Fractions are used in everyday life A fraction is a part of a whole. It is a number between 0 and 1. You might see that you have a quarter of a tank of gas, or your child only ate half of their green vegetables at dinner. Whatever the case may be, knowing fractions and the relationship between fractions, improper fractions and mixed numbers are crutial.
What are Fractions?
Fractions are a way of conveying a relationship of numbers. The top part of the fraction is called the numerator; the bottom part is called the denominator. The numerator is the number of parts you are interested in and the denominator is the number of all the parts together.
For example, it’s pizza night at your house and you eat two slices of pizza and your child eats one slice of pizza. Now there are 5 out of 8 slices of pizza left. We can express that like this:
What is an Improper Fraction?
What we just saw is called a proper fraction. Now is there such a thing as an improper fraction? Yes. For a fraction to be “proper” it must be a part of a whole, meaning it is less than 1 whole thing (like a pizza or tank of gas) but greater than 0 – or, in other words, greater than nothing. So an improper fraction does not follow one of these rules. Well, for what we are talking about here, we cannot be less than 0, so the only way for a fraction to be improper is if it is greater than 1.
Let’s go back to pizza night. It turns out that there are actually 2 pizza pies, instead of 1. If we want to know how many slices there are left after the 3 that have been eaten, then we simply need to count. We already know that there are 8 slices in a pie so the denominator stays the same. Our numerator is no longer 5 but 13, because there are 13 slices of pizza left. This looks like this:
What is a Mixed Number?
Have you ever heard someone say “I have 13 8ths of a pizza left?” Probably not. They would probably say “I have 1 and 5 8ths of a pizza left.” This way of expressing fractions is called a mixed number. A mixed number is any whole number together with a fraction. Mixed numbers cannot be considered whole numbers because part of the number is a fraction. To write how much pizza is left as a mixed number, we would write:
Converting between Mixed Numbers and Improper Fractions
At some point your child will have to convert between mixed numbers and improper fractions. To do so is quite simple.If we had for a mixed number and we need to make this an improper fraction, we simply multiply the denominator and the whole number to get . As you can see, there are 17 shaded boxes but there are 2 whole rows filled and 3 boxes filled in the last row.
If we had the improper fraction , to make this into a mixed number we divide the numerator by the denominator. Most of the time there will be a remainder. This remainder becomes the new numerator while the quotient, the whole number answer to 32 divided by 5, is the whole number of the mixed number. as a mixed number is. Once again, there are 32 boxes shaded but also the first 6 rows are completely shaded and there are 2 boxes left over in the last row.
Fractions is something that every child should have some familiarity with. Some children know only fractions as "a half of a cookie" or "a slice of pizza". As the child gets older and as their studies continue fractions will always be there in same shape or form. Being familiar with fractions at an early age and being comfortable with them throughout a child's time at school will be a huge boost in confidence and aptitude. As you going about your every day life, point out some fractions to your child. They are everywhere!