Basic Operations Reviewer (Professional)

Reviewer's Note: Speed and accuracy are your best friends. Since calculators are prohibited, practice mental math and the long-hand division of decimals daily.

Numerical Ability tests your basic mathematical skills. The foundation of this section is mastering basic operations: Addition, Subtraction, Multiplication, and Division, especially when applied to fractions, decimals, and percentages.

Sa madaling salita: Mahalaga ang bilis at kawastuhan. Dahil bawal ang calculator, sanayin ang sarili sa mental math at manu-manong pag-compute.

1. Order of Operations (PEMDAS)

When solving mathematical expressions with multiple operations, always follow the PEMDAS rule:

1. Parentheses: Solve everything inside brackets or parentheses first. (Unahin ang nasa loob.)
2. Exponents: Solve powers and roots.
3. Multiplication and Division: Solve from left to right. (Kung ano ang mauna sa kaliwa.)
4. Addition and Subtraction: Solve from left to right. (Kung ano ang mauna sa kaliwa.)

Example: $10 + 5 \times 2 - (4 + 2)$

1. Parentheses: $10 + 5 \times 2 - 6$
2. Multiplication: $10 + 10 - 6$
3. Addition/Subtraction (Left to Right): $20 - 6 = 14$

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2. Fractions

Fractions represent a part of a whole. Mastering how to add, subtract, multiply, and divide them is essential for the exam.

Addition and Subtraction

• Same Denominator: Add/Subtract numerators, keep the denominator.
• Different Denominators: Find the Least Common Denominator (LCD). (Hanapin ang LCD kapag magkaiba ang ilalim.)

Multiplication

• Multiply numerators together and denominators together. (Taas sa taas, baba sa baba.)
  • $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$

Division

• Invert the second fraction (find its reciprocal) and then multiply. (Baliktarin ang pangalawa at i-multiply.)
  • $\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$

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3. Decimals

Decimals are another way of expressing fractions. Always ensure your decimal points are aligned during addition and subtraction.

• Addition/Subtraction: Align the decimal points vertically. (Pag-tapatin ang mga tuldok.)
• Multiplication: Multiply as whole numbers, then count total decimal places in the factors and place the point in the product.
• Division: Move the decimal point in the divisor to make it a whole number, and move the point in the dividend the same number of places.

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4. Percentages

Percentages are ubiquitous in word problems. The basic formula for percentages is: Part = Rate \times Whole

• To convert decimal to percent: Move decimal point two places to the right and add "%". (Ex: $0.75 \to 75\%$)

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Practice Questions

1. **$25 + 5 \times (10 - 2) =$

   • A. 240
   • B. 65
   • C. 40
   • D. 33
   • Answer: B (65).
   • Hack (Ibig sabihin): Unahin ang parenthesis $(10-2=8)$. Sunod ang multiplication $5 \times 8 = 40$. Huli ang addition $25 + 40 = 65$.

2. **$\frac{1}{2} + \frac{1}{4} =$

   • A. $\frac{2}{6}$
   • B. $\frac{3}{4}$
   • C. $\frac{1}{2}$
   • D. $\frac{2}{4}$
   • Answer: B ($\frac{3}{4}$).
   • Hack (Ibig sabihin): Ang LCD ng 2 at 4 ay 4. Ang $\frac{1}{2}$ ay nagiging $\frac{2}{4}$. Kaya $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.

3. **What is 15% of 200?

   • A. 15
   • B. 20
   • C. 30
   • D. 45
   • Answer: C (30).
   • Hack (Ibig sabihin): $0.15 \times 200 = 30$.

4. **Simplify: $12 \div 3 \times 2 =$

   • A. 2
   • B. 8
   • C. 6
   • D. 18
   • Answer: B (8).
   • Hack (Ibig sabihin): Left to Right rule. $12 \div 3 = 4$. Tapos $4 \times 2 = 8$.

5. **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 ($\frac{2}{3}$).
   • Hack (Ibig sabihin): $3 \times 10 = 30$, $5 \times 9 = 45$. Ang $\frac{30}{45}$ ay simplify sa $\frac{2}{3}$ (divide by 15).

6. **Subtract: $5 - 2.25 =$

   • A. 3.25
   • B. 2.75
   • C. 3.75
   • D. 2.25
   • Answer: B (2.75).
   • Hack (Ibig sabihin): Gawing $5.00$ para maitapat sa $2.25$. Resulta ay 2.75.

7. **What is the value of $3^3 + 2^4$?

   • A. 17
   • B. 31
   • C. 43
   • D. 25
   • Answer: C (43).
   • Hack (Ibig sabihin): $3 \times 3 \times 3 = 27$. $2 \times 2 \times 2 \times 2 = 16$. Total: 43.

8. **Divide: $\frac{2}{3} \div \frac{4}{6} =$

   • A. 1
   • B. $\frac{8}{18}$
   • C. $\frac{1}{2}$
   • D. 2
   • Answer: A (1).
   • Hack (Ibig sabihin): Reciprocal ng $\frac{4}{6}$ ay $\frac{6}{4}$. Multiply: $\frac{2}{3} \times \frac{6}{4} = \frac{12}{12} = 1$.

9. **If $x + 5 = 12$, what is $x$?

   • A. 5
   • B. 6
   • C. 7
   • D. 17
   • Answer: C (7).
   • Hack (Ibig sabihin): $12 - 5 = 7$.

10. **Convert 0.75 to a fraction.

    • A. $\frac{3}{5}$
    • B. $\frac{3}{4}$
    • C. $\frac{2}{3}$
    • D. $\frac{7}{5}$
    • Answer: B ($\frac{3}{4}$).
    • Hack (Ibig sabihin): $0.75 = \frac{75}{100}$. Simplify (divide by 25) = $\frac{3}{4}$.

11. **$100 - (5 \times 5) + 10 =$

    • A. 85
    • B. 485
    • C. 65
    • D. 35
    • Answer: A (85).
    • Hack (Ibig sabihin): $100 - 25 = 75$. $75 + 10 = 85$.

12. **What is $\frac{1}{5}$ of 500?

    • A. 50
    • B. 100
    • C. 20
    • D. 250
    • Answer: B (100).
    • Hack (Ibig sabihin): $500 \div 5 = 100$.

13. **Add: $3.5 + 4.2 + 1.1 =$

    • A. 8.8
    • B. 9.8
    • C. 7.8
    • D. 8.7
    • Answer: A (8.8).

14. **Which is larger: $\frac{1}{3}$ or 0.30?

    • A. $\frac{1}{3}$
    • B. 0.30
    • C. Equal
    • D. Cannot be determined
    • Answer: A ($\frac{1}{3}$).
    • Hack (Ibig sabihin): $\frac{1}{3} = 0.333...$ mas malaki sa 0.30.

15. **Solve: $8 + 2 \times 4 - 6 \div 2 =$

    • A. 13
    • B. 17
    • C. 14
    • D. 11
    • Answer: A (13).
    • Hack (Ibig sabihin): $8 + (2 \times 4) - (6 \div 2) = 8 + 8 - 3 = 13.