Arithmetic — Multiples, Factors, PEMDAS, Fractions & Decimals - Flashcards
This comprehensive flashcard set covers essential arithmetic concepts for UPCAT preparation. Focus on problem-solving techniques and step-by-step solutions for multiples, factors, order of operations (PEMDAS), fractions, and decimals. Each card emphasizes practical application with worked examples to build your mathematical reasoning skills.
Flashcards
Find all factors of 24
Answer
Step 1: Start with 1 and 24 (always factors). Step 2: Check divisibility: 24÷2=12, 24÷3=8, 24÷4=6. Step 3: Stop when factors repeat. Answer: 1, 2, 3, 4, 6, 8, 12, 24
List the first 5 multiples of 8
Answer
Step 1: Multiply 8 by consecutive integers. Step 2: 8×1=8, 8×2=16, 8×3=24, 8×4=32, 8×5=40. Answer: 8, 16, 24, 32, 40
Determine if 117 is prime or composite
Answer
Step 1: Find √117 ≈ 10.8, so check primes up to 10. Step 2: Test divisibility by 2, 3, 5, 7. Step 3: 117÷3 = 39 (no remainder). Step 4: Since 117 is divisible by 3, it's composite. Answer: Composite (117 = 3 × 39)
Find the prime factorization of 60
Answer
Step 1: 60 = 2 × 30. Step 2: 30 = 2 × 15. Step 3: 15 = 3 × 5. Step 4: All factors (2, 2, 3, 5) are prime. Answer: 60 = 2² × 3 × 5
Find LCM of 12 and 18
Answer
Method 1: Prime factorization. 12 = 2² × 3, 18 = 2 × 3². LCM = 2² × 3² = 4 × 9 = 36. Method 2: List multiples. 12: 12, 24, 36... 18: 18, 36... Answer: LCM = 36
Find GCF of 24 and 36
Answer
Method 1: Prime factorization. 24 = 2³ × 3, 36 = 2² × 3². GCF = 2² × 3 = 12. Method 2: List factors. 24: 1,2,3,4,6,8,12,24. 36: 1,2,3,4,6,9,12,18,36. Answer: GCF = 12
Check if 2,346 is divisible by 3
Answer
Step 1: Add digits: 2 + 3 + 4 + 6 = 15. Step 2: Check if sum is divisible by 3: 15 ÷ 3 = 5. Step 3: Since 15 is divisible by 3, the original number is too. Answer: Yes, 2,346 is divisible by 3
Check if 1,248 is divisible by 4
Answer
Step 1: Look at last two digits: 48. Step 2: Check if 48 is divisible by 4: 48 ÷ 4 = 12. Step 3: Since 48 is divisible by 4, the entire number is. Answer: Yes, 1,248 is divisible by 4
Solve: 3 + 4 × 5 - 2
Answer
Step 1: Apply PEMDAS (multiplication before addition/subtraction). Step 2: 4 × 5 = 20. Step 3: 3 + 20 - 2. Step 4: Work left to right: 23 - 2 = 21. Answer: 21
Solve: (8 + 2) × 3² ÷ 5
Answer
Step 1: Parentheses first: (8 + 2) = 10. Step 2: Exponents: 3² = 9. Step 3: Multiplication/Division left to right: 10 × 9 = 90. Step 4: 90 ÷ 5 = 18. Answer: 18
Convert 3/4 to decimal
Answer
Step 1: Divide numerator by denominator. Step 2: 3 ÷ 4 = 0.75. Step 3: Check: 0.75 × 4 = 3 ✓. Answer: 0.75
Add: 2/5 + 1/3
Answer
Step 1: Find LCD of 5 and 3: LCD = 15. Step 2: Convert fractions: 2/5 = 6/15, 1/3 = 5/15. Step 3: Add: 6/15 + 5/15 = 11/15. Answer: 11/15
Multiply: 2/3 × 4/5
Answer
Step 1: Multiply numerators: 2 × 4 = 8. Step 2: Multiply denominators: 3 × 5 = 15. Step 3: Simplify if possible: 8/15 cannot be simplified. Answer: 8/15
Divide: 3/4 ÷ 2/3
Answer
Step 1: Change division to multiplication by reciprocal. Step 2: 3/4 × 3/2. Step 3: Multiply: (3×3)/(4×2) = 9/8. Step 4: Convert to mixed number: 9/8 = 1 1/8. Answer: 9/8 or 1 1/8
Add: 3.25 + 1.7
Answer
Step 1: Align decimal points. Step 2: Add zeros if needed: 3.25 + 1.70. Step 3: Add column by column: 5 + 0 = 5, 2 + 7 = 9, 3 + 1 = 4. Answer: 4.95
Multiply: 2.5 × 0.4
Answer
Step 1: Ignore decimals temporarily: 25 × 4 = 100. Step 2: Count total decimal places: 1 + 1 = 2. Step 3: Place decimal point: 1.00. Answer: 1.0 or 1
Convert 0.625 to fraction
Answer
Step 1: Write as fraction: 625/1000. Step 2: Find GCF of 625 and 1000: GCF = 125. Step 3: Divide both by GCF: 625÷125 = 5, 1000÷125 = 8. Answer: 5/8
When do you use prime factorization to find LCM?
Answer
Use when: 1) Numbers are large (harder to list multiples), 2) Finding LCM of 3+ numbers, 3) Need to show work systematically. Method: Factor each number, then take highest power of each prime. Example: LCM(12,18) = 2²×3² = 36
What's the difference between factors and multiples of 6?
Answer
Factors divide INTO 6: 1, 2, 3, 6 (finite list, ≤ 6). Multiples are 6 times other numbers: 6, 12, 18, 24... (infinite list, ≥ 6). Memory tip: Factors are Few and small, Multiples are Many and large.
Why does the divisibility rule for 9 work?
Answer
Because 10 ≡ 1 (mod 9), 100 ≡ 1 (mod 9), etc. So any number abc = 100a + 10b + c ≡ a + b + c (mod 9). If digit sum is divisible by 9, so is the original number. Example: 729 → 7+2+9=18 → 1+8=9, divisible by 9.
Diagrams
Arithmetic Concepts Overview
Mind map showing the relationship between all arithmetic concepts covered in this chapter, helping students see how different topics connect.
Problem-Solving Decision Tree
Decision tree flowchart that helps students determine which method to use for different types of arithmetic problems, promoting systematic problem-solving.
PEMDAS Step-by-Step Process
Step-by-step flowchart for applying the order of operations (PEMDAS), ensuring students follow the correct sequence when solving complex expressions.