Key points
- A The result of one integer divided by another. It is written with one integer above the other with a horizontal line between them. The denominator must not be 0 is part of a whole, eg 15 minutes is a quarter of a whole hour.
- A fraction is shown by writing one whole number above another. It can also be shown by a diagram.
- The Number written at the top of a fraction. The numerator is the number of parts used. Eg, for 1⁄3, the numerator is 1 is the top number. This is the number of parts selected or shaded.
- The Number written on the bottom of a fraction. The denominator is the number of equal parts. Eg, for 1⁄3, the denominator is 3 is the bottom number. This is the number of parts the whole has been split into.
What are fractions?
- A fraction is a part of a whole. It is named according to the number of parts the whole is broken up into.
- Fractions split into two, three and four parts are given specific names. These are a One of two equal parts., a One of three equal parts., and a One of four equal parts..
- Fractions must be split into equally sized parts. In a diagram each part is the same size. The shaded fraction and the unshaded fraction make up the whole diagram.
Example: fraction diagrams
Image caption, A fraction is part of a whole.
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Video
Fractions are useful in music.
Watch the video to hear Berry discuss how fractions help her band to perform well together and can affect the feel and rhythm of different songs.
Bobby: So, you’re a musician?
Berry: Yeah, I’m a bassist in a band called Red Ivory.
Bobby: And how did you get into music?
Berry: Well, I’ve always loved listening to music and I started playing with my friends around two years ago.
Bobby: Ah, so when you play together, how do you make sure what you play actually sounds good?
Berry: Well, we have to stay in time with each other and depending on the time signature, that can differ from song to song. We often play in a 4/4 time signature.
Bobby: Can you explain what you mean by that?
Berry: A 4/4 time signature has four beats in a bar.
Bobby: So, each beat is one note?
Berry: No, you can have more notes in a bar. You can have half notes and quarter notes, and so on. I think it would be easier if I demonstrate it.
Bobby: Yes, please.
Berry: So here, I can do one whole note which would be …
(ONE GUITAR STRUM, FOUR FOOT TAPS)
And then I can do a half note, which would be …
(TWO GUITAR STRUMS, FOUR FOOT TAPS)
And then I can have a quarter note, which would be …
(FOUR GUITAR STRUMS, FOUR FOOT TAPS)
Bobby: Thank you, so if you’re playing notes of different lengths, how does that change the music?
Berry: Having longer, less frequent notes can create a more relaxed feeling for the song, whereas faster and a lot more notes can create a very intense feeling for the song.
Bobby: Ah, so fractions and maths are an important part of your music?
Berry: Yeah, definitely.
Writing and recognising fractions
- A fraction can be shown by a diagram split into equal parts.
- Fractions are written symbolically as one Integers are numbers with no fraction or decimal part. They can be positive, negative or zero. 42, 8, and 10000 are examples of integers. vertically above another.
- The top number is the Number written at the top of a fraction. The numerator is the number of parts used. Eg, for 1⁄3, the numerator is 1. This gives the number of parts shaded or selected.
- The bottom number is the Number written on the bottom of a fraction. The denominator is the number of equal parts. Eg, for 1⁄3, the denominator is 3. This gives the number of equal parts the whole is broken up into.
Example: writing and recognising fractions
Image caption, Fractions can be shown by a diagram or written in numbers.
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Fractions on a number line
- A fraction can be a specific value or measurement on a number line.
- A number line is split into regular The value between equally spaced markings on a number line. between two labelled values.
- The intervals represent equal amounts - these can be whole numbers or fractions.
How to find the size of an interval on a number line
Find the The numerical difference between two numbers is found by comparing the quantities. A difference is always a positive value. The difference between 3 and 5 is 2, the difference between 5 and 3 is 2 between the two given values on the number line.
Count the number of intervals between the two values.
Divide the difference by the number of intervals.
This gives you the size of the interval. Use this to complete the fraction labels on the number line.
Example: fractions on a number line
Image caption, Work out the size of each interval on the number line and the missing labels.
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Practise fractions
Activity: recognising fractions
Try this activity to practise recognising fractions.
Fractions quiz
Practise what you've learned about fractions with this quiz.
Real-world maths
Fractions are used in lots of places every day. For example, you use fractions when telling the time, measuring lengths and weighing ingredients.
- Fractions are used in food production.
Understanding equal parts is important when giving equal slices of cake or pie. Fractions are also important when measuring and weighing ingredients. If a recipe uses \( \frac{1}{4} \) of a teaspoon of salt, the taste would be very different if \( \frac{1}{2} \) a teaspoon was used.
In construction, builders use fractions as a proportion of the whole for different building materials.
A concrete mix is 1 part cement, 2 parts sand and 4 parts aggregate - a rock-like material.
This means \( \frac{1}{7} \) of the mix is cement, \( \frac{2}{7} \) is sand and \( \frac{4}{7} \) is aggregate.
Game - Divided Islands
Play the Divided Islands game! game
Using your maths skills, help to build bridges and bring light back to the islands in this free game from BBC Bitesize.
More on Fractions
Find out more by working through a topic
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- count3 of 14
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