Mixed Fractions Practice Problems & Solutions Online

Master mixed numbers with step-by-step practice problems. Convert mixed fractions to improper fractions, add, subtract, multiply & divide with detailed solutions.

πŸ“šMaster Mixed Numbers with Interactive Practice
  • Convert mixed numbers to improper fractions using multiplication and addition
  • Add and subtract mixed numbers by finding common denominators
  • Multiply mixed numbers by converting to fractions first
  • Divide mixed numbers using the reciprocal method
  • Convert whole numbers to fractions for complex operations
  • Solve real-world word problems involving mixed fractions

Understanding Mixed Fractions

Complete explanation with examples

Mixed Numbers

In this article, we will teach you the basics of everything you need to know about mixed numbers.
If you wish to delve deeper into a specific topic, you can access the corresponding extensive article.

Mixed Number and Fraction Greater Than 1

A fraction that is greater than 1 is a fraction whose numerator is larger than its denominator, this type of fractions can be converted into mixed numbers.

It is important that we remember similar topics:

How do you convert a mixed number to a fraction?

Multiply the whole number by the denominator.
To the obtained product, add the numerator. The final result will be the new numerator.
Nothing is changed in the denominator.

How do you convert an integer to a fraction?

The whole number is written in the numerator and the 1 in the denominator.

You can continue reading in these articles:

Detailed explanation

Practice Mixed Fractions

Test your knowledge with 22 quizzes

\( 3:\frac{5}{6}= \)

Examples with solutions for Mixed Fractions

Step-by-step solutions included
Exercise #1

3:57= 3:\frac{5}{7}=

Step-by-Step Solution

To divide the whole number 3 by the fraction 57\frac{5}{7}, we follow these steps:

  • Step 1: Identify the reciprocal of the fraction. The reciprocal of 57\frac{5}{7} is 75\frac{7}{5}.
  • Step 2: Multiply the whole number 3 by this reciprocal.
  • Step 3: Perform the multiplication to find the result.

Let's calculate this:
Step 1: The reciprocal of 57\frac{5}{7} is 75\frac{7}{5}.
Step 2: Multiply: 3Γ—75=3Γ—75=2153 \times \frac{7}{5} = \frac{3 \times 7}{5} = \frac{21}{5}.
Step 3: Convert the improper fraction 215\frac{21}{5} to a mixed number:

  • Divide 21 by 5. It goes 4 times with a remainder of 1.
  • The quotient is 4, and the remainder is 1. Therefore, 215=415\frac{21}{5} = 4\frac{1}{5}.

Thus, the solution to 3:573 : \frac{5}{7} is 4154\frac{1}{5}.

The correct choice among the given answers is: 4154\frac{1}{5}.

Answer:

415 4\frac{1}{5}

Video Solution
Exercise #2

1:14= 1:\frac{1}{4}=

Step-by-Step Solution

To solve the division problem 1:14 1 : \frac{1}{4} , we will follow these steps:

  • Step 1: Express the division as a fraction operation: 1Γ·14 1 \div \frac{1}{4} .
  • Step 2: Use the invert-and-multiply rule. Find the reciprocal of 14\frac{1}{4}, which is 44.
  • Step 3: Multiply the whole number by the reciprocal: 1Γ—4=4 1 \times 4 = 4 .

Thus, after performing these operations, we find that the result of the division 1:14 1 : \frac{1}{4} is 4 4 .

Answer:

4 4

Video Solution
Exercise #3

2:23= 2:\frac{2}{3}=

Step-by-Step Solution

To solve the expression 2:232:\frac{2}{3}, follow these steps:

  • Step 1: Rewrite the expression as a division problem:
    This means 2Γ·232 \div \frac{2}{3}.
  • Step 2: Convert the division to a multiplication by using the reciprocal:
    The reciprocal of 23\frac{2}{3} is 32\frac{3}{2}.
  • Step 3: Multiply by the reciprocal:
    2Γ—32=2β‹…32β‹…1=62=32 \times \frac{3}{2} = \frac{2 \cdot 3}{2 \cdot 1} = \frac{6}{2} = 3.

Therefore, the solution to the problem is 3 3 .

