Ordering Fractions on a Number Line
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Theory
On a number line every fraction has its own place: the further right, the larger. To compare fractions, write them with the same denominator. This Year 7 maths page shows how to read fractions and negative fractions on a number line, compare them using a common denominator, and order fractions, decimals and percentages.
Reading a point. Count the equal parts between two whole numbers next to each other. If there are \(5\) parts, each part is \(\dfrac{1}{5}\). Then count the parts past the whole number: \(2\) parts past \(1\) is \(1\dfrac{2}{5}\).
Negative fractions sit to the left of \(0\). The point \(3\) quarters left of \(0\) is \(-\dfrac{3}{4}\).
To compare fractions, make the denominators the same. Either multiply the denominators together, or use the lowest common multiple (LCM) of the denominators, also called the lowest common denominator (LCD).
Ascending means smallest first; descending means largest first.
Two ways to get a common denominator for \(\dfrac{7}{12}\) and \(\dfrac{5}{8}\):
Multiplying the denominators gives \(96\). The LCD of \(12\) and \(8\) is \(24\), which gives smaller numbers:
How to read a fraction on a number line
- Count the equal parts between two whole numbers: that gives the denominator.
- Count the parts past the whole number on the left.
- Write the mixed numeral (negative if left of \(0\)).
How to order fractions
- Find the LCD of all the denominators.
- Rename each fraction with the LCD.
- Order the numerators, then write the original fractions in that order.
Each space is \(\dfrac{1}{3}\), so the arrow is at \(1\dfrac{2}{3}\).
| \(4 + \dfrac{5}{6}\) | \(=\) | \(\dfrac{24}{6} + \dfrac{5}{6}\) |
| \(\) | \(=\) | \(\dfrac{29}{6}\) |
\(4\dfrac{5}{6} = \dfrac{29}{6}\)
(i) Write A and B.
(ii) Which is larger?
(i) A \(= -1\dfrac{2}{3}\), B \(= -\dfrac{1}{3}\)
(ii) B is further right, so B is larger.
The LCD of \(3\), \(9\), \(12\) and \(4\) is \(36\): \(\dfrac{24}{36}\), \(\dfrac{20}{36}\), \(\dfrac{21}{36}\), \(\dfrac{27}{36}\).
\(\dfrac{3}{4}, \dfrac{2}{3}, \dfrac{7}{12}, \dfrac{5}{9}\)
As decimals: \(-\dfrac{1}{4} = -0.25\), \(\dfrac{2}{5} = 0.4\), \(1\dfrac{1}{5} = 1.2\), \(48\% = 0.48\).
\(-0.25 < 0.4 < 0.45 < 0.48 < 1.2\), so \(-\dfrac{1}{4}, \dfrac{2}{5}, 0.45, 48\%, 1\dfrac{1}{5}\).
Common pitfalls
Frequently asked questions
How do you find a fraction on a number line?
Count the equal parts in one whole to get the denominator, then count the parts from the whole number.
What is the lowest common denominator?
The smallest number that all the denominators divide into. The LCD of \(10\) and \(8\) is \(40\).
Which is bigger, 7/12 or 5/8?
\(\dfrac{7}{12} = \dfrac{14}{24}\) and \(\dfrac{5}{8} = \dfrac{15}{24}\), so \(\dfrac{5}{8}\) is bigger.
Where do negative fractions go?
To the left of zero. \(-\dfrac{3}{4}\) is three quarters left of \(0\).
How do you order fractions, decimals and percentages together?
Change them all to decimals, then order the decimals.