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Thirds: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">ThirdsThirds: Definition and ExampleTable of ContentsThirds Definition of Thirds

Thirds are equal parts that result when we divide a whole into three equal pieces. Each piece is called one-third, written as 13\frac{1}{3}31​ or 0.333...0.333...0.333... (where the 333 repeats forever). When we have something divided into thirds, it means that three of these equal parts make up the whole. For example, if we divide a circle into three equal parts, each part is one-third of the circle, and all three thirds together make the complete circle.

Thirds help us understand fractions and division, especially when we need to share things equally among three people or groups. Thirds are special because when written as decimals, they create repeating patterns (0.333...0.333...0.333...) rather than terminating like halves (0.50.50.5) or quarters (0.250.250.25). We can also combine thirds to make larger fractions, such as two-thirds (23\frac{2}{3}32​), which is two of the three equal parts that make up a whole. Understanding thirds is an important step in learning about fractions and their uses in everyday life.

Examples of Thirds Example 1: Identifying and Comparing Thirds Problem:

Which picture shows 23\frac{2}{3}32​ of the shape shaded? Rectangle Shaded

A. one-third shaded B. two-thirds shaded C. one-half shaded D. three-fourths shaded

Step-by-step solution:

Step 1, Understand what 23\frac{2}{3}32​ means. 23\frac{2}{3}32​ means 222 out of 333 equal parts are shaded.

Step 2, Look at each shape and see how it's divided and shaded.

A. The rectangle is divided into 333 equal parts with 111 part shaded (this shows 13\frac{1}{3}31​)

B. The rectangle is divided into 333 equal parts with 222 parts shaded (this shows 23\frac{2}{3}32​)

C. The rectangle is divided into 222 equal parts with 111 part shaded (this shows 12\frac{1}{2}21​)

D. The rectangle is divided into 444 equal parts with 333 parts shaded (this shows 34\frac{3}{4}43​)

Step 3, Find the shape that has exactly 23\frac{2}{3}32​ shaded. Only B has 222 out of 333 equal parts shaded.

Step 4, State the answer. The answer is B.

Example 2: Adding Fractions with Thirds Problem:

What is 13+13\frac{1}{3} + \frac{1}{3}31​+31​?

Step-by-step solution:

Step 1, Check if the fractions have the same denominator. Yes, both fractions have 333 as the denominator.

Step 2, Add the numerators while keeping the same denominator.

13+13=1+13=23\frac{1}{3} + \frac{1}{3} = \frac{1+1}{3} = \frac{2}{3}31​+31​=31+1​=32​

Step 3, Check if the fraction can be simplified. 23\frac{2}{3}32​ is already in its simplest form because 222 and 333 have no common factors.

Example 3: Finding a Third of a Quantity Problem:

If there are 242424 students in a class and one-third of them are wearing blue shirts, how many students are wearing blue shirts?

Step-by-step solution:

Step 1, Understand what finding "one-third of" means. One-third of a quantity means dividing the quantity by 333.

Step 2, Set up the math problem. One-third of 242424 students= 13×24\frac{1}{3} \times 2431​×24

Step 3, Solve the problem.

13×24=8\frac{1}{3} \times 24 = 831​×24=8

Step 4, Check our answer by multiplying by 333.

8×3=248 \times 3 = 248×3=24

Step 5, State the answer. 888 students are wearing blue shirts.

Step 6, Check that our answer makes sense. If 888 students are wearing blue shirts, then 16 students are not wearing blue shirts. 8+16=248 + 16 = 248+16=24, which is the total number of students. 888 is indeed one-third of 242424.

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