Mixed Numbers and Fractions Greater Than 1 Practice Problems

Master converting mixed numbers to fractions and fractions greater than 1 to mixed numbers with step-by-step practice problems and solutions

📚Practice Converting Between Mixed Numbers and Improper Fractions
  • Convert mixed numbers like 2⅔ to improper fractions using multiplication and addition
  • Transform fractions greater than 1 into mixed numbers through division
  • Add and subtract mixed numbers by converting to common denominators
  • Multiply and divide mixed numbers after converting to improper fractions
  • Compare mixed numbers and improper fractions using equivalent forms
  • Solve real-world problems involving mixed numbers and fractions greater than 1

Understanding Mixed Numbers and Fractions Greater than 1

Complete explanation with examples

How do you convert a mixed number to a fraction?

The integer is multiplied by the denominator. The obtained product is then added to the numerator. The final result is placed as the new numerator.
Nothing is changed in the denominator.
A fraction greater than 11 is a fraction whose numerator is larger than the denominator.

Detailed explanation

Practice Mixed Numbers and Fractions Greater than 1

Test your knowledge with 11 quizzes

Write the fraction as a mixed number:

\( \frac{10}{6}= \)

Examples with solutions for Mixed Numbers and Fractions Greater than 1

Step-by-step solutions included
Exercise #1

Write the fraction as a mixed number:

62= \frac{6}{2}=

Step-by-Step Solution

To convert the improper fraction 62 \frac{6}{2} into a mixed number, we need to divide the numerator by the denominator:

Step 1: Evaluate the division 6÷2 6 \div 2 .
By performing this division, we find that 6÷2=3 6 \div 2 = 3 .

Since the division results in a whole number, the mixed number equivalent of 62 \frac{6}{2} is simply 3 3 . Therefore, there is no fractional part remaining.

Thus, the fraction 62 \frac{6}{2} expressed as a mixed number is 3 3 .

Answer:

3 3

Video Solution
Exercise #2

Write the fraction shown in the drawing:

Step-by-Step Solution

The problem involves finding the fraction represented by shaded parts in a drawing. Here's a step-by-step guide to solve it:

  • Step 1: Count the total number of sections in the drawing. There are 7 blocks arranged linearly.
  • Step 2: Since each block appears to be fully shaded, count those shaded. Each of the 7 blocks is shaded.
  • Step 3: The fraction is formed by placing the number of shaded sections over the total sections. Thus, the fraction is 77\frac{7}{7}.

The fraction for the shaded portion of the drawing is 77\frac{7}{7}, which is a complete whole, as every block is shaded.

Therefore, the solution to the problem is 77\frac{7}{7}.

Answer:

77 \frac{7}{7}

Video Solution
Exercise #3

Write the fraction shown in the drawing:

Step-by-Step Solution

To find the fraction represented by the shaded areas, follow these steps:

  • Step 1: Count the total number of rectangles. There are 7 rectangles in the drawing.
  • Step 2: Count the number of shaded rectangles. There are 3 shaded rectangles.
  • Step 3: Form the fraction, using the number of shaded rectangles as the numerator and the total number of rectangles as the denominator.

Therefore, the fraction of the drawing that is shaded is 37 \frac{3}{7} .

This value corresponds to option 4 in the provided choices, confirming 37 \frac{3}{7} is the correct answer.

Answer:

37 \frac{3}{7}

Video Solution
Exercise #4

Write the fraction shown in the drawing:

Step-by-Step Solution

To solve the problem, we will follow these steps:

  • Step 1: Count the total number of equal parts shown in the drawing.
  • Step 2: Count the number of shaded parts in the drawing.
  • Step 3: Form the fraction using the number of shaded parts over the total number of parts.

Now, let's address these steps in detail:

Step 1: Count the total equal parts.
From the drawing, it appears there are 7 equal parts.

Step 2: Count the shaded parts.
There are 5 shaded parts highlighted in the drawing.

Step 3: Write the fraction.
Now, we write the fraction as:
57\frac{5}{7}

This fraction represents the shaded area of the total, therefore the solution to the problem is 57\frac{5}{7}.

Answer:

57 \frac{5}{7}

Video Solution
Exercise #5

Write the fraction shown in the drawing:

Step-by-Step Solution

To determine the fraction illustrated in the drawing, we must follow these procedures:

  • Step 1: Count the Total Number of Parts
    Examine the drawing to determine how many equal parts the entire shape is divided into. According to the drawing, the shape is divided into a total of 6 parts.
  • Step 2: Count the Shaded Parts
    Next, count the number of parts that are shaded. From the drawing, we can identify that 3 of these parts are shaded.
  • Step 3: Write the Fraction
    The fraction is represented by placing the number of shaded parts as the numerator and the total number of parts as the denominator. Therefore, we write the fraction as 36 \frac{3}{6} .

Thus, the solution to the problem is 36 \frac{3}{6} .

Answer:

36 \frac{3}{6}

Video Solution

Frequently Asked Questions

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

+
Multiply the whole number by the denominator, then add the numerator. This becomes your new numerator while the denominator stays the same. For example, 2⅔ becomes (2×3+2)/3 = 8/3.

What makes a fraction greater than 1?

+
A fraction is greater than 1 when its numerator is larger than its denominator. Examples include 5/3, 7/4, and 11/8. These are also called improper fractions.

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

+
Divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same. For 27/7: 27÷7 = 3 remainder 6, so the answer is 3⁶⁄₇.

Can you add mixed numbers directly?

+
It's easier to convert mixed numbers to improper fractions first. Then find a common denominator and add the numerators. For example: 1½ + 2⅓ = 3/2 + 7/3 = 9/6 + 14/6 = 23/6 = 3⅚.

What's the difference between proper and improper fractions?

+
Proper fractions have numerators smaller than denominators (like ¾) and are less than 1. Improper fractions have numerators larger than or equal to denominators (like 5/3) and are greater than or equal to 1.

How do you multiply mixed numbers step by step?

+
1. Convert all mixed numbers to improper fractions 2. Multiply numerators together 3. Multiply denominators together 4. Simplify if possible 5. Convert back to mixed number if needed

When should you use mixed numbers vs improper fractions?

+
Use mixed numbers for measurements and real-world contexts (like 2½ cups). Use improper fractions for calculations and algebraic operations since they're easier to work with mathematically.

How do you compare a mixed number with an improper fraction?

+
Convert both to the same form (either both mixed numbers or both improper fractions), then find a common denominator to compare. The fraction with the larger numerator is greater.

More Mixed Numbers and Fractions Greater than 1 Questions

Continue Your Math Journey

Practice by Question Type