Is one and twenty-nine forty-thirds a proper fraction, an improper fraction or a mixed number?
The value that we need to think about in this question is one and 29 over 43. And the question asks us what this is and it gives us three choices. Would we call it a proper fraction, an improper fraction or a mixed number? Let’s remind ourselves what each of these terms means.
In a proper fraction, the numerator, or the top number, is less than the denominator, or the bottom number. In other words, the number of parts that we’ve selected in this example, we’ve selected two parts, are less than the total number of parts. This case, it shows quarters. The top number is smaller than the bottom number. And so, the whole fraction is less than one.
An improper fraction has the numerator that is greater than its denominator. So, for example, instead of something like two-quarters, an improper fraction might have five-quarters. The top number is larger than the bottom number. How can we have a fraction that shows five-quarters? Well, we can see that an improper fraction represents an amount that’s more than one whole. That’s why the numerator is larger than the denominator. We can see that this particular improper fraction is worth one and one-quarter. It’s worth more than one whole.
Which brings us onto our last definition, a mixed number. A mixed number is an amount more than one whole. And it starts off with a whole number. And it’s followed by a fraction. So, one and a quarter is an example of a mixed number. Which of these terms can we use to describe one and 29 over 43?
Well, firstly, we can see that 29 over 43 is actually a proper fraction. The numerator is less than the denominator. But we’ve also got another value to consider. There’s a whole number at the start, the number one. So, this value is worth more than one. It’s worth one and twenty-nine forty-thirds. This must be a mixed number because it’s a combination of a whole number and a fraction. So, the number one and 29 over 43 is made up of a whole number and also a fraction. And we call this number a mixed number.