Basic Operations (Sub-Professional)

Numerical Ability for the Sub-Professional level focuses on core mathematical operations. You must be comfortable working with whole numbers, fractions, and decimals without a calculator.

Sa madaling salita: Kailangan mong maging komportable sa pag-add, subtract, multiply, at divide nang walang calculator.

1. PEMDAS (Order of Operations)

Always follow this order:

Parentheses (Unahin ang nasa loob ng panaklong)
Exponents (Isunod ang mga exponents o powers)
Multiplication and Division (from left to right / kung ano ang mauna sa kaliwa)
Addition and Subtraction (from left to right / kung ano ang mauna sa kaliwa)

2. Working with Fractions

To add/subtract: Find the LCD if denominators are different. (Hanapin ang LCD kapag magkaiba ang numero sa ilalim.)
To multiply: Multiply the tops and the bottoms. (I-multiply ang mga numerator sa isa't isa, at ang mga denominator sa isa't isa.)
To divide: Flip the second fraction and multiply. (Baliktarin ang pangalawang fraction at i-multiply.)

3. Percentages and Ratios

Percent to Decimal: Move decimal 2 places left. (I-usog ang tuldok nang dalawang beses pakaliwa. Halimbawa: 50% = 0.50).
Decimal to Percent: Move decimal 2 places right. (I-usog ang tuldok nang dalawang beses pakanan. Halimbawa: 0.25 = 25%).

