Here we will learn about ordering fractions. Show
What is ordering fractions?Ordering fractions is where we rearrange a set of fractions so that the smallest is at the start, followed by the next smallest and so on. This is called ascending order. To do this we rewrite the fractions so that they have the same denominators which we can then compare. We can order any type of fraction including proper fractions, improper fractions and mixed numbers. E.g. Write these fractions in ascending order: In ascending order: What is ordering fractions?How to order fractionsIn order to put fractions in ascending order:
Explain how to put fractions in ascending order in 3 stepsOrdering fractions worksheetGet your free ordering fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions. DOWNLOAD FREE Ordering fractions worksheetGet your free ordering fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions. DOWNLOAD FREE Ordering fractions examplesExample 1: ordering proper fractionsWrite the following fractions in order of size: \[\frac{3}{4} \quad \quad \frac{1}{2} \quad \quad \frac{5}{6} \quad \quad \frac{7}{12}\]
The fractions have different denominators. \[\frac{3\times3}{4\times3}=\frac{9}{12} \] \[\frac{1\times6}{2\times6}=\frac{6}{12} \] \[\frac{5\times2}{6\times2}=\frac{10}{12} \] 2Find the smallest fraction by comparing the numerators and order the fractions Here are the fractions with their common denominator of 12 \[\frac{9}{12} \quad \quad \frac{6}{12} \quad \quad \frac{10}{12} \quad \quad \frac{7}{12} \] Writing them in size order would give \[\frac{6}{12} \quad \quad \frac{7}{12} \quad \quad \frac{9}{12} \quad \quad \frac{10}{12} \] 3Rewrite the numbers as they appear in the question in size order \[\frac{6}{12} \quad \quad \frac{7}{12} \quad \quad \frac{9}{12} \quad \quad \frac{10}{12} \] \[\frac{1}{2} \quad \quad \;\; \frac{7}{12} \quad \quad \;\frac{3}{4} \quad \quad \; \frac{5}{6}\] Example 2: ordering proper fractionsWrite the following fractions in order of size: \[\frac{11}{30} \quad \quad \frac{4}{15} \quad \quad \frac{2}{5} \quad \quad \frac{1}{3} \] Write all the fractions so that they have a common denominator The fractions have different denominators. \[\frac{4\times2}{15\times2}=\frac{8}{30} \] \[\frac{2\times6}{5\times6}=\frac{12}{30} \] \[\frac{1\times10}{3\times10}=\frac{10}{30} \] Find the smallest fraction by comparing the numerators and order the fractions Here are the fractions with their common denominator of 30\[\frac{11}{30} \quad \quad \frac{8}{30} \quad \quad \frac{12}{30} \quad \quad \frac{10}{30} \] Writing them in size order would give \[\frac{8}{30} \quad \quad \frac{10}{30} \quad \quad \frac{11}{30} \quad \quad \frac{12}{30} \] Rewrite the numbers as they appear in the question in size order \[\frac{8}{30} \quad \quad \frac{10}{30} \quad \quad \frac{11}{30} \quad \quad \frac{12}{30} \] \[\frac{4}{15} \quad \quad \;\frac{1}{3} \quad \quad \;\frac{11}{30} \quad \quad \;\frac{2}{5}\] Example 3: ordering improper fractions and mixed numbersWrite the following fractions in order of size: \[\frac{7}{4} \quad \quad 1\frac{1}{2} \quad \quad 1\frac{2}{3} \quad \quad \frac{29}{24}\] Write all the fractions so that they have a common denominator We can either write all the fractions as improper fractions or as mixed numbers. It is simpler to write them as mixed numbers and concentrate on the fractional part of the mixed number. \[\frac{29}{24}=1\frac{5}{24} \quad \quad \quad \frac{7}{4}=1\frac{3}{4}\] The fractions have different denominators. and 24. 