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Mixed and Improper Fractions
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Foundational skills
Identify an improper fraction
\[ \frac{7}{4} \text{ is improper} \]
Identify which fraction has numerator ≥ denominator.
Identify a mixed number
\[ 2\frac{1}{4} \text{ is mixed} \]
Identify which number combines a whole number with a fraction.
Recognise if a fraction is improper
\[ \text{Is } \frac{9}{4} \text{ improper?} \]
Decide whether a given fraction is improper.
Identify the whole number part
\[ 3\frac{2}{5} \rightarrow 3 \]
Read and identify the whole number component.
Identify the fractional part
\[ 4\frac{3}{8} \rightarrow \frac{3}{8} \]
Read and identify the fraction component.
Interpret a mixed number from a diagram
\[ \text{Diagram} \rightarrow 2\frac{1}{4} \]
Read a visual and write it as a mixed number.
Interpret an improper fraction from a diagram
\[ \text{Diagram} \rightarrow \frac{7}{4} \]
Read a visual and express as an improper fraction.
Converting improper to mixed
Convert improper to mixed (halves)
\[ \frac{7}{2} \rightarrow 3\frac{1}{2} \]
Convert improper fractions with denominator 2.
Convert improper to mixed (thirds)
\[ \frac{10}{3} \rightarrow 3\frac{1}{3} \]
Convert improper fractions with denominator 3.
Convert improper to mixed (quarters)
\[ \frac{11}{4} \rightarrow 2\frac{3}{4} \]
Convert improper fractions with denominator 4.
Convert improper to mixed (fifths)
\[ \frac{17}{5} \rightarrow 3\frac{2}{5} \]
Convert improper fractions with denominator 5.
Convert improper to mixed (tenths)
\[ \frac{23}{10} \rightarrow 2\frac{3}{10} \]
Convert improper fractions with denominator 10.
Convert improper to mixed (any)
\[ \frac{19}{6} \rightarrow 3\frac{1}{6} \]
Convert with any common denominator.
Convert improper (whole = 1)
\[ \frac{5}{3} \rightarrow 1\frac{2}{3} \]
Convert where result has whole part = 1.
Convert improper (larger whole)
\[ \frac{29}{4} \rightarrow 7\frac{1}{4} \]
Convert where result has whole part 5+.
Converting mixed to improper
Convert mixed to improper (halves)
\[ 3\frac{1}{2} \rightarrow \frac{7}{2} \]
Convert mixed numbers with denominator 2.
Convert mixed to improper (thirds)
\[ 2\frac{2}{3} \rightarrow \frac{8}{3} \]
Convert mixed numbers with denominator 3.
Convert mixed to improper (quarters)
\[ 4\frac{3}{4} \rightarrow \frac{19}{4} \]
Convert mixed numbers with denominator 4.
Convert mixed to improper (fifths)
\[ 3\frac{2}{5} \rightarrow \frac{17}{5} \]
Convert mixed numbers with denominator 5.
Convert mixed to improper (tenths)
\[ 2\frac{7}{10} \rightarrow \frac{27}{10} \]
Convert mixed numbers with denominator 10.
Convert mixed to improper (any)
\[ 5\frac{3}{8} \rightarrow \frac{43}{8} \]
Convert with any common denominator.
Convert mixed (larger whole)
\[ 8\frac{2}{3} \rightarrow \frac{26}{3} \]
Convert with whole number part 6+.
Special cases
Improper fraction = whole number
\[ \frac{12}{4} = 3 \]
Recognise when improper fraction equals a whole.
Convert whole to improper fraction
\[ 4 = \frac{12}{3} \]
Express a whole number as an improper fraction.
Simplify fractional part
\[ 3\frac{4}{8} = 3\frac{1}{2} \]
Simplify the fractional part of a mixed number.
Fractional part equals 1
\[ 3\frac{4}{4} = 4 \]
Recognise when fractional part equals one whole.
Convert improper and simplify
\[ \frac{14}{4} = 3\frac{1}{2} \]
Convert and simplify the result.
Identify equivalent fractions
\[ \frac{11}{4} = \text{?} \]
Select equivalent mixed number from options.
Complete equivalent: mixed to improper
\[ 2\frac{?}{5} = \frac{13}{5} \]
Find the missing numerator in the mixed number.
Complete equivalent: improper to mixed
\[ \frac{?}{4} = 3\frac{1}{4} \]
Find the missing numerator in the improper fraction.
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