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

\( 4:\frac{4}{7}= \)

Examples with solutions for Mixed Fractions

Step-by-step solutions included
Exercise #1

5:25= 5:\frac{2}{5}=

Step-by-Step Solution

To solve this problem, we'll perform the division 5Γ·25 5 \div \frac{2}{5} by converting it into multiplication:

  • Step 1: Recognize that dividing by a fraction is the same as multiplying by its reciprocal.
  • Step 2: Convert the division into multiplication: 5Γ·25=5Γ—52 5 \div \frac{2}{5} = 5 \times \frac{5}{2} .
  • Step 3: Multiply the whole number by the reciprocal of the fraction: 5Γ—52=252 5 \times \frac{5}{2} = \frac{25}{2} .
  • Step 4: Convert the improper fraction to a mixed number: 252=1212 \frac{25}{2} = 12 \frac{1}{2} .

Through these steps, we find that the solution to the division problem is 1212 12 \frac{1}{2} .

Answer:

1212 12\frac{1}{2}

Video Solution
Exercise #2

1:23= 1:\frac{2}{3}=

Step-by-Step Solution

We need to evaluate the expression 1Γ·23 1 \div \frac{2}{3} .

To do this, we use the principle that dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, the expression becomes:

1Γ—32 1 \times \frac{3}{2} .

Next, we multiply the whole number by the reciprocal:

1Γ—32=32 1 \times \frac{3}{2} = \frac{3}{2} .

To express 32\frac{3}{2} as a mixed number, we write it as:

112 1\frac{1}{2} .

Thus, the solution to the problem is 112 1\frac{1}{2} , which matches choice 3 from the options provided.

Answer:

112 1\frac{1}{2}

Video Solution
Exercise #3

1:34= 1:\frac{3}{4}=

Step-by-Step Solution

To solve this problem, let's divide 11 by 34\frac{3}{4}. The solution involves converting the division into a multiplication:

  • Step 1: Recognize  1:34 \,1:\frac{3}{4}\, as the division 134\frac{1}{\frac{3}{4}}.

  • Step 2: Convert division into multiplication: 134=1Γ—43\frac{1}{\frac{3}{4}} = 1 \times \frac{4}{3}.

  • Step 3: Compute the multiplication: 1Γ—43=431 \times \frac{4}{3} = \frac{4}{3}.

  • Step 4: Convert 43\frac{4}{3} into a mixed number: 1131\frac{1}{3}.

Therefore, the solution to the division 1:341 : \frac{3}{4} is 113 1\frac{1}{3}

The correct answer is (113)(1 \frac{1}{3}).

Answer:

113 1\frac{1}{3}

Video Solution
Exercise #4

3:34= 3:\frac{3}{4}=

Step-by-Step Solution

To solve the problem 3:34 3:\frac{3}{4} , we must perform division of the whole number 3 by the fraction 34\frac{3}{4}. Here are the steps:

  • Step 1: Recall the rule for dividing by a fraction. Dividing by 34\frac{3}{4} is the same as multiplying by its reciprocal, 43\frac{4}{3}.
  • Step 2: Rewrite the expression as a multiplication problem: 3Γ—433 \times \frac{4}{3}.
  • Step 3: Perform the multiplication: 3Γ—43=3Γ—43=1233 \times \frac{4}{3} = \frac{3 \times 4}{3} = \frac{12}{3}.
  • Step 4: Simplify the fraction: 123=4\frac{12}{3} = 4.

The solution to the division 3:34 3:\frac{3}{4} is 4 4 .

Answer:

4 4

Video Solution
Exercise #5

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

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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