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 shown in the drawing:

Examples with solutions for Mixed Numbers and Fractions Greater than 1

Step-by-step solutions included
Exercise #1

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 #2

Write the fraction as a mixed number:

1311= \frac{13}{11}=

Step-by-Step Solution

To convert the improper fraction 1311\frac{13}{11} into a mixed number, we need to perform division to separate the whole number from the fractional part.

  • Step 1: Divide the numerator by the denominator. - Perform the division: 13÷11=113 \div 11 = 1. Since 13 is not a multiple of 11, we obtain a quotient and a remainder. - The division gives a quotient of 1 and a remainder of 2 (since 1311×1=213 - 11 \times 1 = 2).
  • Step 2: Express the remainder as part of the fraction. - The remainder is 2, and this will be the numerator of the fractional part. - The denominator remains the same, 11.
  • Step 3: Write the mixed number. - Combine the whole number and the fraction. - The mixed number is 12111\frac{2}{11}.

Now, let's verify our solution with the given choices. The correct option matches Choice 2, which is 12111\frac{2}{11}.

Therefore, the fraction 1311\frac{13}{11} as a mixed number is 12111\frac{2}{11}.

Answer:

1211 1\frac{2}{11}

Video Solution
Exercise #3

Write the fraction as a mixed number:

139= \frac{13}{9}=

Step-by-Step Solution

To convert the improper fraction 139\frac{13}{9} into a mixed number, we follow these steps:

  • Step 1: Perform the division of the numerator by the denominator. Divide 13 by 9.
  • Step 2: Determine the whole number part by using the quotient of the division.
  • Step 3: Find the remainder to establish the fractional part.
  • Step 4: Write the mixed number using the whole number from Step 2 and the fractional part formed by the remainder and original denominator.

Let's carry out these steps in detail:

Divide 13 by 9:

13÷9=1 13 \div 9 = 1 with a remainder of 4 4 .

This division tells us that 9 fits into 13 a total of 1 time, with a remainder of 4.

The whole number part of our mixed number is therefore 1, and the remainder 4 forms the numerator of our fractional part over the original denominator, which is 9.

So, the fractional part is 49\frac{4}{9}.

Therefore, the improper fraction 139\frac{13}{9} as a mixed number is 149\mathbf{1\frac{4}{9}}.

Answer:

149 1\frac{4}{9}

Video Solution
Exercise #4

Write the fraction as a mixed number:

1711= \frac{17}{11}=

Step-by-Step Solution

To convert the improper fraction 1711 \frac{17}{11} to a mixed number, we proceed as follows:

  • Step 1: Perform the division 17÷11 17 \div 11 . We find: - The quotient (whole number) is 1 since 11 goes into 17 once.
    - The remainder is 6 because 17(11×1)=6 17 - (11 \times 1) = 6 .

  • Step 2: Express the remainder as a fraction over the original denominator. Hence, the fractional part is 611 \frac{6}{11} .

  • Step 3: Combine the quotient and the remainder fraction to form the mixed number: 1611 1\frac{6}{11} .

Therefore, the mixed number equivalent of the fraction 1711 \frac{17}{11} is 1611 1\frac{6}{11} .

Answer:

1611 1\frac{6}{11}

Video Solution
Exercise #5

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

Frequently Asked Questions

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

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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?

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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?

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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?

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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?

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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?

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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?

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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?

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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.

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