Fractions Greater than 1 on a Number Line

Axel and Tank are at the fair. They can't wait to play Racing Seahorses! The player whose seahorse finishes first wins a prize! Ready, set, go! As they race, Axel and Tank want to identify where their seahorses are, but they don't know how! Let's help them by identifying fractions greater than 1 on a number line. Fractions greater than one on a number line can be identified as improper fractions or mixed numbers. Improper fractions have numerators that are greater than their denominators. Mixed numbers have a whole number and a fraction. To identify the improper fraction, begin by locating the value on the number line. Next, count the spaces on the number line until you reach the point you have marked. Let's count the number of spaces: one, two, three, four, five, six, seven, eight. The point is on eight. Write this number here as the numerator, or top part of the fraction. Then, count how many parts one whole is divided into. Let's count together, one, two, three. Write three here as the denominator, or bottom part of the fraction. Eight-thirds is the location of this improper fraction on the number line. We could also read it as the mixed number two and two-thirds because this fraction has two wholes plus two more thirds remaining. Now, let's help Tank locate the position of his seahorse in the race. First, we locate the seahorse as a point on the number line. Next, we count the number of spaces until we reach it: one, two, three, four, five, six, seven! Write seven as the numerator. Then, count how many parts one whole is divided into: one, two, three, four, five. Write five as the denominator. Tank's seahorse is located at seven-fifths on the number line. We could also say it's located at one and two-fifths because this fraction has one whole plus two more fifths remaining. Let's help Axel find his seahorse! First, we locate the seahorse as a point on the number line. What do we do next? We count the spaces along the number line to that point- one, two, three, four and write four as the numerator. What should we do next? Next, we count how many parts one whole is divided into- one, two. Write two as the denominator. Where is Axel's seahorse located? Axel's seahorse is located at four halves on the number line. Do you notice anything else about this improper fraction? Four halves is also written as two on the number line. This means that four halves is the same as, or equivalent to, the number two. The third player's seahorse is here. What is the numerator? The numerator is thirteen because we counted thirteen spaces to get to their seahorse. What is the denominator? The denominator is seven because one whole is divided into seven spaces. Where is the third player's seahorse? The third player's seahorse is at thirteen-sevenths on the number line. What is the equivalent mixed number? It's one and six-sevenths because this fraction has one whole plus six more sevenths remaining. "Ladies and Gentlemen! We have a winner!" Before, we find out who won, let's remember. We can identify fractions greater than one on a number line as improper fractions or mixed numbers. Improper fractions have numerators that are larger than their denominators. Mixed numbers have whole numbers and fractions. To read the improper fraction, first, locate the point. Secondly, count the number of spaces to that point. Write this number as the numerator. Then, count how many parts one whole is divided into. Write this number as the denominator. The final number is the location of the improper fraction on the number line. For mixed numbers, count the whole numbers first, then add on the remaining fractions. Here, we have 2 wholes and 2 more thirds remaining. Congratulations, Tank, you came from behind but, slow and steady always wins the race. So, you can have two prizes!