Fractions in UPCAT Problems
Build fraction sense, choose the correct model, and solve unfamiliar fraction problems without turning every value into a decimal.
Fractions
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Fractions describe both amounts and operations
A fraction can mean a part of a whole, a quotient, a ratio, or an operation. Before calculating, ask what the denominator describes and whether later fractions refer to the original whole or to a remaining amount.
ab means a ÷ b, where b ≠ 0Fraction of an amount: (ab)NFraction of a remainder: multiply the remaining factorsAdd or subtract
Use a common denominator because the pieces must have the same size.
Multiply
Multiply numerators and denominators; cancel common factors before multiplying.
Divide
Multiply by the reciprocal of the divisor.
Reverse a fraction
If ab of N equals k, then N = k(ba).
Name the whole before touching the numbers
1. Circle the reference whole. Total capacity? Original class? Remaining pages?
2. Translate “of” as multiplication. A fraction of a remainder means successive multiplication.
3. Cancel early. Reduce across factors before multiplying large numbers.
4. Estimate. A result greater than the whole may be impossible unless the problem asks for an improper fraction or rate.
Why it works
Most difficult fraction errors come from using the wrong reference amount, not from the arithmetic itself.
Five forms you should recognize
The denominator 36 creates equal-sized pieces.
Cancel 14 with 28 and 25 with 15 first.
The reciprocal reverses the divisor’s scaling effect.
After 27 is read, 57 remains. Reading 13 of the remainder means:
(13)(57) = 521 of the wholeIf 35 of an allowance is ₱540:
A = 540(53) = ₱900Multiply by the reciprocal to recover the whole.
Check before you commit
- Adding denominators when adding fractions
- Dividing without using the reciprocal
- Treating a fraction of the remainder as a fraction of the original
- Failing to reduce a final fraction
- Converting awkward fractions to rounded decimals too early
- Ignoring whether an answer should be less than or greater than one
Do you need the lesson-or just practice?
One original question in each form recommends your next step. It does not yet verify mastery.
Work at the level you need.
Foundations
Build the core procedure with immediate explanations.
Core Practice
Use mixed forms with less scaffolding.
UPCAT-Style Transfer
Apply the competency in unfamiliar representations.
Ready to verify this competency?
A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.
Fractions in UPCAT Problems FAQ
Should I always use the least common denominator?
It is usually fastest, but any common denominator works if you simplify correctly.
When should I cross-multiply?
Use it to compare two fractions or solve a proportion—not as a universal fraction operation.
Can I use decimals?
Yes when values terminate cleanly, but exact fractions are safer when rounding could alter the answer.
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