2.1 Number Sense, Operations, and Fraction–Decimal–Percent Conversions

Adamson University College Entrance Test AdUCET

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1 Introduction & Exam Overview

1.1 AdUCET Overview, Format, and Admission Process 1.2 Test-Taking and Time-Management Strategies

2 Chapter 2: Mathematics I — Numbers, Algebra, and Functions

2.1 Number Sense, Operations, and Fraction–Decimal–Percent Conversions 2.2 Algebra, Polynomials, and Linear/Quadratic Equations 2.3 Inequalities, Absolute Value, and Systems of Equations 2.4 Radicals, Rational Expressions, and Scientific Notation 2.5 Coordinate Geometry, Lines, and Functions

3 Chapter 3: Mathematics II — Geometry, Measurement, and Trigonometry

3.1 Plane Geometry: Angles, Triangles, Polygons, and Circles 3.2 Solid Mensuration, Measurement, and Unit Conversion 3.3 Right-Triangle Trigonometry and Applications

4 Chapter 4: Mathematics III — Sequences, Proportion, and Data

4.1 Arithmetic and Geometric Sequences and Series 4.2 Ratio, Proportion, Percentage, Work, and Mixture Problems 4.3 Descriptive Statistics and Data Interpretation 4.4 Probability: Rules, Compound Events, and Conditional Probability 4.5 Counting Principles: Permutations and Combinations

5 Chapter 5: English I — Reading Comprehension and Vocabulary

5.1 Reading Comprehension: Main Idea, Purpose, and Passage Structure 5.2 Inference, Supporting Detail, and Author's Tone 5.3 Word Roots, Prefixes, and Suffixes 5.4 Vocabulary in Context, Synonyms, Antonyms, and Confusables

6 Chapter 6: English II — Grammar, Usage, and Written Expression

6.1 Subject-Verb Agreement and Verb Tenses 6.2 Pronouns, Modifiers, and Parallel Structure 6.3 Sentence Boundaries, Clauses, and Punctuation 6.4 Sentence Correction, Redundancy, and Idiomatic Usage 6.5 Verbal Analogies and Relationship Bridges 6.6 Paragraph Organization, Coherence, and Transitions

7 Chapter 7: General Science I — Biology and Chemistry

7.1 Cell Biology, Transport, and Cellular Energetics 7.2 Genetics, Heredity, and Molecular Biology 7.3 Human Body Systems, Ecology, and Evolution 7.4 Matter, Phase Changes, and Atomic Structure 7.5 Periodic Trends, Chemical Bonding, Reactions, Acids and Bases

8 Chapter 8: General Science II — Physics and Earth Science

8.1 Mechanics: Motion, Newton's Laws, Work, and Energy 8.2 Waves, Sound, Light, Heat, Electricity, and Magnetism 8.3 Earth's Structure, Plate Tectonics, and the Rock Cycle 8.4 The Atmosphere, Weather, the Water Cycle, and Astronomy

9 Chapter 9: Aptitude and Abstract Reasoning

9.1 Figure Series and Pattern Progression 9.2 Matrix Reasoning and Figural Analogies 9.3 Spatial Reasoning: Rotation, Reflection, and Chirality 9.4 Paper Folding, Cube Nets, and Orthographic Views 9.5 Deductive Reasoning, Syllogisms, and Venn Diagrams 9.6 Number, Letter, and Alphanumeric Series 9.7 Odd-One-Out, Classification, and Logic Puzzles

2.1 Number Sense, Operations, and Fraction–Decimal–Percent Conversions

Key Takeaways Explain This Topic AI

GEMDAS is two shared levels, not four ranked steps: multiplication and division run left to right together, and so do addition and subtraction, so 24 ÷ 6 × 2 = 8 24 \div 6 \times 2 = 8 24 ÷ 6 × 2 = 8 .

− 3 2 = − 9 -3^2 = -9 − 3 2 = − 9 but ( − 3 ) 2 = 9 (-3)^2 = 9 ( − 3 ) 2 = 9 — the exponent binds to the base alone unless parentheses capture the negative sign.

GCF times LCM equals the product of the two numbers: GCF(84, 126) = 42 and LCM(84, 126) = 252, and 42 × 252 = 84 × 126 = 10,584 42 \times 252 = 84 \times 126 = 10{,}584 42 × 252 = 84 × 126 = 10 , 584 .