2, 3and 4go into 24. , so we can convert the fractions so they have a common denominator of 24. \[1\frac{3\times6}{4\times6}=1\frac{18}{24}\] \[1\frac{1\times12}{2\times12}=1\frac{12}{24} \] \[1\frac{2\times8}{3\times8}=1\frac{16}{24}\] Find the smallest fraction by comparing the numerators and order the fractions Here are the fractions with their common denominator of 24\[1\frac{18}{24} \quad \quad 1\frac{12}{24} \quad \quad 1\frac{16}{24} \quad \quad 1\frac{5}{24} \] Writing them in size order would give \[1\frac{5}{24} \quad \quad 1\frac{12}{24} \quad \quad 1\frac{16}{24} \quad \quad 1\frac{18}{24} \] Rewrite the numbers as they appear in the question in size order \[1\frac{5}{24} \quad \quad 1\frac{12}{24} \quad \quad 1\frac{16}{24} \quad \quad 1\frac{18}{24} \] \[\frac{29}{24} \quad \quad \;\;1\frac{1}{2} \quad \quad \;\;\; 1\frac{2}{3} \quad \quad \;\; \frac{7}{4}\] Example 4: ordering improper fractions and mixed numbersWrite the following fractions in order of size: \[\frac{12}{5} \quad \quad 2\frac{3}{10} \quad \quad 2\frac{7}{20} \quad \quad \frac{9}{4} \] Write all the fractions so that they have a common denominator We can either write all the fractions as improper fractions or as mixed numbers. It is simpler to write them as mixed numbers and concentrate on the fractional part of the mixed number. \[\frac{12}{5}=2\frac{2}{5} \quad \quad \quad \frac{9}{4}=2\frac{1}{4}\] The fractions have different denominators. and 20. 4, 5and 10go into 20. , so we can convert the fractions so they have a common denominator of 20. \[2\frac{2\times4}{5\times4}=2\frac{8}{20}\] \[2\frac{3\times2}{10\times2}=2\frac{6}{20} \] \[2\frac{1\times5}{4\times5}=2\frac{5}{20}\] Find the smallest fraction by comparing the numerators and order the fractions Here are the fractions with their common denominator of 20\[2\frac{8}{20}\quad \quad 2\frac{6}{20} \quad \quad 2\frac{7}{20} \quad \quad 2\frac{5}{20} \] Writing them in size order would give \[2\frac{5}{20} \quad \quad 2\frac{6}{20} \quad \quad 2\frac{7}{20} \quad \quad 2\frac{8}{20} \] Rewrite the numbers as they appear in the question in size order \[2\frac{5}{20} \quad \quad 2\frac{6}{20} \quad \quad 2\frac{7}{20} \quad \quad 2\frac{8}{20} \] \[\frac{9}{4} \quad \quad \;\;\;2\frac{3}{10} \quad \quad \;2\frac{7}{20} \quad \quad \;\;\frac{12}{5} \] Example 5: ordering fractions and decimalsWrite the following fractions in order of size: \[\frac{3}{4} \quad \quad 0.55 \quad \quad \frac{1}{2} \quad \quad 0.6 \] Write all the fractions so that they have a common denominator When there is a mixture of decimals and fractions it is sometimes easier to write them all as decimals. Some fractions and their decimal equivalents may be well known, otherwise we may need to work out a division. \[\frac{3}{4}=3\div4=0.75\] \[\frac{1}{2}=1\div2=0.5\] Find the smallest fraction by comparing the numerators and order the fractions Here are the numbers as decimals. To help with comparing it is a good idea to put in a zero in the hundredths column for 0.5and 0.6. We can compare the hundredths. \[0.75 \quad \quad 0.55 \quad \quad 0.50 \quad \quad 0.60 \] Writing them in size order would give \[0.50 \quad \quad 0.55 \quad \quad 0.60 \quad \quad 0.75 \] Rewrite the numbers as they appear in the question in size order \[0.50 \quad \quad 0.55 \quad \quad 0.60 \quad \quad 0.75 \] \[\frac{1}{2} \quad \quad \;\;\;0.55 \quad \quad \; 0.6 \quad \quad \;\; \frac{3}{4} \] Example 6: ordering fractions and decimalsWrite the following numbers in order of size: \[0.67 \quad \quad \frac{2}{3} \quad \quad 0.603 \quad \quad \frac{5}{8} \] Write all the fractions so that they have a common denominator When there is a mixture of decimals and fractions it is sometimes easier to write them all as decimal fractions (decimals). Some fractions and their decimal equivalents may be well known, otherwise we may need to work out a division. \[\frac{2}{3}=2\div3=0.666…\] \[\frac{5}{8}=5\div8=0.625\] Find the smallest fraction by comparing the numerators and order the fractions Here are the numbers as decimals. To help with comparing it is a good idea to put in a zero in the thousandths column for 0.67so we can compare the hundredths. \[0.670 \quad \quad 0.666… \quad \quad 0.603 \quad \quad 0.625 \] Writing them in size order would give \[0.603 \quad \quad 0.625 \quad \quad \quad 0.666… \quad \quad 0.670 \] Rewrite the numbers as they appear in the question in size order \[0.603 \quad \quad 0.625 \quad \quad 0.666… \quad \quad 0.670 \] \[0.603 \quad \quad \;\;\;\frac{5}{8} \quad \quad \;\; \; \; \;\frac{2}{3} \quad \quad \; \; \;\;\; 0.67 \] Common misconceptions
It is much easier to change the fractions so that they have a common denominator and then compare the numerators.
