Mixed Numbers & Improper Fractions (Grades 4–5)
Sometimes a fraction holds more than one whole. 7/4 means seven quarter-pieces — and four quarters make a whole, so 7/4 is one whole with 3 quarters left over: 1 3/4. A number written as a whole plus a fraction (like 1 3/4) is a mixed number; a fraction whose top is bigger than its bottom (like 7/4) is an improper fraction. They're two ways to write the same amount.
Understanding mixed numbers & improper fractions
Sometimes a fraction holds more than one whole. 7/4 means seven quarter-pieces — and four quarters make a whole, so 7/4 is one whole with 3 quarters left over: 1 3/4. A number written as a whole plus a fraction (like 1 3/4) is a mixed number; a fraction whose top is bigger than its bottom (like 7/4) is an improper fraction. They're two ways to write the same amount.
To go from improper to mixed: divide the top by the bottom. The quotient is the whole number; the remainder is the new top; the bottom stays. To go back: multiply the whole by the bottom, add the top, and put it over the bottom.
Key Idea
To go from improper to mixed: divide the top by the bottom. The quotient is the whole number; the remainder is the new top; the bottom stays. To go back: multiply the whole by the bottom, add the top, and put it over the bottom.
Seeing it in action
Worked example
Write 7/4 as a mixed number.
7 ÷ 4 = 1 remainder 3. So 7/4 = 1 3/4. (Visual: two bars in quarters — the first fully shaded (4/4 = 1 whole), the second with 3 of 4 shaded.)
Worked example 2
Write 2 1/3 as an improper fraction.
2 × 3 = 6, plus 1 = 7, over 3. → 7/3.
Try a few
Write 9/2 as a mixed number.
Write 11/4 as a mixed number.
Write 3 2/5 as an improper fraction.
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Put the reasoning on paper.
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