Convert a percent to a decimal by moving the point two places left, so 0.5 % = 0.005 0.5\% = 0.005 0.5% = 0.005 and 125 % = 1.25 125\% = 1.25 125% = 1.25 , not 0.05 0.05 0.05 and 12.5 12.5 12.5 .

Eighths give exact percents ending in .5 ( 1 8 = 12.5 % \frac{1}{8} = 12.5\% 8 1 ​ = 12.5% , 3 8 = 37.5 % \frac{3}{8} = 37.5\% 8 3 ​ = 37.5% , 5 8 = 62.5 % \frac{5}{8} = 62.5\% 8 5 ​ = 62.5% , 7 8 = 87.5 % \frac{7}{8} = 87.5\% 8 7 ​ = 87.5% ) while thirds and sixths repeat ( 1 3 = 33 1 3 % \frac{1}{3} = 33\frac{1}{3}\% 3 1 ​ = 33 3 1 ​ % , 1 6 = 16 2 3 % \frac{1}{6} = 16\frac{2}{3}\% 6 1 ​ = 16 3 2 ​ % ).

Last updated: August 2026

2.1 Number Sense, Operations, and Fraction–Decimal–Percent Conversions

Candidate reports single out number sense as the highest-yield mathematics skill on the AdUCET, describing the mathematics portion as broad rather than deep: fractions, decimals, percentages and signed numbers reappear inside geometry items, science items and data-table items, so an examinee who can turn 5 8 \frac{5}{8} 8 5 ​ into 62.5 % 62.5\% 62.5% in one beat saves seconds on dozens of questions. Adamson University publishes no content outline, so nobody can tell you how many items any topic receives — but the arithmetic below sits underneath all of them.

1. Order of Operations: GEMDAS

The Philippine K-12 curriculum teaches GEMDAS — G rouping, E xponents, M ultiplication and D ivision, A ddition and S ubtraction — the same rule taught elsewhere as PEMDAS (parentheses in place of grouping). The detail that costs marks is that the last four letters are two levels, not four :

Multiplication and division share one level and run left to right : 24 ÷ 6 × 2 = 4 × 2 = 8 24 \div 6 \times 2 = 4 \times 2 = 8 24 ÷ 6 × 2 = 4 × 2 = 8 , never 24 ÷ 12 = 2 24 \div 12 = 2 24 ÷ 12 = 2 .

Addition and subtraction share one level and also run left to right : 10 − 4 + 3 = 9 10 - 4 + 3 = 9 10 − 4 + 3 = 9 , not 10 − 7 = 3 10 - 7 = 3 10 − 7 = 3 .

A fraction bar, a radical sign and the bars of an absolute value are all invisible grouping symbols — finish the numerator and the denominator before you divide.

Worked Example 1 — signed numbers inside GEMDAS

Evaluate − 3 2 + ( − 4 ) 2 ÷ 8 × 2 − ( 5 − 7 ) 3 -3^2 + (-4)^2 \div 8 \times 2 - (5-7)^3 − 3 2 + ( − 4 ) 2 ÷ 8 × 2 − ( 5 − 7 ) 3 .

Grouping. 5 − 7 = − 2 5 - 7 = -2 5 − 7 = − 2 .

Exponents. − 3 2 = − ( 3 ⋅ 3 ) = − 9 -3^2 = -(3 \cdot 3) = -9 − 3 2 = − ( 3 ⋅ 3 ) = − 9 , because the exponent attaches to the 3 alone. ( − 4 ) 2 = + 16 (-4)^2 = +16 ( − 4 ) 2 = + 16 , because the parentheses capture the sign. ( − 2 ) 3 = − 8 (-2)^3 = -8 ( − 2 ) 3 = − 8 . The line now reads − 9 + 16 ÷ 8 × 2 − ( − 8 ) -9 + 16 \div 8 \times 2 - (-8) − 9 + 16 ÷ 8 × 2 − ( − 8 ) .

Multiply and divide, left to right. 16 ÷ 8 = 2 16 \div 8 = 2 16 ÷ 8 = 2 , then 2 × 2 = 4 2 \times 2 = 4 2 × 2 = 4 , giving − 9 + 4 − ( − 8 ) -9 + 4 - (-8) − 9 + 4 − ( − 8 ) .

Add and subtract, left to right. − 9 + 4 = − 5 -9 + 4 = -5 − 9 + 4 = − 5 , then − 5 − ( − 8 ) = − 5 + 8 = 3 -5 - (-8) = -5 + 8 = 3 − 5 − ( − 8 ) = − 5 + 8 = 3 .

