If we divide a number by a larger number, the result is always less than 1.
23 ÷ 12> 1, 12 ÷ 23 < 1, see solution.
Practice makes perfect
We are asked to determine whether the following quotient is greater than or less than 1.
2/3 ÷ 1/2
Before we answer the question, let's remember what we know about quotients. Consider 4 and 5. The quotient of 4 and 5 is less than 1 because 4 is less than 5.
4 ÷ 5 < 1 because 4< 5
Using the same logic, the quotient of 7 and 5 is greater than 1 because 7 is greater than 5.
7 ÷ 5 > 1 because 7> 5
The quotient is 1 only if the divided numbers are equal.
5 ÷ 5= 1 because 5= 5
Now, we want to decide if 23 ÷ 12 is greater than or less than 1. To do so, we should find out which of the fractions is greater.
2/3 ? 1/2
Let's think about these numbers in terms of cake. Two-thirds, or 23, is the same as 2 portions of a cake that was divided into 3 equal pieces. One-half, or 12, is the same as one portion of a cake divided into two equal halves.
We can see that the first fraction represents more cake, which means that 23 is greater than 12. Let's now remember what we said earlier — if we divide a greater number by a smaller one, the outcome is greater than 1. This applies to our fractions!
2/3 ÷ 1/2 > 1 because 2/3> 1/2
For similar reasons, if we divide 12 by 23, the outcome will be less than 1.
1/2 ÷ 2/3 < 1 because 1/2< 2/3