Sometimes finding a common denominator can be very difficult so it can be easier to convert the fractions to decimals and compare them instead.
Usually “in size order” means from smallest to largest. But the question might want you to put the numbers in descending order from largest to smallest. E.g. \[\frac{4}{7} \quad \quad\frac{11}{14}\quad \quad \frac{1}{2}\] Convert the fractions so they have the same denominator: \[\frac{8}{14} \quad \quad \frac{11}{14} \quad \quad \frac{7}{14}\] Write the fractions in order of size from largest to smallest: \[\frac{11}{14} \quad \quad\frac{8}{14} \quad \quad \frac{7}{14}\] The final answer is: \[\frac{11}{14} \quad \quad \frac{4}{7} \quad \quad \frac{1}{2} \] Practice ordering fractions questions\frac{5}{12} \quad \quad \frac{2}{3} \quad \quad \frac{5}{6} \quad \quad \frac{1}{2} \frac{5}{12} \quad \quad \frac{1}{2} \quad \quad \frac{2}{3} \quad \quad \frac{5}{6} \frac{2}{3} \quad \quad \frac{1}{2} \quad \quad \frac{5}{12} \quad \quad \frac{5}{6} \frac{1}{2} \quad \quad \frac{2}{3} \quad \quad \frac{5}{6} \quad \quad \frac{5}{12} \frac{5}{12} \quad \quad \frac{1}{2}=\frac{6}{12} \quad \quad \frac{2}{3}=\frac{8}{12} \quad \quad \frac{5}{6}=\frac{10}{12} \frac{5}{8} \quad \quad \frac{13}{24} \quad \quad \frac{7}{12} \quad \quad \frac{3}{4} \frac{13}{24} \quad \quad \frac{3}{4} \quad \quad \frac{7}{12} \quad \quad \frac{5}{8} \frac{13}{24} \quad \quad \frac{7}{12} \quad \quad \frac{5}{8} \quad \quad \frac{3}{4} \frac{3}{4} \quad \quad \frac{5}{8} \quad \quad \frac{7}{12} \quad \quad \frac{13}{24} \frac{13}{24} \quad \quad \frac{7}{12}=\frac{14}{24} \quad \quad \frac{5}{8}=\frac{15}{24} \quad \quad \frac{3}{4}=\frac{18}{24} \frac{7}{6} \quad \quad 1\frac{11}{30} \quad \quad 1\frac{2}{5} \quad \quad \frac{19}{15} \frac{7}{6} \quad \quad \frac{19}{15} \quad \quad 1\frac{2}{5} \quad \quad 1\frac{11}{30} \frac{7}{6} \quad \quad \frac{19}{15} \quad \quad 1\frac{11}{30} \quad \quad 1\frac{2}{5} 1\frac{2}{5} \quad \quad \frac{7}{6} \quad \quad \frac{19}{15} \quad \quad 1\frac{11}{30} \frac{7}{6}=1\frac{5}{30} \quad \quad \frac{19}{15}=1\frac{8}{30} \quad \quad 1\frac{11}{30} \quad \quad 1\frac{2}{5}=1\frac{12}{30} \frac{67}{20} \quad \quad \frac{17}{5} \quad \quad 3\frac{7}{10} \quad \quad 3\frac{3}{4} 3\frac{3}{4} \quad \quad 3\frac{7}{10} \quad \quad \frac{17}{5} \quad \quad \frac{67}{20} 3\frac{3}{4} \quad \quad \frac{17}{5} \quad \quad 3\frac{7}{10} \quad \quad \frac{67}{20} \frac{67}{20} \quad \quad 3\frac{7}{10} \quad \quad \frac{17}{5} \quad \quad 3\frac{3}{4} \frac{67}{20}=3\frac{7}{20} \quad \quad \frac{17}{5}=3\frac{8}{20} \quad \quad 3\frac{7}{10}=3\frac{14}{20} \quad \quad 3\frac{3}{4}=3\frac{15}{20} 0.2 \quad \quad \frac{1}{2} \quad \quad 0.3 \quad \quad \frac{1}{4} 0.2 \quad \quad \frac{1}{4} \quad \quad 0.3 \quad \quad \frac{1}{2} 0.3 \quad \quad \frac{1}{2} \quad \quad 0.2 \quad \quad \frac{1}{4} \frac{1}{4} \quad \quad 0.3 \quad \quad \frac{1}{2} \quad \quad 0.2 0.2=0.20 \quad \quad \frac{1}{4}=0.25 \quad \quad 0.3=0.30 \quad \quad \frac{1}{2}=0.50 0.71 \quad \quad \frac{3}{4} \quad \quad \frac{4}{5} \quad \quad 0.82 0.71 \quad \quad \frac{3}{4} \quad \quad 0.82 \quad \quad \frac{4}{5} 0.71 \quad \quad \frac{4}{5} \quad \quad 0.82 \quad \quad \frac{3}{4} \frac{3}{4} \quad \quad 0.71 \quad \quad 0.82 \quad \quad \frac{4}{5} 0.71=0.71 \quad \quad \frac{3}{4}=0.75 \quad \quad \frac{4}{5}=0.80 \quad \quad 0.82=0.82 Ordering fractions GCSE questions1. Here are four fractions: \frac{17}{20} \quad \quad \frac{7}{10} \quad \quad \frac{3}{4} \quad \quad \frac{3}{5}
Starting with the smallest fraction. (2 Marks) Show answer \frac{17}{20} \quad \quad \frac{7}{10}=\frac{14} {20} \quad \quad \frac{3}{5}=\frac{12}{20} \quad \quad \frac{3}{4}=\frac{15}{20} (1) \frac{3}{5} \quad \quad \frac{7}{10} \quad \quad \frac{3}{4} \quad \quad \frac{17}{20} (1) 2. Here are four fractions: \frac{2}{5} \quad \quad \frac{1}{4}\quad \quad \frac{4}{13}\quad \quad \frac{3}{10}
Starting with the smallest fraction. (2 Marks) Show answer \frac{2}{5}=0.4 \quad \quad \frac{1}{4}=0.25 \quad \quad \frac{4}{13}=0.307… \quad \quad \frac{3}{10}=0.3 (1) \frac{1}{4}\quad \quad \frac{3}{10}\quad \quad \frac{4}{13}\quad \quad \frac{2}{5} (1) 3. Place the following numbers in order of size, smallest first: 2\frac{1}{4} \quad \quad 1.76^2 \quad \quad 2.14 \quad \quad \frac{17}{6} (2 Marks) Show answer 2\frac{1}{4}=2\frac{3}{12}=2.25 \quad \quad 1.76^2=3.0976 \quad \quad \frac{17}{6}=2\frac{10}{12}=2.833… (1) 2.14 \quad \quad 2\frac{1}{4} \quad \quad \frac{17}{6} \quad \quad 1.76^2 (1) Learning checklistYou have now learned how to:
Still stuck?Prepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors. Find out more about our GCSE maths revision programme. How do you put fractions in order from least to greatest?To order fractions from least to greatest, start by finding the lowest common denominator for all of the fractions. Next, convert each of the fractions by dividing the lowest common denominator by the denominator and then multiplying the top and bottom of the fraction by your answer.
How do you order fractions in 4th grade?Ordering Fractions Example
List some equivalent fractions for each. Then, pick the equivalent fractions that have the same denominators. Finally, we replace the equivalent fractions with the original fractions.
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