Answer: 3 3 3 . Two sign traps are buried in that one line: − 3 2 ≠ 9 -3^2 \neq 9 − 3 2  = 9 , and subtracting a negative adds.

2. Divisibility, Prime Factorisation, GCF and LCM

Divisibility tests let you factor and reduce fractions without long division.

• Divisor Test Example
• 2 last digit is even 3,174 3{,}174 3 , 174 ends in 4
• 3 digit sum divisible by 3 4,512 → 4 + 5 + 1 + 2 = 12 4{,}512 \to 4+5+1+2 = 12 4 , 512 → 4 + 5 + 1 + 2 = 12
• 4 last two digits divisible by 4 7,316 → 16 7{,}316 \to 16 7 , 316 → 16
• 5 last digit 0 or 5 2,085 2{,}085 2 , 085
• 6 passes the 2-test and the 3-test 4,512 4{,}512 4 , 512 is even, digit sum 12
• 8 last three digits divisible by 8 5,120 → 120 = 8 × 15 5{,}120 \to 120 = 8 \times 15 5 , 120 → 120 = 8 × 15
• 9 digit sum divisible by 9 6,318 → 6 + 3 + 1 + 8 = 18 6{,}318 \to 6+3+1+8 = 18 6 , 318 → 6 + 3 + 1 + 8 = 18
• 10 last digit 0 4,780 4{,}780 4 , 780

11 alternating digit sum divisible by 11 2,915 → 2 − 9 + 1 − 5 = − 11 2{,}915 \to 2-9+1-5 = -11 2 , 915 → 2 − 9 + 1 − 5 = − 11

Prime factorisation rewrites a number as a product of primes: 84 = 2 2 ⋅ 3 ⋅ 7 84 = 2^2 \cdot 3 \cdot 7 84 = 2 2 ⋅ 3 ⋅ 7 and 126 = 2 ⋅ 3 2 ⋅ 7 126 = 2 \cdot 3^2 \cdot 7 126 = 2 ⋅ 3 2 ⋅ 7 .

The greatest common factor (GCF) takes every shared prime to its lowest power: 2 1 ⋅ 3 1 ⋅ 7 1 = 42 2^1 \cdot 3^1 \cdot 7^1 = 42 2 1 ⋅ 3 1 ⋅ 7 1 = 42 .

The least common multiple (LCM) takes every prime that appears to its highest power: 2 2 ⋅ 3 2 ⋅ 7 = 252 2^2 \cdot 3^2 \cdot 7 = 252 2 2 ⋅ 3 2 ⋅ 7 = 252 .

Fast check: GCF × LCM \text{GCF} \times \text{LCM} GCF × LCM equals the product of the two numbers, since 42 × 252 = 10,584 = 84 × 126 42 \times 252 = 10{,}584 = 84 \times 126 42 × 252 = 10 , 584 = 84 × 126 .

Worked Example 2 — deciding between GCF and LCM

A vendor along San Marcelino has 84 pieces of suman and 126 pieces of puto and wants identical baskets with nothing left over. "Largest identical groups" means GCF : 42 baskets, each holding 84 ÷ 42 = 2 84 \div 42 = 2 84 ÷ 42 = 2 suman and 126 ÷ 42 = 3 126 \div 42 = 3 126 ÷ 42 = 3 puto.

Now a different question. Jeepneys on Route A leave the terminal every 18 minutes and Route B every 24 minutes, both departing at 6:00 AM. "When do the cycles coincide again?" means LCM : 18 = 2 ⋅ 3 2 18 = 2 \cdot 3^2 18 = 2 ⋅ 3 2 and 24 = 2 3 ⋅ 3 24 = 2^3 \cdot 3 24 = 2 3 ⋅ 3 , so the LCM is 2 3 ⋅ 3 2 = 72 2^3 \cdot 3^2 = 72 2 3 ⋅ 3 2 = 72 minutes — the next simultaneous departure is 7:12 AM . The working rule is short: dividing into groups uses GCF; repeating cycles meeting again uses LCM.

3. Fraction Arithmetic Without a Calculator

Like denominators: combine numerators only. 5 9 + 2 9 = 7 9 \frac{5}{9} + \frac{2}{9} = \frac{7}{9} 9 5 ​ + 9 2 ​ = 9 7 ​ .