Answer:

3 3

Video Solution
Exercise #4

7Γ—68= 7\times\frac{6}{8}=

Step-by-Step Solution

To solve the multiplication of an integer with a fraction, we need to follow these steps:

  • Step 1: Multiply the integer 7 by the numerator of the fraction, which is 6.
  • Step 2: Keep 8 as the denominator.
  • Step 3: Simplify the resulting fraction.
  • Step 4: Convert to a mixed number if needed.

Now, let's work through each step:

Step 1: Multiply 7 by 6, which gives us 42 42 as the numerator.

Step 2: The denominator remains 8, so we have the fraction 428\frac{42}{8}.

Step 3: Simplify 428\frac{42}{8} by finding the greatest common divisor (GCD) of 42 and 8. The GCD is 2.

We divide the numerator and the denominator by 2: 42Γ·28Γ·2=214\frac{42 \div 2}{8 \div 2} = \frac{21}{4}.

Step 4: Convert 214\frac{21}{4} into a mixed number:

Divide 21 by 4, which equals 5 with a remainder of 1. Thus, 214\frac{21}{4} is equivalent to the mixed number 5145\frac{1}{4}.

Therefore, the solution to the problem is 5145\frac{1}{4}.

Answer:

514 5\frac{1}{4}

Video Solution
Exercise #5

8Γ—59= 8\times\frac{5}{9}=

Step-by-Step Solution

To solve the problem of multiplying 88 by 59\frac{5}{9}, we can follow these steps:

  • Step 1: Convert the whole number 88 into a fraction by expressing it as 81\frac{8}{1}.
  • Step 2: Multiply the numerators together: 8Γ—5=408 \times 5 = 40.
  • Step 3: Multiply the denominators together: 1Γ—9=91 \times 9 = 9.
  • Step 4: Write the product as a fraction: 409\frac{40}{9}.
  • Step 5: Convert the improper fraction 409\frac{40}{9} into a mixed number:
    • Divide 40 by 9, which gives 4 (quotient) with a remainder of 4.
    • Write the mixed number as 4494\frac{4}{9}.

Therefore, the solution to the multiplication problem 8Γ—598 \times \frac{5}{9} is 449 4\frac{4}{9} .

Answer:

449 4\frac{4}{9}

Video Solution

Frequently Asked Questions

How do you convert a mixed number to an improper fraction?

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To convert a mixed number to an improper fraction: 1) Multiply the whole number by the denominator, 2) Add the numerator to this product, 3) Write the result as the new numerator, keeping the same denominator. For example, 2ΒΎ = (2Γ—4+3)/4 = 11/4.

What's the easiest way to add mixed numbers?

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The easiest method is to convert both mixed numbers to improper fractions first, then find a common denominator and add the numerators. Finally, convert back to a mixed number if needed.

How do you multiply mixed numbers step by step?

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Follow these steps: 1) Convert all mixed numbers to improper fractions, 2) Multiply numerators together and denominators together, 3) Simplify the resulting fraction, 4) Convert back to a mixed number if the fraction is greater than 1.

Why do you need to convert mixed numbers before dividing?

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Converting to improper fractions makes division easier because you can use the standard rule: multiply by the reciprocal of the divisor. Mixed numbers in division form can be confusing and lead to calculation errors.

What are common mistakes when working with mixed fractions?

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Common errors include: β€’ Forgetting to convert mixed numbers before operations β€’ Adding whole numbers and fractions separately instead of converting β€’ Not finding common denominators for addition/subtraction β€’ Multiplying mixed numbers without converting first

How do you convert a whole number to a fraction?

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Write the whole number as the numerator and 1 as the denominator. For example, 5 becomes 5/1. This allows you to perform operations with fractions and mixed numbers more easily.

When should you use mixed numbers vs improper fractions?

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Use mixed numbers for final answers in word problems as they're easier to visualize (like 2Β½ cups). Use improper fractions during calculations as they're easier to work with mathematically.

What real-world situations use mixed fractions?

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Mixed fractions appear in cooking measurements (1ΒΎ cups flour), construction (2β…œ inches), time calculations (1Β½ hours), and sports statistics. Understanding mixed numbers helps in practical problem-solving.

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