Simple Fractions Practice Problems & Solutions Online

Master fraction basics with step-by-step practice problems. Learn addition, subtraction, multiplication, and division of fractions with visual examples and solutions.

📚What You'll Practice with Simple Fractions
  • Identify numerators and denominators in proper and improper fractions
  • Add and subtract fractions with same and different denominators
  • Convert mixed numbers to improper fractions and vice versa
  • Multiply fractions using cross multiplication techniques
  • Divide fractions by applying reciprocal rules correctly
  • Simplify fractions to their lowest terms using common factors

Understanding Simple Fractions

Complete explanation with examples

What are fractions?

Fractions refer to the number of parts that equal the whole.

Suppose we have a cake divided into equal portions, the fraction comes to represent each of the portions into which we have cut the cake. Thus, if we have four equal portions, each of them represents a quarter of the pie. This is expressed numerically as follows: 141 \over 4.

The number 1 1 refers to the specific slice of the total pie set. We can look at it in the following way: we are talking about one slice and, therefore, we express it with a 1 1 . If we were talking about two slices, instead of 1 1 we would write 2 2 .

The number 4 4 refers to all equal portions of the pie. Since we have divided the pie into four equal portions, the number that should represent this division is 4 4 .

Cake visually divided

Detailed explanation

Practice Simple Fractions

Test your knowledge with 27 quizzes

Write the fraction shown in the drawing, in numbers:

Examples with solutions for Simple Fractions

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

What is the marked part?

Step-by-Step Solution

To solve this problem, we will count the total number of equal sections in the grid and the number of these sections that the marked area covers.

  • Step 1: Determine Total Sections. The grid is divided into several vertical sections. By examining the grid lines, we see that the total number of vertical sections is 7.
  • Step 2: Determine Marked Sections. The marked (colored) part spans 3 of these vertical sections within the total grid.
  • Step 3: Compute Fraction. The fraction of the total area covered by the marked part is calculated as the number of marked sections divided by the total number of sections: 37 \frac{3}{7} .

Therefore, the fraction of the area that is marked is 37 \frac{3}{7} .

Answer:

37 \frac{3}{7}

Video Solution
Exercise #3

What is the marked part?

Step-by-Step Solution

To determine the marked part, we need to calculate the fraction of the diagram that is shaded red.

First, we count the total number of rectangles in the diagram. There are 10 rectangles visible along a straight line.

Next, we count the number of rectangles shaded red. There are 8 red rectangles in the diagram.

Therefore, the fraction of the total diagram that is marked red is calculated as Number of Red RectanglesTotal Number of Rectangles=810 \frac{\text{Number of Red Rectangles}}{\text{Total Number of Rectangles}} = \frac{8}{10} .

This fraction simplifies to 45 \frac{4}{5} , but the answer provided is in the form 810 \frac{8}{10} , which is equivalent.

Therefore, the marked part of the diagram is 810 \frac{8}{10} .

Answer:

810 \frac{8}{10}

Video Solution
Exercise #4

What fraction does the part shaded in red represent?

Step-by-Step Solution

To work out what the marked part is, we need to count how many coloured squares there are compared to how many squares there are in total.

If we count the coloured squares, we see that there are four such squares.

If we count all the squares, we see that there are seven in all.

Therefore, 4/7 of the squares are shaded in red.

Answer:

47 \frac{4}{7}

Video Solution
Exercise #5

What is the marked part?

Step-by-Step Solution

To solve the problem of finding the fraction of the marked part in the grid:

The grid consists of a series of squares, each of equal size. The task is to count how many squares are marked compared to the entire grid.

  • First, count the total number of squares in the entire grid.
  • Next, count the number of marked (colored) squares.
  • Then, calculate the fraction of the marked part by dividing the number of marked squares by the total number of squares.

Let's perform these steps:

The grid displays several rows of columns. Visually, there appear to be a total of 10 squares in one row with corresponding columns, forming a grid.

Count the marked squares from the provided SVG graphic:

  • There are 4 shaded (marked) regions.

Total squares: 10 (lines are shown for organizing squares, as seen).

Calculate the fraction:

marked squarestotal squares=410 \frac{\text{marked squares}}{\text{total squares}} = \frac{4}{10}

Thus, the marked part of the shape can be given as a fraction: 410 \frac{4}{10} .

Answer:

410 \frac{4}{10}

Video Solution

Frequently Asked Questions

What is the difference between numerator and denominator in fractions?

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The numerator is the top number that shows how many parts you have, while the denominator is the bottom number showing how many equal parts make up the whole. For example, in 3/4, the numerator 3 represents three parts, and the denominator 4 shows the whole is divided into four equal parts.

How do you add fractions with different denominators?

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To add fractions with different denominators, first find the lowest common denominator (LCD). Then convert each fraction to an equivalent fraction with the LCD, and finally add the numerators while keeping the same denominator. For example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

What are mixed numbers and how do you work with them?

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Mixed numbers combine whole numbers with fractions, like 2 1/3. To work with them in calculations, convert them to improper fractions first. For 2 1/3: multiply the whole number by the denominator (2×3=6), add the numerator (6+1=7), and place over the original denominator (7/3).

Why do you flip fractions when dividing?

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When dividing fractions, you multiply by the reciprocal (flip the second fraction) because division is the opposite of multiplication. This method works because dividing by a fraction is the same as multiplying by its reciprocal. For example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.

How do you simplify fractions to lowest terms?

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To simplify fractions, divide both the numerator and denominator by their greatest common factor (GCF). Keep dividing until no common factors remain except 1. For example: 6/12 ÷ 6/6 = 1/2, or 15/20 ÷ 5/5 = 3/4.

What is an improper fraction and when do you use it?

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An improper fraction has a numerator larger than or equal to its denominator, like 7/4 or 5/5. These fractions represent values greater than or equal to 1. They're useful in calculations because they're easier to work with than mixed numbers, and you can convert them to mixed numbers when needed.

How do you find the lowest common denominator for fraction addition?

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Find the LCD by listing multiples of the larger denominator until you find one divisible by the smaller denominator. For denominators 4 and 6: multiples of 6 are 6, 12, 18... Since 12 is divisible by 4, the LCD is 12. Alternatively, find the least common multiple (LCM) of both denominators.

What are the most common mistakes when working with fractions?

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Common fraction mistakes include: adding denominators when adding fractions (incorrect), forgetting to find common denominators before adding/subtracting, not simplifying final answers, and confusing multiplication/division rules. Always remember to only add/subtract numerators when denominators are the same, and always simplify your final answer.

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