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Ordering Fractions
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Foundational skills
Identify fractions with same denominator
\[ \frac{2}{5}, \frac{3}{7}, \frac{4}{5} \]
Recognise when fractions share a common denominator.
Identify unit fractions
\[ \frac{1}{4}, \frac{2}{5}, \frac{1}{8} \]
Recognise unit fractions (numerator 1).
Compare fraction to one half
\[ \frac{3}{8} \text{ vs } \frac{1}{2} \]
Determine if fraction is less than, equal to, or greater than ½.
Same denominator
Order 3 proper fractions with same denominator
\[ \frac{4}{7}, \frac{2}{7}, \frac{6}{7} \]
Order by comparing numerators.
Order fractions with same denominator including improper
\[ \frac{5}{4}, \frac{3}{4}, \frac{7}{4} \]
At least one fraction is improper.
Order fractions – larger denominators
\[ \frac{7}{12}, \frac{11}{12}, \frac{5}{12} \]
Same denominator (9-12).
Unit fractions
Order 3 unit fractions – small denominators
\[ \frac{1}{3}, \frac{1}{6}, \frac{1}{2} \]
Denominators up to 6.
Order 3 unit fractions – denominators to 12
\[ \frac{1}{8}, \frac{1}{3}, \frac{1}{12} \]
Larger denominators included.
Same numerator
Order 3 fractions with numerator 2
\[ \frac{2}{3}, \frac{2}{7}, \frac{2}{5} \]
All have numerator 2.
Order 3 fractions with numerator 3+
\[ \frac{3}{4}, \frac{3}{10}, \frac{3}{8} \]
Numerator is 3, 4, or 5.
Denominators as multiples
Order fractions – one denominator divides others
\[ \frac{3}{4}, \frac{5}{8}, \frac{1}{2} \]
One denominator is factor of others.
Order fractions – denominators 2, 4, 8
\[ \frac{1}{2}, \frac{3}{8}, \frac{3}{4} \]
Convert all to eighths.
Order fractions – denominators 3, 6, 12
\[ \frac{2}{3}, \frac{7}{12}, \frac{5}{6} \]
Convert all to twelfths.
Order fractions – denominators 2, 5, 10
\[ \frac{3}{5}, \frac{1}{2}, \frac{7}{10} \]
Convert all to tenths.
Finding common denominator
Order fractions – denominators 3 and 4
\[ \frac{2}{3}, \frac{1}{4}, \frac{3}{4} \]
LCD = 12.
Order fractions – denominators 4 and 5
\[ \frac{3}{4}, \frac{4}{5}, \frac{2}{5} \]
LCD = 20.
Order fractions – denominators 3 and 5
\[ \frac{2}{5}, \frac{1}{3}, \frac{4}{5} \]
LCD = 15.
Order fractions – three different denominators
\[ \frac{1}{2}, \frac{2}{3}, \frac{3}{4} \]
Find LCD for all three.
Order fractions – denominators requiring LCM
\[ \frac{5}{6}, \frac{3}{4}, \frac{7}{8} \]
LCD ≠ product of denominators.
Benchmark comparisons
Order fractions by comparing to one half
\[ \frac{2}{5}, \frac{5}{8}, \frac{3}{7} \]
Compare each to ½ first.
Order fractions all less than one half
\[ \frac{2}{5}, \frac{3}{8}, \frac{2}{7} \]
All fractions < ½.
Order fractions all greater than one half
\[ \frac{5}{8}, \frac{2}{3}, \frac{5}{9} \]
All fractions > ½.
Order fractions using distance from one
\[ \frac{3}{4}, \frac{5}{6}, \frac{7}{8} \]
Compare how close each is to 1.
Mixed numbers
Order mixed numbers – same whole, same denominator
\[ 2\frac{3}{5}, 2\frac{1}{5}, 2\frac{4}{5} \]
Compare fractional parts only.
Order mixed numbers – same whole, different denominators
\[ 3\frac{1}{2}, 3\frac{2}{3}, 3\frac{3}{4} \]
Find common denominator for fractions.
Order mixed numbers – different whole parts
\[ 2\frac{3}{4}, 4\frac{1}{4}, 3\frac{1}{2} \]
Whole parts determine order.
Order mixed numbers – two same, one different
\[ 3\frac{1}{4}, 3\frac{3}{4}, 2\frac{7}{8} \]
Compare systematically.
Improper fractions
Order improper fractions with same denominator
\[ \frac{9}{4}, \frac{5}{4}, \frac{7}{4} \]
Compare numerators directly.
Order improper fractions with different denominators
\[ \frac{7}{4}, \frac{8}{5}, \frac{5}{3} \]
Convert to mixed numbers.
Order mix of improper fractions and mixed numbers
\[ \frac{9}{4}, 2\frac{1}{3}, \frac{7}{3} \]
Convert to same form first.
Equivalent fractions in ordering
Order fractions where two are equivalent
\[ \frac{2}{3}, \frac{1}{2}, \frac{4}{6} \]
Recognise equivalent pair.
Identify equivalent fractions when ordering
\[ \frac{3}{4}, \frac{2}{3}, \frac{9}{12} \]
Which two are equal?
Fractions greater than one
Order proper and improper fractions together
\[ \frac{3}{4}, \frac{5}{4}, \frac{2}{3} \]
Proper fractions < improper.
Order fractions including whole numbers
\[ \frac{3}{4}, 2, \frac{5}{2} \]
Mix of fractions and integers.
Fractions near each other
Order fractions that are close in value
\[ \frac{2}{3}, \frac{3}{4}, \frac{5}{6} \]
Requires careful comparison.
Order fractions very close to one half
\[ \frac{4}{9}, \frac{5}{9}, \frac{1}{2} \]
All near ½ – precision needed.
Special cases
Order fractions with numerator one less than denominator
\[ \frac{4}{5}, \frac{2}{3}, \frac{5}{6} \]
Each is “one piece from whole”.
Order fractions with consecutive denominators
\[ \frac{3}{5}, \frac{3}{6}, \frac{3}{7} \]
Same numerator, consecutive denominators.
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