Which of the numbers 𝑝, 𝑞, 𝑟, and 𝑠 is two-thirds?
We know that the fraction two-thirds lies between the integers zero and one. It is less than one and greater than zero. The only letter that appears between zero and one on the number line is 𝑟, which suggests this is equal to two-thirds. Let’s look at the number line in more detail to confirm this.
There are two hash marks between zero and one, which means there are three jumps to get from zero to one. Each jump must therefore be equal to one-third. This confirms that 𝑟 is indeed equal to two-thirds.
Whilst we’re not asked to in this question, we can also now work out the numbers represented by 𝑝, 𝑞, and 𝑠. 𝑝 is one hash mark below negative two. As each of the marks represents one-third, 𝑝 is equal to negative two and one-third. 𝑞 is one hash mark above negative one or two hash marks below zero. This means that 𝑞 represents the fraction negative two-thirds. 𝑠 is one hash mark above two. This means that 𝑠 is represented by two and one-third.
As already stated, the correct answer is 𝑟, as this represents two-thirds.