Mixed fractions questions and answers will help students grasp the topic more quickly. Many “Mixed Fractions” questions appear on almost every board test. Students can use these questions to get a fast overview of the topics and practise answering them to improve their understanding. To double-check your answers, learn the complete explanations for each question. Click here to learn more about mixed fractions.
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What are Mixed Fractions? A mixed fraction is one that is made up of a whole number and a fraction. 4 ⅓ is a mixed fraction as 4 is a whole number, and 1/3 is a fraction. We can perform arithmetic operations on mixed fractions in the same manner that we add, subtract, multiply, and divide integers. Also, read: Fractions. |
For learning and practising, here are some mixed fractions questions and answers.
Mixed Fractions Questions with Solutions
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Converting Improper Fraction to Mixed Fraction A fraction with a numerator larger than the denominator is called an improper fraction since it cannot be simplified further. Let’s see how to make a mixed fraction out of this improper fraction. Step 1: Divide the numerator by the denominator. Step 2: Determine the remainder. Step 3: Organise the numbers in the sequence: quotient, remainder/divisor fraction. Also, read: Improper Fraction. |
1. Convert 75/6 into a mixed fraction.
Solution:
Step 1: Divide 75/6.
Step 2: If we divide 75/6, we get the quotient 12 and the remainder 3.
Step 3: Now, arrange the sequence in the form: 12 (3/6).
Now, the fractional part 3/6 is further simplified as ½.
Hence, 75/6 in a mixed fraction is 12 ½.
2. Convert the mixed fraction 2 (6/13) into an improper fraction.
Solution:
Given mixed fraction: 2 (6/13)
To convert the mixed fraction into an improper fraction, multiply 2 by 13 and add the product value with 6 to get the numerator and keep the denominator 13.
Finding numerator:
= (2 × 13) + 6
= 26 + 6
= 32
Hence, the mixed fraction 2 (6/13) into an improper fraction is 32/13.
3. How to write 4 ⅗ as an improper fraction?
Solution:
Given mixed fraction: 4 (3/5)
For converting the mixed fraction into an improper fraction, multiply 4 by 5 and add the product value with 3 to get the numerator and keep the denominator 5.
Finding numerator:
= (4 × 5) + 3
= 20 + 3
= 23
Hence, the mixed fraction 4 (3/5) into an improper fraction is 23/5.
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Adding Mixed Fractions Follow the steps below to add mixed fractions: 1. Transform the mixed fractions to improper fractions. 2. Determine whether the denominators are equal. 3. If yes, add the fractions’ numerators and write the result down. 4. If the denominators aren’t equal, get the LCM of the denominators to make them equal. 5. To get the result of the addition, add the numerators. Also, read: Least Common Multiple (LCM). |
4. Add the mixed fractions: 4 (¼) + 2 (¼).
Solution:
Step 1: Convert the mixed fractions 4 (¼) and 2 (¼) into an improper fraction.
4 (¼) = 17/4
2 (¼) = 9/4
Step 2: Check whether the denominators of both the improper fractions are the same.
The fractions 17/4 and 9/4 have the same denominator.
Step 3: Now, add the numerators of the fractions:
Thus,
4 (¼) + 2 (¼) = (17/4) + (9/4)
4 (¼) + 2 (¼) = (17 + 9)/4
4 (¼) + 2 (¼) = 26/4
Now, the obtained fractions can be simplified further.
Hence, we get
4 (¼) + 2 (¼) = 13/2.
5. Find the sum: 3(¼) + 3(⅝).
Solution:
Step 1: Convert 3(¼) and 3(⅝) into an improper fraction.
3(¼) = 13/4
3(⅝) = 29/8
Step 2: Now, check the denominators of the fractions, whether they are equal or not.
Step 3: Since the denominators are not equal, take the LCM of 4 and 8.
Thus, The LCM of 4 and 8 is 8.
3(¼) + 3(⅝) = (13/4) + (29/8)
3(¼) + 3(⅝) = (26 + 29)/8
3(¼) + 3(⅝) = 55/8.
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Subtracting Mixed Fractions Follow the steps described below to subtract mixed fractions: Step 1: Make improper fractions from mixed fractions. Step 2: Verify whether the denominators are equal. Step 3: If true, subtract the fractions’ numerators and write the answer down. Step 4: If the denominators aren’t similar, find the LCM of the denominators to make them equal. Step 5: To get the answer to the subtraction, subtract the numerators. |
6. Subtract the mixed fractions: 8 ½ – 4 ½.
Solution:
First, convert the mixed fraction to an improper fraction.
8 ½ = 17/2
4 ½ = 9/2
Since the denominators are equal, now subtract the numerators.
8 ½ – 4 ½ = (17/2) – (9/2)
8 ½ – 4 ½ = (17 – 9)/2
8 ½ – 4 ½ = 8/2.
This can be further simplified as follows:
8 ½ – 4 ½ = 4/1.
7. Find the difference: 6 ¾ – 2 ⅙.
Solution:
6 ¾ – 2 ⅙ = (27/4) – (13/6)
Since the denominators of the improper fractions are not equal, take the LCM of 4 and 6.
Thus, the LCM of 4 and 6 is 12.
(27/4) – (13/6) = (81 – 26) /12
(27/4) – (13/6) = 55/12.
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Multiplying Mixed Fractions Follow the instructions below to multiply mixed fractions: 1: Construct improper fractions from mixed fractions. 2: Write down the result of multiplying the numerator by the numerator and the denominator by the denominator. 3: Simplify the result to its simplest form, and leave it as an improper fraction, or change it to a mixed fraction. |
8. Multiply 4 ⅘ × 3 ⅘.
Solution:
4 ⅘ × 3 ⅘ is written as 24/5 × 19/5.
Now, multiply the numerator with the numerator and the denominator with the denominator.
4 ⅘ × 3 ⅘ = (24 × 19) / (5 × 5)
4 ⅘ × 3 ⅘ = 456/25
Hence, the product of 4 ⅘ × 3 ⅘ is 456/25.
9. Find the product of 7 ⅔ and 11 ½.
Solution:
First, convert the mixed fraction into an improper fraction.
7 ⅔ = 23/3
11 ½ = 23/2
7 ⅔ × 11 ½ = (23/3) × (23/2)
7 ⅔ × 11 ½ = (23×23) / (3×2)
7 ⅔ × 11 ½ = 529/6.
Thus, the product of 7 ⅔ and 11 ½ is 529/6.
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Dividing Mixed Fractions Read the instructions below to divide mixed fractions: Step 1: Change the mixed fractions into improper fractions. Step 2: Multiply the first fraction by the second fraction’s multiplicative inverse. Step 3: Simplify the result to its simplest form or keep it as an improper or mixed fraction. |
10. Divide 4½ by 2 ¼.
Solution:
Convert the mixed fractions 4½ and 2¼ into an improper fraction.
First fraction: 4½ = 9/2
Second fraction: 2¼ = 9/4
Now, take the reciprocal of the second fraction.
Thus, the reciprocal of 9/4 is 4/9.
To divide 4½ by 2 ¼, multiply the first fraction by the reciprocal of the second fraction.
4½ ÷ 2 ¼ = (9/2) × (4/9)
4½ ÷ 2 ¼ = 2/1.
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Practice Questions
1. Find the sum of 6 ⅘ and 11 ⅗.
2. Subtract 5 (3/7) from 12 (1/7).
3. Multiply 12 ⅘ and 17 ⅓.
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