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 diagram as a number:

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'll write the fraction shown in the picture in words. The steps to solve this are straightforward:

  1. Count the number of total equal parts in the grid. In the picture, the grid consists of 9 equal parts.

  2. Identify the number of shaded parts. There are 6 shaded parts in total.

  3. Write the fraction using the total parts and shaded parts. The fraction is 69\frac{6}{9}.

  4. Express the fraction in words. In words, 69\frac{6}{9} is "six ninths."

Therefore, the written fraction from the picture in words is "Six ninths".

Answer:

Six ninths

Exercise #2

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 #3

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 #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 picture, in words:

Step-by-Step Solution

To solve this problem, we need to follow these steps:

  • Step 1: Understand the problem scenario using the given circle representation.
  • Step 2: Determine the number of sections, which is eight, as indicated by the circle division.
  • Step 3: Count the shaded sections, which number four.
  • Step 4: Write the fraction in words based on this information.

Steps in detail:

Step 1: The diagram shows a circle divided into eight equal parts. This step lets us determine the denominator, which is eight.

Step 2: The circle has four parts marked as shaded. This provides the numerator of the fraction, which is four.

Step 3: Therefore, the fraction can be written by combining these numbers. The numerator (shaded parts) is four, and the denominator (total sections) is eight.

Step 4: In words, we express the fraction 48\frac{4}{8} as "four eighths." This corresponds with option 3 in the choices given.

In conclusion, the fraction in the picture represented in words is four eighths.

Answer:

Four eighths

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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