Unlike denominators: rewrite both over the least common denominator (LCD), which is the LCM of the denominators.

Mixed numbers: convert to improper fractions before operating; convert back only if the options are written as mixed numbers.

Multiplying: cross-cancel first, then multiply straight across.

Dividing: multiply by the reciprocal of the divisor.

Compute 2 3 4 − 1 5 6 + 2 3 2\frac{3}{4} - 1\frac{5}{6} + \frac{2}{3} 2 4 3 ​ − 1 6 5 ​ + 3 2 ​ . The improper forms are 11 4 \frac{11}{4} 4 11 ​ , 11 6 \frac{11}{6} 6 11 ​ and 2 3 \frac{2}{3} 3 2 ​ ; the LCD of 4, 6 and 3 is 12, so the expression becomes 33 12 − 22 12 + 8 12 = 19 12 = 1 7 12 \frac{33}{12} - \frac{22}{12} + \frac{8}{12} = \frac{19}{12} = 1\frac{7}{12} 12 33 ​ − 12 22 ​ + 12 8 ​ = 12 19 ​ = 1 12 7 ​ .

A complex fraction has fractions inside its numerator or denominator. Simplify top and bottom separately, then divide: 3 4 + 1 2 5 6 − 1 3 = 5 4 1 2 = 5 4 × 2 1 = 10 4 = 5 2 = 2.5 \frac{\frac{3}{4} + \frac{1}{2}}{\frac{5}{6} - \frac{1}{3}} = \frac{\frac{5}{4}}{\frac{1}{2}} = \frac{5}{4} \times \frac{2}{1} = \frac{10}{4} = \frac{5}{2} = 2.5 6 5 ​ − 3 1 ​ 4 3 ​ + 2 1 ​ ​ = 2 1 ​ 4 5 ​ ​ = 4 5 ​ × 1 2 ​ = 4 10 ​ = 2 5 ​ = 2.5

4. The Conversion Table to Memorise

• Fraction Decimal Percent
• 1 8 \frac{1}{8} 8 1 ​ 0.125 0.125 0.125 12.5 % 12.5\% 12.5%
• 1 6 \frac{1}{6} 6 1 ​ 0.1 6 ‾ 0.1\overline{6} 0.1 6 16 2 3 % 16\frac{2}{3}\% 16 3 2 ​ %
• 1 5 \frac{1}{5} 5 1 ​ 0.2 0.2 0.2 20 % 20\% 20%
• 1 4 \frac{1}{4} 4 1 ​ 0.25 0.25 0.25 25 % 25\% 25%
• 1 3 \frac{1}{3} 3 1 ​ 0. 3 ‾ 0.\overline{3} 0. 3 33 1 3 % 33\frac{1}{3}\% 33 3 1 ​ %
• 3 8 \frac{3}{8} 8 3 ​ 0.375 0.375 0.375 37.5 % 37.5\% 37.5%
• 2 5 \frac{2}{5} 5 2 ​ 0.4 0.4 0.4 40 % 40\% 40%
• 1 2 \frac{1}{2} 2 1 ​ 0.5 0.5 0.5 50 % 50\% 50%
• 5 8 \frac{5}{8} 8 5 ​ 0.625 0.625 0.625 62.5 % 62.5\% 62.5%
• 2 3 \frac{2}{3} 3 2 ​ 0. 6 ‾ 0.\overline{6} 0. 6 66 2 3 % 66\frac{2}{3}\% 66 3 2 ​ %
• 3 4 \frac{3}{4} 4 3 ​ 0.75 0.75 0.75 75 % 75\% 75%
• 4 5 \frac{4}{5} 5 4 ​ 0.8 0.8 0.8 80 % 80\% 80%
• 7 8 \frac{7}{8} 8 7 ​ 0.875 0.875 0.875 87.5 % 87.5\% 87.5%

When a value is not in the table, use the procedures:

Fraction to decimal: divide numerator by denominator.

Decimal to percent: move the point two places right ( 0.045 → 4.5 % 0.045 \to 4.5\% 0.045 → 4.5% ).

Percent to decimal: move the point two places left ( 0.5 % → 0.005 0.5\% \to 0.005 0.5% → 0.005 ).

Decimal to fraction: write over the place-value denominator and reduce ( 0.36 = 36 100 = 9 25 0.36 = \frac{36}{100} = \frac{9}{25} 0.36 = 100 36 ​ = 25 9 ​ ).

