Fractions and Decimals • Topic 2 of 7

Improper Fractions

An improper fraction has a numerator greater than or equal to its denominator, so its value is 1 or more — for example 7/3 or 9/9. Improper fractions are the natural form for calculation: it is far easier to multiply, divide and combine fractions in improper form than as mixed numbers. Every improper fraction can be written as a mixed number by dividing: the quotient is the whole part and the remainder over the divisor is the fractional part. The SAT often expects answers left as improper fractions, so do not always convert to mixed form.

✅ Solved examples

1. Convert 17/5 to a mixed number.
17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5.
2. Which is improper: 2/7, 5/8, 11/4, 1/2?
An improper fraction has numerator ≥ denominator. Only 11/4 qualifies (11 > 4).
3. Write 9/9 as a whole number.
Numerator equals denominator, so 9/9 = 1.
4. Convert the mixed number 2 3/4 to an improper fraction.
Multiply the whole number by the denominator and add the numerator: 2·4 + 3 = 11, over 4, giving 11/4.

✏️ Practice — try these, take hints as needed

1. Convert 23/4 to a mixed number.
Divide 23 by 4.
23 ÷ 4 = 5 remainder 3.
Write the remainder over 4.
5 3/4.
2. Convert 3 2/5 to an improper fraction.
Multiply the whole number by the denominator.
3 · 5 = 15, then add the numerator 2.
Put 17 over 5.
17/5.
3. Which is improper: 4/9, 7/7, 2/3, 1/8?
Improper means numerator ≥ denominator.
Compare top and bottom.
7 = 7.
7/7.
4. Convert 30/7 to a mixed number.
Divide 30 by 7.
30 ÷ 7 = 4 remainder 2.
Remainder over 7.
4 2/7.
5. Convert 5 1/2 to an improper fraction.
5 · 2 = 10.
Add the numerator 1.
Put 11 over 2.
11/2.

📝 Topic test — 8 questions

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