Fraction Remainder Practice Problems - Mixed Numbers & Division

Master finding remainders in fractions with step-by-step practice problems. Learn to identify remainders in mixed numbers and improper fractions through guided examples.

📚Master Fraction Remainders with Interactive Practice
  • Identify remainders in mixed numbers like 4 2/5 instantly
  • Convert improper fractions to find whole numbers and remainders
  • Determine when fractions have no remainder through division
  • Solve real-world problems involving fraction division and remainders
  • Practice with fractions where numerator equals denominator
  • Apply remainder concepts to fractions less than 1

Understanding Fractions as Divisors

Complete explanation with examples

Remainder of a fraction

In a mixed number of a whole number and a fraction -
the fraction is the remainder.

In a fraction greater than 11 where the numerator is greater than the denominator -
The remainder consists of a denominator and numerator, which is the part left after finding how many whole numbers are in the fraction.

Detailed explanation

Practice Fractions as Divisors

Test your knowledge with 37 quizzes

Write the fraction shown in the picture, in words:

Examples with solutions for Fractions as Divisors

Step-by-step solutions included
Exercise #1

Write the fraction shown in the diagram as a number:

Step-by-Step Solution

The number of parts in the circle represents the denominator of the fraction, while the number of coloured parts represents the numerator.

The circle is divided into 2 parts and 1 part is coloured.

If we rewrite this as a fraction, we obtain the following:

12 \frac{1}{2}

Answer:

12 \frac{1}{2}

Video Solution
Exercise #2

Write the fraction shown in the diagram as a number:

Step-by-Step Solution

The number of parts in the circle represents the denominator of the fraction, while the number of coloured parts represents the numerator.

The circle is divided into 3 parts and 2 parts are coloured.

Hence:

23 \frac{2}{3}

Answer:

23 \frac{2}{3}

Video Solution
Exercise #3

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 3 parts, 1 part is colored.

Hence:

13 \frac{1}{3}

Answer:

13 \frac{1}{3}

Video Solution
Exercise #4

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 3 parts, 3 parts are colored.

Hence:

33=1 \frac{3}{3}=1

Answer:

33=1 \frac{3}{3}=1

Video Solution
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, 2 parts are colored.

Hence:

24 \frac{2}{4}

Answer:

24 \frac{2}{4}

Video Solution

Frequently Asked Questions

Everything you need to know about Fractions as Divisors

What is the remainder of a fraction in math?

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The remainder of a fraction is the fractional part left over after finding how many whole numbers fit into an improper fraction. In mixed numbers like 3 1/4, the remainder is 1/4. In improper fractions like 9/2, you divide to find 4 whole numbers with remainder 1/2.

How do you find the remainder when dividing fractions?

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To find the remainder in an improper fraction: 1) Divide the numerator by the denominator to get whole numbers, 2) Multiply the whole number by the denominator, 3) Subtract this from the original numerator, 4) Write the result over the original denominator. For example, 14/3 = 4 remainder 2/3.

Do all fractions with larger numerators have remainders?

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No, not all fractions where the numerator is larger than the denominator have remainders. If the denominator divides evenly into the numerator, there's no remainder. For example, 8/4 = 2 with no remainder, while 9/4 = 2 remainder 1/4.

What is the remainder of a proper fraction like 3/5?

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For proper fractions (where numerator < denominator), the entire fraction is the remainder since the whole number part is 0. So for 3/5, the remainder is 3/5 because there are zero whole numbers.

How do you convert improper fractions to mixed numbers?

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Steps to convert improper fractions to mixed numbers: • Divide numerator by denominator for whole number • Find remainder using: numerator - (whole number × denominator) • Write as: whole number + remainder/original denominator • Example: 7/3 = 2 1/3

When does a fraction equal exactly 1 with no remainder?

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A fraction equals 1 with no remainder when the numerator equals the denominator. Examples include 2/2 = 1, 5/5 = 1, and 10/10 = 1. These fractions represent one complete whole with nothing left over.

Why is understanding fraction remainders important?

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Understanding fraction remainders helps with real-world division problems, converting between fraction forms, and building foundation skills for algebra. It's essential for sharing items equally, measuring ingredients, and solving word problems involving division.

What's the fastest way to identify remainders in mixed numbers?

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In mixed numbers, the remainder is immediately visible as the fractional part. For 4 2/5, the remainder is 2/5. For 1 3/8, the remainder is 3/8. No calculation needed - just identify the fraction portion after the whole number.

More Fractions as Divisors Questions

Click on any question to see the complete solution with step-by-step explanations

Mixed Numbers and Fractions Greater than 1

Visual Representation of the Fraction 3/4: Choose the Correct Diagram Visual Representation of the Fraction 8/40: Match the Correct Diagram Visual Representation of the Fraction 9/6: Choose the Correct Model Visual Representation of the Fraction 25/15: Choose the Correct Diagram Visual Representation of Improper Fraction 27/12: Choose the Correct Image

Part of an Amount

Grid Fraction Problem: Find the Ratio of Shaded Squares to Total Area Grid Fraction Analysis: Identifying the 4/7 Shaded Region Find the Fraction: Identifying the Shaded Region in a 3x4 Grid Calculate the Shaded Region: Rectangle Grid Proportion Problem Grid Fraction Problem: Identifying the 3/7 Shaded Region

Fractions as Divisors

Division Problem: Is 5:6 Less Than 1 Without Calculating? Compare Quotient to 1: Analyzing 1÷2 Without Calculation Calculate 3/5 of 15: A Fraction Distribution Problem Fraction Distribution Problem: Calculate Remaining Strawberry Cakes from 45 Total Calculate One-Third of 45: Daily Chocolate Cake Production Problem

Continue Your Math Journey

Master Fractions as Divisors first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

A fraction as a divisorNumeratorDenominatorFractionsPart of a quantityRemaindersPlacing Fractions on the Number LineCommon denominatorHow do you simplify fractions?Simplification and Expansion of Simple Fractions

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems
Basic identification Calculate the fraction Converting the fraction to digits Reducing the fraction Using negative numbers Worded problems Writing a fraction verbally Writing the fraction Visual representation of a fraction Writing fractions from drawings Writing fractions in their simplest form Approximate the area of the colored part of the shape Identify the greater value Matching description to fraction Visual representation of a fraction