# More Than One Whole > **Can a fraction be bigger than 1?** Yes. A fraction is bigger than 1 whenever its top number is bigger than its bottom number. 6/4 means six fourths, and since four fourths make one whole, the other two make half of another, so 6/4 is 1 1/2. - Big idea: A fraction can be bigger than one whole. Four fourths fill one whole, so six fourths is a whole and two fourths more. - Common confusion: Fractions are always less than one, so a fraction such as 6/4 cannot be a real number. - It often sounds like this: “6/4 can’t be real. There are only 4 fourths in a pizza.” - Family: [Fractions Have Size](https://slices.org/explore/fraction-size) (slice 8 of 20) - [Try the lesson yourself](https://slices.org/slices/more-than-one-whole): about 3 minutes, free, with no sign-in. ## In plain words A fraction counts equal parts of one whole. In 6/4, the 4 says the whole is cut into 4 equal parts (fourths), and the 6 says we have six of those parts. Four fourths fill exactly one whole, so 4/4 = 1. Nothing stops us from counting on, though, and the next two fourths start to fill a second whole. So 6/4 is one whole and two fourths more. Two fourths is the same as one half, so 6/4 = 1 2/4, which is 1 1/2. On a number line, make fourth-size hops from 0. The fourth hop lands on 1, and the sixth hop lands halfway between 1 and 2, because fractions keep going past 1 just as whole numbers do. A fraction is less than 1 when its top number is smaller than its bottom number, equal to 1 when the two match, and more than 1 when the top number is bigger. ## A worked example A recipe needs 6/4 cups of flour, and your scoop holds 1/4 cup, so you fill it six times. The first four scoops make one full cup and the last two make half a cup more, so 6/4 cups is 1 1/2 cups. ## Why this confusion is common Most of us first meet fractions as parts of one shape, such as one pizza or one bar, and you cannot shade more than all of a single shape. From that, it is reasonable to conclude that fractions are always less than one. The name “improper fraction” does not help, because it makes these numbers sound like mistakes. Building fractions from unit pieces, and placing them on a number line, shows that fractions keep going past 1. ## Try this away from the screen Cut a few paper circles into fourths and ask the learner to make 6/4 using only fourth pieces. When the first circle is full, where do the extra pieces go? Then try 5/3 with thirds and 8/4 with fourths, and ask what they notice about 8/4. ## Helpful ways to talk about it | Instead of saying | Try saying | | --- | --- | | “The top number can’t be bigger than the bottom number.” | “What happens if we keep counting fourths after the whole is full?” | | “6/4 is improper, so we need to fix it.” | “6/4 is a perfectly good number. Can you also say it in wholes and fourths?” | ## Practice questions [Try these questions one at a time](https://slices.org/set?t=Practice%3A+More+Than+One+Whole&q=s08-transfer-1%2Cs08-transfer-2%2Cs08-review-1%2Cs08-review-2), with pictures you can change and a reply to every answer. 1. Place 7/4 on the number line. **Answer:** place the point at 7/4. 7/4 is seven fourths. Four of them take you to 1, and the other three take you three fourths of the way from 1 to 2. 2. If each bar is one whole, how much do these 1/3 pieces make altogether? The choices are 5/3, 5/6 and 2/3. **Answer:** 5/3. Three thirds fill the first whole, and two more thirds sit in the second. That makes five thirds, or 5/3, which is one whole and 2/3 more. 3. Which of these is the largest? The choices are 7/8, 3/3 and 5/4. **Answer:** 5/4. 7/8 is less than one whole, and 3/3 is exactly one whole. 5/4 is one whole and one more fourth, so it’s the largest. 4. Two pizzas are each cut into 6 equal slices, and Mia’s family eats 8 slices. How much pizza is that? The choices are “8/6 of a pizza”, “8/12 of a pizza” and “6/8 of a pizza”. **Answer:** 8/6 of a pizza. Each slice is 1/6 of a pizza, so 8 slices are 8/6 of a pizza. That’s one whole pizza and 2/6 more. ## Questions people ask ### Is 6/4 a real fraction? Yes. 6/4 means six fourths, and four of them make one whole while the other two make half of another, so 6/4 is 1 1/2. It sits halfway between 1 and 2 on the number line. ### What is an improper fraction? It’s a fraction whose top number is equal to or bigger than its bottom number, such as 5/5 or 7/4, so it’s worth one whole or more. Despite the name, there’s nothing improper about it. ### How do you turn 7/4 into a mixed number? See how many groups of four fourths fit into seven fourths. There’s one group, which makes one whole, with three fourths left over, so 7/4 = 1 3/4. ### Is 4/4 a fraction or a whole number? It’s both, because 4/4 names the same number as 1, just as 8/4 names the same number as 2. Any fraction whose top and bottom numbers match, such as 3/3 or 10/10, is equal to one whole. ## Curriculum connections (US Common Core) - [3.NF.A.3.c](https://www.thecorestandards.org/Math/Content/3/NF/A/3/c/): Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. - [4.NF.B.3](https://www.thecorestandards.org/Math/Content/4/NF/B/3/): Understand a fraction a/b with a > 1 as a sum of fractions 1/b. - [3.NF.A.2.b](https://www.thecorestandards.org/Math/Content/3/NF/A/2/b/): Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. ## Words to know - [Improper fraction](https://slices.org/glossary/improper-fraction): An improper fraction has a top number as big as its bottom number or bigger, like 6/4 or 5/5, so it’s worth one whole or more. - [Mixed number](https://slices.org/glossary/mixed-number): A mixed number is a whole number and a fraction written together, like 1 2/4, which means one whole and two fourths more. - [Whole](https://slices.org/glossary/whole): The whole is the complete thing that a fraction is part of. It might be a pizza, a length on a number line or a group of objects. - [Unit fraction](https://slices.org/glossary/unit-fraction): A unit fraction has 1 on top, like 1/2, 1/3 or 1/8, so it’s exactly one of the equal parts of a whole. ## Related slices - [What’s the Whole?](https://slices.org/slices/whats-the-whole): Half of a big pizza is more than half of a small one, because a fraction is always a fraction of something. - [The Top Number](https://slices.org/slices/the-top-number): The top number counts the parts you have, so 3/5 means 3 of the 5 equal parts. - [Counting Spaces, Not Ticks](https://slices.org/slices/counting-spaces-not-ticks): On a number line you count the spaces between the marks, starting from 0, rather than the marks themselves. - [One Number, Not Two](https://slices.org/slices/one-number-not-two): The fraction 2/5 is a single number, and it sits two fifths of the way from 0 to 1.