Practice Questions

** $25 + 5 \times (10 - 2) =$
- A. 240
- B. 65
- C. 40
- D. 33
- Answer: B (65).
- Solution:
  1. Parentheses: $10 - 2 = 8$ .
  2. Multiplication: $5 \times 8 = 40$ .
  3. Addition: $25 + 40 = 65$ .
- Hack: Unahin ang nasa loob ng parenthesis $(10-2=8)$ . Tapos i-multiply ang 5 sa 8 ( $5 \times 8 = 40$ ). Huli ang addition ( $25 + 40 = 65$ ).
** $\frac{1}{2} + \frac{1}{4} =$
- A. $\frac{2}{6}$
- B. $\frac{3}{4}$
- C. $\frac{1}{2}$
- D. $\frac{2}{4}$
- Answer: B ( $\frac{3}{4}$ ).
- Solution: Convert $\frac{1}{2}$ to $\frac{2}{4}$ . Then $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$ .
- Hack: Gawing magkapareho ang denominator. Ang $\frac{1}{2}$ ay pareho sa $\frac{2}{4}$ . Kapag pinagsama ang $\frac{2}{4}$ at $\frac{1}{4}$ , ang sagot ay $\frac{3}{4}$ .
What is 15% of 200?
- A. 15
- B. 20
- C. 30
- D. 45
- Answer: C (30).
- Solution: $0.15 \times 200 = 30$ .
- Hack: I-multiply ang 0.15 sa 200. Tip: Ang 10% ng 200 ay 20. Ang 5% ay kalahati ng 20 (so 10). $20 + 10 = 30$ .
**Simplify: $12 \div 3 \times 2 =$
- A. 2
- B. 8
- C. 6
- D. 18
- Answer: B (8).
- Solution: Left to right rule. $12 \div 3 = 4$ . Then $4 \times 2 = 8$ .
- Hack: Tandaan ang "Left to Right" rule sa Multiplication at Division. Unahin ang $12 \div 3$ (sagot ay 4), tapos i-multiply sa 2. Huwag unahin ang multiplication kahit nasa huli ang "M" sa MDAS.
**Calculate: $\frac{3}{5} \times \frac{10}{9} =$
- A. $\frac{2}{3}$
- B. $\frac{30}{45}$
- C. $\frac{1}{3}$
- D. $\frac{13}{14}$
- Answer: A ( $\frac{2}{3}$ ).
- Solution: $\frac{3 \times 10}{5 \times 9} = \frac{30}{45}$ . Simplify by dividing both by 15: $\frac{2}{3}$ .
- Hack: I-multiply ang taas sa taas ( $3 \times 10 = 30$ ) at baba sa baba ( $5 \times 9 = 45$ ). Ang $\frac{30}{45}$ ay pwedeng i-simplify (divide by 15) para maging $\frac{2}{3}$ . Pwede ring mag-cancel method bago mag-multiply.
**Subtract: $5 - 2.25 =$
- A. 3.25
- B. 2.75
- C. 3.75
- D. 2.25
- Answer: B (2.75).
- Solution: Align decimals: $5.00 - 2.25 = 2.75$ .
- Hack: Maglagay ng decimal point at zeros sa whole number ( $5.00$ ) para maitapat sa $2.25$ . Saka mag-subtract.
What is the value of $3^3 + 2^4$ ?
- A. 17
- B. 31
- C. 43
- D. 25
- Answer: C (43).
- Solution: $3 \times 3 \times 3 = 27$ . $2 \times 2 \times 2 \times 2 = 16$ . $27 + 16 = 43$ .
- Hack: I-compute muna ang powers. Ang $3^3$ ay 27. Ang $2^4$ ay 16. I-add ang results: $27 + 16 = 43$ .
**Divide: $\frac{2}{3} \div \frac{4}{6} =$
- A. 1
- B. $\frac{8}{18}$
- C. $\frac{1}{2}$
- D. 2
- Answer: A (1).
- Solution: $\frac{2}{3} \times \frac{6}{4} = \frac{12}{12} = 1$ .
- Hack: Sa division ng fraction, kopyahin ang una ( $rac{2}{3}$ ), palitan ang division ng multiplication, at baliktarin ang pangalawa ( $rac{6}{4}$ ).
If $x + 5 = 12$ , what is $x$ ?
- A. 5
- B. 6
- C. 7
- D. 17
- Answer: C (7).
- Solution: $x = 12 - 5$ . $x = 7$ .
- Hack: Para makuha ang $x$ , ilipat ang $+5$ sa kabila at gawing negative. $12 - 5 = 7$ .
Convert 0.75 to a fraction.
- A. $\frac{3}{5}$
- B. $\frac{3}{4}$
- C. $\frac{2}{3}$
- D. $\frac{7}{5}$
- Answer: B ( $\frac{3}{4}$ ).
- Solution: $0.75 = \frac{75}{100}$ . Simplify by dividing by 25: $\frac{3}{4}$ .
- Hack: Ang $0.75$ ay seventy-five hundredths o $\frac{75}{100}$ . I-divide pareho sa 25 para ma-simplify.
** $100 - (5 \times 5) + 10 =$
- A. 85
- B. 485
- C. 65
- D. 35
- Answer: A (85).
- Solution: $100 - 25 + 10$ . Then $75 + 10 = 85$ .
- Hack: Unahin ang parenthesis ( $5 \times 5 = 25$ ). Tapos left to right sa subtraction at addition: $100 - 25 = 75$ , tapos $75 + 10 = 85$ .
What is $\frac{1}{5}$ of 500?
- A. 50
- B. 100
- C. 20
- D. 250
- Answer: B (100).
- Solution: $500 \div 5 = 100$ .
- Hack: Ang "of" ay multiplication. $\frac{1}{5} \times 500$ ay pareho ng pag-divide ng 500 sa 5.
**Add: $3.5 + 4.2 + 1.1 =$
- A. 8.8
- B. 9.8
- C. 7.8
- D. 8.7
- Answer: A (8.8).
- Solution: $3.5 + 4.2 = 7.7$ . $7.7 + 1.1 = 8.8$ .
- Hack: I-add lang nang diretso. Siguraduhing magkakatapat ang decimal points.
Which is larger: $\frac{1}{3}$ or 0.30?
- A. $\frac{1}{3}$
- B. 0.30
- C. Equal
- D. Cannot be determined
- Answer: A ( $\frac{1}{3}$ ).
- Solution: $\frac{1}{3} = 0.333...$ which is greater than $0.30$ .
- Hack: Ang $\frac{1}{3}$ kung gagawing decimal ay $0.333...$ Mas malaki ito kaysa sa $0.30$ .
**Solve: $8 + 2 \times 4 - 6 \div 2 =$
- A. 13
- B. 17
- C. 14
- D. 11
- Answer: A (13).
- Solution:
  1. Mult/Div: $2 \times 4 = 8$ , $6 \div 2 = 3$ . Equation: $8 + 8 - 3$ .
  2. Add/Sub: $16 - 3 = 13$ .
- Hack: Unahin ang multiplication at division. $2 \times 4$ ay 8. $6 \div 2$ ay 3. Kaya magiging $8 + 8 - 3$ . Sagot ay 13.

Tip: Practice basic multiplication table daily to speed up your computations. (Ugaliing mag-practice ng multiplication table araw-araw para bumilis ang pag-compute.)