Fractions can look confusing at first, but they usually have simple answers. One question you might see is, “What is one-half of two-thirds?” It may sound tricky, but you just need to multiply. This guide will show you each step, so you can solve this problem and others like it. By the end, you’ll feel confident multiplying fractions.
What is one-half of two-thirds?
In math, the word “of” means you should multiply. (Multiplication, 2025) So, when you see a question like “What is one-half of two-thirds?” you can turn it into a multiplication problem.
1/2 × 2/3
Multiplying fractions is a fundamental skill that involves just a few simple steps. (Robertson, n.d.) Let’s break down exactly how to get to the answer.
The Answer Explained
To solve 1/2 × 2/3, you need to follow the rules for multiplying fractions. The final answer is 1/3.
Here’s the step-by-step process:
- First, multiply the numerators, which are the top numbers. Here, they are 1 and 2.
- 1 × 2 = 2
- Next, multiply the denominators, or the bottom numbers. In this example, they are 2 and 3.
- 2 × 3 = 6
- Now, make a new fraction by putting the answer from the numerators over the answer from the denominators.
- 2/6
- The last step is to simplify the fraction. Find the greatest common divisor (GCD) of the top and bottom numbers. (Simplifying Fractions, n.d.) For 2 and 6, the GCD is 2. Divide both numbers by 2.
- This gives you the simplest form: 1/3.
- 2 ÷ 2 = 1
- 6 ÷ 2 = 3
So, one-half of two-thirds is 1/3.
Visualizing the Problem
Looking at the problem visually can help. Picture a pie cut into three equal pieces, or thirds. If you take two pieces, that shows two-thirds (2/3) of the pie.
To find one-half of those two pieces, split them in half. Half of two pieces is one piece. Each piece is one-third of the whole pie, so you end up with one-third (1/3). This shows that one-half of two-thirds is one-third.
Practice Problems
The best way to get better at multiplying fractions is to practice. Try using the steps above to solve these similar problems:
- What is one-third of three-fourths? (1/3 × 3/4)
- What is one-half of four-fifths? (1/2 × 4/5)
- What is two-thirds of three-fifths? (2/3 × 3/5)
Answers:
- 1/4
- 2/5
- 2/5
Frequently Asked Questions
What does “of” mean in math?
In mathematics, particularly when working with fractions and percentages, the word “of” almost always signifies multiplication. (6.1 Understanding Percent – Contemporary Mathematics, 2025) For example, “50% of 100” means 0.50 × 100. Similarly, “one-half of two-thirds” means 1/2 × 2/3.
How do you simplify fractions?
To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder. Once you find the GCD, divide both the numerator and the denominator by it. The result is the fraction in its simplest form. (Fix Those Fractions!! Self-Help Guide!, 2023) For example, to simplify 12/18, the GCD is 6. Dividing both numbers by 6 gives you 2/3.
Can you multiply a fraction by a whole number?
Yes. To multiply a fraction by a whole number, you first need to convert the whole number into a fraction by placing it over a denominator of 1. (Multiplying Fractions and Mixed Numbers, n.d.) For example, the entire number 5 can be written as 5/1. After that, you multiply the fractions as you normally would: multiply the numerators together and the denominators together. For example, to find 1/2 of 5, you would calculate 1/2 × 5/1, which equals 5/2.
Master Your Math Skills
Knowing how to multiply fractions is an important math skill. (Teaching Fractions in Middle Grades Mathematics, 2018) If you remember that “of” means to multiply and follow the simple steps, you can solve questions like “What is one-half of two-thirds?” easily. With some practice, you’ll be ready for any fraction multiplication problem.