Percent to fraction: write over 100 and reduce ( 45 % = 45 100 = 9 20 45\% = \frac{45}{100} = \frac{9}{20} 45% = 100 45 ​ = 20 9 ​ ).

Repeating decimal to fraction: put the repeating block over as many 9s as it has digits ( 0. 27 ‾ = 27 99 = 3 11 0.\overline{27} = \frac{27}{99} = \frac{3}{11} 0. 27 = 99 27 ​ = 11 3 ​ ).

The table is not trivia — it is a speed tool. Reading 37.5 % 37.5\% 37.5% of 64 as 3 8 × 64 \frac{3}{8} \times 64 8 3 ​ × 64 gives 24 instantly; 16 2 3 % 16\frac{2}{3}\% 16 3 2 ​ % of 42 is 42 6 = 7 \frac{42}{6} = 7 6 42 ​ = 7 ; 62.5 % 62.5\% 62.5% of 240 is 5 8 × 240 = 150 \frac{5}{8} \times 240 = 150 8 5 ​ × 240 = 150 . Each of those is a one-line mental computation only if the conversion is automatic.

5. Place Value, Rounding and Estimation

In 3,847.652 3{,}847.652 3 , 847.652 the 8 sits in the hundreds place, the 6 in the tenths, the 5 in the hundredths and the 2 in the thousandths. To round, look at the digit immediately to the right of the target place: rounding to the nearest tenth gives 3,847.7 3{,}847.7 3 , 847.7 (the hundredths digit is 5, so round up), while rounding to the nearest hundred gives 3,800 3{,}800 3 , 800 (the tens digit is 4, so round down).

Estimation is a scoring tool when four options are far apart. 7 8 × 401 ≈ 0.875 × 400 = 350 \frac{7}{8} \times 401 \approx 0.875 \times 400 = 350 8 7 ​ × 401 ≈ 0.875 × 400 = 350 , which is close enough to identify the true value 350.875 350.875 350.875 without long multiplication.

6. Ordering Mixed Forms

Convert every value to a decimal , then compare digit by digit. Order 0.6 0.6 0.6 , 5 8 \frac{5}{8} 8 5 ​ , 58 % 58\% 58% , 3 5 \frac{3}{5} 5 3 ​ and 0. 6 ‾ 0.\overline{6} 0. 6 from least to greatest: the decimals are 0.6 0.6 0.6 , 0.625 0.625 0.625 , 0.58 0.58 0.58 , 0.6 0.6 0.6 and 0.666 … 0.666\ldots 0.666 … , so the order is 58 % < 0.6 = 3 5 < 5 8 < 0. 6 ‾ 58\% < 0.6 = \frac{3}{5} < \frac{5}{8} < 0.\overline{6} 58% < 0.6 = 5 3 ​ < 8 5 ​ < 0. 6 . Note that two of the five are equal — options that force a strict "<" between them are wrong.

For negatives the number line reverses your instinct: − 3 4 = − 0.75 -\frac{3}{4} = -0.75 − 4 3 ​ = − 0.75 lies to the left of − 0.7 -0.7 − 0.7 , so − 3 4 < − 0.7 -\frac{3}{4} < -0.7 − 4 3 ​ < − 0.7 even though 75 is larger than 70.

Common Traps

Treating GEMDAS as four ranked steps instead of two shared levels.

Reading − 5 2 -5^2 − 5 2 as 25 25 25 ; it is − 25 -25 − 25 unless the base is written ( − 5 ) (-5) ( − 5 ) .

Adding denominators: 1 2 + 1 3 \frac{1}{2} + \frac{1}{3} 2 1 ​ + 3 1 ​ is 5 6 \frac{5}{6} 6 5 ​ , not 2 5 \frac{2}{5} 5 2 ​ .

Converting 0.5 % 0.5\% 0.5% to 0.05 0.05 0.05 instead of 0.005 0.005 0.005 .

Forgetting that a percent greater than 100 is legal: 125 % = 1.25 = 5 4 125\% = 1.25 = \frac{5}{4} 125% = 1.25 = 4 5 ​ .

Comparing 7 9 \frac{7}{9} 9 7 ​ and 5 7 \frac{5}{7} 7 5 ​ by eye; cross-multiply instead ( 7 × 7 = 49 7 \times 7 = 49 7 × 7 = 49 against 5 × 9 = 45 5 \times 9 = 45 5 × 9 = 45 , so 7 9 \frac{7}{9} 9 7 ​ is larger).