutions
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How to Convert an Improper Fraction to a Mixed Fraction? For converting the improper fractions into the mixed fractions, go through the steps provided below:
Quotient (Remainder/Divisor of a fraction) Also, read: Mixed Fraction. |
1. Convert the fraction 14/3 into a mixed fraction.
Solution:
Given fraction: 14/3
The fraction 14/3 given is an improper fraction since the numerator of a fraction is larger than the denominator of the fraction.
To convert the improper fraction 14/3 into a mixed fraction, follow the steps below:
Step 1: Divide 14 by 3.
Step 2: We get quotient = 4 and remainder = 2, if 14 is divided by 3.
Step 3: Now, arrange the obtained result in the form: Quotient (Remainder/Divisor of a fraction)
I.e., 4 ⅔.
2. Convert the given mixed fraction 12 ⅔ into an improper fraction.
Solution:
Given: 12 ⅔ is a mixed fraction.
To find the numerator of the improper fraction from the mixed fraction, first, multiply the whole number with the denominator of the fractional part and add the resultant product value with the numerator of the fractional part. The denominator of the improper fractions should be the same divisor provided in the fractional part of the mixed number.
I.e.,
= [(12 × 3) + 2] / 3
= (36 + 2)/3
= 38/3
Hence, the mixed fraction 12 ⅔ into an improper fraction is 38/3.
3. Convert the improper fraction 41/2 into a decimal form.
Solution:
To convert the improper fraction 41/2 into a decimal, just simply divide the numerator by the denominator.
I.e., 41/2 = 20.5
Hence, the decimal number 20.5 is equivalent to the improper fraction 41/2.
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How to Add Improper Fractions? To add improper fractions, follow the instructions below: 1. Determine whether the provided fractions’ denominators are equal. 2. If yes, add the numerators of the fractions and write down the result. 3. If the denominators aren’t equal, use the denominators’ LCM to make them equal. 4. Add the numerators to get the result of the addition of improper fractions. Check out the article Least Common Multiple (LCM) as well. |
4. Add the Improper fractions: 17/4 + 21/4
Solution:
Given:17/4 + 21/4
As the denominators of both the improper fractions are equal, we can directly add the numerators of the improper fractions.
17/4 + 21/4 = (17 + 21)/4
17/4 + 21/4 = 38/4.
Therefore, the sum of 17/4 and 21/4 is 38/4.
5. Find the sum of 7/3 and 6/5.
Solution:
To find: 7/3 + 6/5
As the denominators of the given improper fraction are different, take the LCM of 3 and 5 to make the denominators equal.
Thus, the LCM of 3 and 5 is 15.
7/3 + 6/5 = (35 + 18)/15
7/3 + 6/5 = 53/15
Therefore, the sum of 7/3 and 6/5 is 53/15.
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How to Subtract Improper Fractions? To subtract improper fractions, use the steps listed below: Step 1: Check and see whether the improper fractions’ denominators are equal. Step 2: If this is the case, subtract the numerators of the fractions and write the result down. Step 3: Find the LCM of the denominators to make them equal if the denominators aren’t similar. Step 4: Subtract the numerators to find the answer to the subtraction. |
6. Subtract 6/2 from 12/2.
Solution:
To find: 12/2 – 6/2
As the denominator of both the fractions are equal, subtract the numerators of the improper fractions.
12/2 – 6/2 = (12 – 6)/2
12/2 – 6/2 = 6/2
Now, the result can be further simplified as follows:
12/2 – 6/2 = 3/1.
7. Find the difference: 11/4 – 17/3.
Solution:
Given: 11/4 – 17/3.
Since the denominators are different, take the LCM of 3 and 4 to make the denominators equal.
Thus, the LCM of 3 and 4 is 12.
11/4 – 17/3 = (33 – 68) / 12
11/4 – 17/3 = -35/12.
Hence, 11/4 – 17/3 is -35/12.
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How to Multiply Improper Fractions? Follow the below steps to multiply improper fractions: 1: Multiply the numerator and denominator of the first fraction with the numerator and the denominator of the second fraction. 2. Reduce the result obtained in step 1 to its simplest form, if required. |
8. Multiply the improper fractions: 21/12 and 4/3.
Solution:
To find: Product of 21/12 and 4/3.
(21/12) × (4/3) = (21 × 4) / (12 × 3)
(21/12) × (4/3) = 84/36
Further , 84/36 can be simplified as follows:
(21/12) × (4/3) = 21/9 = 7/3
Therefore, the product of 21/12 and 4/3 is 7/3.
9. Find the product of 41/2 and 11/2.
Solution:
To find: (41/2) × (11/2)
To get the product of 41/2 and 11/2, multiply the numerator with the numerator and the denominator with the denominator.
(41/2) × (11/2) = (41 × 11) /(2 × 2)
(41/2) × (11/2) = 451 / 4
Therefore, the product of 41/2 and 11/2 is 451/4.
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How to Divide Improper Fractions? To divide the improper fractions, go through the steps provided below: Step 1: Take the reciprocal of the second fraction. Step 2: Now, multiply the first fraction with the result obtained in step 1. Step 3: Reduce the answer to the simplest, if needed. |
10. Divide the improper fraction 16/7 by 9/7.
Solution:
To find the value of (16/7) ÷ (9/7)
Here, first take the reciprocal of the second fraction.
Hence, 9/7 becomes 7/9.
Now, multiply 16/7 by 7/9, and we get
(16/7) ÷ (9/7) = (16/7) × (7/9)
(16/7) ÷ (9/7) = 16/9.
Hence, the division of 16/7 by 9/7 is 16/9.
Explore More Articles
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Practice Questions
Answer the following improper fractions questions:
1. Calculate the sum: (51/2) + (9/2).
2. Find the difference: (83/7) – (11/8)
3. Multiply the improper fractions 11/9 and 35/4.
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