L2 · Converting between improper fractions and mixed numbers

Learning goal

“I can convert an improper fraction to a mixed number and a mixed number to an improper fraction, and I can check each conversion by converting back.”

Convert — rewrite the same amount in a different form. Converting never changes the amount, only its name.

Equivalent — naming the same amount. 11/4 and 2 3/4 are equivalent: same point on the number line.

Whole-number part — the whole number in a mixed number: in 2 3/4 the whole-number part is 2.

Fraction part — the fraction written after the whole-number part: in 2 3/4 the fraction part is 3/4.

Worked example

Convert 2 3/4 to an improper fraction. Step 1: Each whole is split into quarters, so each whole holds 4 quarter-parts. Step 2: The 2 wholes hold 2 x 4 = 8 quarter-parts. Step 3: Add the fraction part: 8 + 3 = 11 quarter-parts. So 2 3/4 = 11/4. Model both ways, side by side: two whole bars in quarters plus a 3/4 bar, with all 11 quarter-parts counted, AND a number line marked in quarters (extended to 3): 11/4 and 2 3/4 land on exactly the same mark, between 2 and 3. Say it plainly: multiplying the whole-number part by the denominator counts the parts hiding inside the wholes. Nothing is created - the parts were always there.

Check yourself — explain it

Why do we multiply 2 x 4 when converting 2 3/4?

Paired problem — example still visible

Convert 1 2/3 -> 1 whole = 3 thirds, plus 2 -> 5/3

Faded completion — last step is yours

"3 1/5: the 3 wholes hold 3 x 5 = 15 fifths. Add the fraction part: 15 + 1 = ___ fifths, so 3 1/5 = ___/5." -> 16; 16/5

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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