Fractions as Divisors Practice Problems with Solutions

Master converting division problems to fractions and mixed numbers with step-by-step practice exercises. Learn numerator, denominator rules and real-world applications.

📚Practice Converting Division to Fractions
  • Convert division exercises like 4÷2 and 10÷3 into proper fractions
  • Transform improper fractions into mixed numbers using division methods
  • Solve real-world sharing problems with cookies, pizzas, and cakes
  • Apply numerator and denominator rules in division contexts
  • Practice identifying when fractions cannot be simplified further
  • Master the relationship between division quotients and fraction notation

Understanding Fractions as Divisors

Complete explanation with examples

A fraction is actually a division exercise! A result obtained from a division exercise is called a quotient and if it is incomplete, it will appear in the form of a fraction.

Remember the rules:
The fraction line - symbolizes the division operation.
The numerator - symbolizes the number that is being divided (the divided number - what needs to be divided equally among all).
The denominator – symbolizes the number that divides the numerator.

Detailed explanation

Practice Fractions as Divisors

Test your knowledge with 19 quizzes

Write the fraction shown in the drawing, in numbers:

Examples with solutions for Fractions as Divisors

Step-by-step solutions included
Exercise #1

Write the fraction shown in the picture, in words:

Step-by-Step Solution

To solve this problem, we need to convert the visual representation of a fraction into words. Let's break down the process step by step:

Step 1: Identify the given visual information

The given image is a circle, which represents a whole. It has two distinct halves divided by a vertical line. One half is shaded, which indicates the fraction that we need to express in words.

Step 2: Determine the fraction represented

Given that one half of the circle is shaded, it indicates that this is one part of two equal parts.

Step 3: Write the fraction in words

The fraction that corresponds to one out of two equal parts is 12 \frac{1}{2} , expressed in words as "half."

Therefore, the fraction shown in the picture, expressed in words, is Half.

Answer:

Half

Exercise #2

Write the fraction shown in the picture, in words:

Step-by-Step Solution

To solve this problem, we need to translate the visual fraction representation into words:

  • Step 1: Recognize the grid is a 3x3 matrix, making a total of 3×3=9 3 \times 3 = 9 squares.
  • Step 2: Count the shaded squares, which appear to number 3 squares.
  • Step 3: Write this as a fraction: the number of shaded squares (3) over the total squares (9). This fraction is 39\frac{3}{9}.
  • Step 4: Convert the fraction 39\frac{3}{9} into words. This is read as "three ninths".

Thus, the fraction shown in the picture, in words, is three ninths.

Answer:

Three ninths

Exercise #3

Write the fraction shown in the picture, in words:

Step-by-Step Solution

To solve the problem of expressing the fraction in words, follow these steps:

  • Step 1: Count the total number of sections in the grid to determine the denominator.
  • Step 2: Count the number of shaded sections to determine the numerator.
  • Step 3: Write the fraction as a phrase using words.

Now, let's work through these steps:

Step 1: The grid consists of a 3×33 \times 3 layout, which means there are 9 total sections. Therefore, the denominator of our fraction is 9.

Step 2: Observe and count the number of shaded sections within the grid. In this case, there are 4 shaded sections. Therefore, the numerator is 4.

Step 3: With a fraction identified as 49\frac{4}{9}, we can express this in words as "four ninths."

Therefore, the solution to the problem is four ninths.

Answer:

Four ninths

Exercise #4

Write the fraction shown in the picture, in words:

Step-by-Step Solution

Step 1: Count the total sections
The circle is divided into 8 equal sections.
Step 2: Count the shaded sections
There are 6 shaded sections in the diagram.
Step 3: Formulate the fraction
The fraction of the shaded area is 68\frac{6}{8}.
Step 4: Express in words
The fraction 68\frac{6}{8} in words is "six eighths".

Therefore, the solution to the problem is "six eighths".

Answer:

Six eighths

Exercise #5

Write the fraction shown in the drawing, in numbers:

Step-by-Step Solution

The number of parts in the circle represents the denominator of the fraction, and the number of colored parts represents the numerator.

The circle is divided into 4 parts, 3 parts are colored.

34 \frac{3}{4}

Answer:

34 \frac{3}{4}

Video Solution

Frequently Asked Questions

How do you convert a division problem into a fraction?

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Place the dividend (number being divided) in the numerator and the divisor (number dividing) in the denominator. For example, 4÷2 becomes 4/2, which simplifies to 2.

What is the difference between numerator and denominator in division?

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The numerator represents the dividend (what's being divided), while the denominator represents the divisor (what divides the numerator). The fraction line symbolizes the division operation itself.

When should I convert an improper fraction to a mixed number?

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Convert to mixed numbers when the numerator is larger than the denominator and you need a more practical answer. For example, 10/3 becomes 3⅓, showing 3 whole parts plus 1/3 remaining.

How do I solve word problems involving fractions as divisors?

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1. Identify what needs to be divided (numerator) 2. Identify how many groups to divide into (denominator) 3. Write as a fraction 4. Convert to mixed number if needed for practical interpretation

What does it mean when a fraction cannot be simplified?

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Some fractions like 2/3 are already in lowest terms and represent the exact answer. This happens when the numerator and denominator share no common factors other than 1.

Why do we use fractions instead of decimals for division?

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Fractions show exact values without rounding errors and are easier to work with in further calculations. They also clearly represent parts of a whole in real-world sharing situations.

How do I check if my fraction division answer is correct?

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Multiply the denominator by the whole number part (if mixed), add the numerator, then divide by the denominator. The result should equal your original dividend.

What are common mistakes when converting division to fractions?

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Common errors include: switching numerator and denominator positions, forgetting to simplify the final answer, and incorrectly converting improper fractions to mixed numbers by using wrong division steps.

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