PODMAS

 If you’re having trouble remembering PODMAS (also called BODMAS in some regions), here’s a simple breakdown and some tips to make it easier to apply and remember.

What is PODMAS?

PODMAS stands for:

• P: Parentheses (brackets)
• O: Orders (exponents, powers)
• D: Division
• M: Multiplication
• A: Addition
• S: Subtraction

This rule tells you the order in which to perform operations when solving mathematical expressions.

How to Apply PODMAS:

When faced with a complex mathematical expression, follow these steps in order:

1. Parentheses (P): Solve anything inside brackets first.

   • Example: $(3+2)\times 4$ → Solve $3+2=5$, so it becomes $5\times 4=20$.

2. Orders (O): Solve any exponents or powers next.

   • Example: $2^3=8$

3. Division and Multiplication (DM): Perform division and multiplication from left to right.

   • Example: $10÷2\times 3$ → First divide $10÷2=5$, then multiply $5\times 3=15$.

4. Addition and Subtraction (AS): Finally, do any addition or subtraction from left to right.

   • Example: $7+2-5$ → First add $7+2=9$, then subtract $9-5=4$.

Example Problem:

Solve $3+6\times (5+4)÷3^2$:

1. Parentheses: Solve $(5+4)=9$, so the expression becomes $3+6\times 9÷3^2$.
2. Orders: Solve $3^2=9$, so the expression becomes $3+6\times 9÷9$.
3. Multiplication and Division:
   • First, divide: $9÷9=1$, so the expression becomes $3+6\times 1$.
   • Then, multiply: $6\times 1=6$, so the expression becomes $3+6$.
4. Addition: Add $3+6=9$.

Final Answer: 9.

Tips to Help You Remember PODMAS:

1. Use Mnemonics: Try remembering the order using a phrase like:

   • "Please Order Delicious Meals After School" (PODMAS)
   • "Big Elephants Destroy Mice And Snakes" (BODMAS)

2. Visual Aids: Write down the rule and post it where you study or work on math problems. The more you see it, the easier it will be to recall.

3. Practice Daily: Solve small equations regularly using PODMAS. Repetition will help solidify the rule in your mind.

4. Chunk Learning: Break down problems into smaller steps. Don’t try to remember all the rules at once—tackle one operation at a time.

5. Digital Tools: Use online calculators or apps that show you step-by-step solutions using PODMAS. This will help reinforce the steps.

Why You Forget Easily (and How to Improve Memory):

• Active Recall: Instead of just reading about PODMAS, actively practice solving problems without looking at examples.
• Spaced Repetition: Practice equations over time (e.g., practice a few daily rather than cramming in one session).
• Use Examples in Real Life: Relate math problems to things you encounter in daily life, like splitting bills, measurements, etc., to make the process more practical and memorable.

By following these steps, applying the PODMAS rule will become second nature over time, and memory retention should improve with practice.

Great! We’ll start with the basic level to build a strong foundation. I’ll provide detailed explanations for each question, helping you to understand the steps and apply the PODMAS rule (or similar methods) as needed.

Basic Level Training:

Question 1:

Simplify:
$5+3\times 2$

Solution:

1. Follow PODMAS: Multiplication comes before addition.
2. Step 1: Perform the multiplication first:
   $3\times 2=6$
3. Step 2: Now, add $5+6$:
   $5+6=11$

Answer: $11$

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Question 2:

Simplify:
$8-2+4$

Solution:

1. Follow PODMAS: Since there are only addition and subtraction, proceed left to right.
2. Step 1: Perform the subtraction:
   $8-2=6$
3. Step 2: Now, add $6+4$:
   $6+4=10$

Answer: $10$

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Question 3:

Simplify:
$(7+3)\times 2$

Solution:

1. Follow PODMAS: Solve the parentheses first, then multiplication.
2. Step 1: Solve inside the parentheses:
   $7+3=10$
3. Step 2: Now, multiply:
   $10\times 2=20$

Answer: $20$

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Question 4:

Simplify:
$4+6÷2$

Solution:

1. Follow PODMAS: Division comes before addition.
2. Step 1: Perform the division first:
   $6÷2=3$
3. Step 2: Now, add:
   $4+3=7$

Answer: $7$

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Question 5:

Simplify:
$(5\times 3)-(8-2)$

Solution:

1. Follow PODMAS: Solve parentheses first, then do multiplication and subtraction.
2. Step 1: Solve each parentheses:
   • $5\times 3=15$
   • $8-2=6$
3. Step 2: Now, subtract:
   $15-6=9$

Answer: $9$

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Question 6:

Simplify:
$12÷3+4\times 2$

Solution:

1. Follow PODMAS: Do division and multiplication before addition.
2. Step 1: Perform the division:
   $12÷3=4$
3. Step 2: Perform the multiplication:
   $4\times 2=8$
4. Step 3: Now, add:
   $4+8=12$

Answer: $12$

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Question 7:

Simplify:
$(9-3)\times 2+5$

Solution:

1. Follow PODMAS: Parentheses first, then multiplication, then addition.
2. Step 1: Solve inside the parentheses:
   $9-3=6$
3. Step 2: Now, multiply:
   $6\times 2=12$
4. Step 3: Add:
   $12+5=17$

Answer: $17$

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Question 8:

Simplify:
$6+2^3$

Solution:

1. Follow PODMAS: Handle the exponent (orders) before addition.
2. Step 1: Solve the exponent:
   $2^3=8$
3. Step 2: Now, add:
   $6+8=14$

Answer: $14$

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Question 9:

Simplify:
$15÷(5+10)$

Solution:

1. Follow PODMAS: Solve the parentheses first.
2. Step 1: Solve inside the parentheses:
   $5+10=15$
3. Step 2: Now, divide:
   $15÷15=1$

Answer: $1$

---

Question 10:

Simplify:
$3+4\times (7-2)$

Solution:

1. Follow PODMAS: Parentheses first, then multiplication, then addition.
2. Step 1: Solve inside the parentheses:
   $7-2=5$
3. Step 2: Now, multiply:
   $4\times 5=20$
4. Step 3: Add:
   $3+20=23$

Answer: $23$

Let’s continue with the next 10 basic-level questions, with detailed explanations for each.

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Question 11:

Simplify:
$9\times 3+5$

Solution:

1. Follow PODMAS: Do multiplication first, then addition.
2. Step 1: Multiply:
   $9\times 3=27$
3. Step 2: Add:
   $27+5=32$

Answer: $32$

---

Question 12:

Simplify:
$(4+2)\times (7-3)$

Solution:

1. Follow PODMAS: Solve both parentheses first, then multiply.
2. Step 1: Solve inside the parentheses:
   • $4+2=6$
   • $7-3=4$
3. Step 2: Now, multiply:
   $6\times 4=24$

Answer: $24$

---

Question 13:

Simplify:
$10-2^2+4$

Solution:

1. Follow PODMAS: Handle the exponent (orders) first, then subtraction and addition from left to right.
2. Step 1: Solve the exponent:
   $2^2=4$
3. Step 2: Subtract:
   $10-4=6$
4. Step 3: Add:
   $6+4=10$

Answer: $10$

---

Question 14:

Simplify:
$(5\times 2)+(6÷3)$

Solution:

1. Follow PODMAS: Solve both the multiplication and division inside the parentheses first, then add.
2. Step 1: Perform the multiplication and division:
   • $5\times 2=10$
   • $6÷3=2$
3. Step 2: Now, add:
   $10+2=12$

Answer: $12$

---

Question 15:

Simplify:
$8÷4+7$

Solution:

1. Follow PODMAS: Division comes before addition.
2. Step 1: Divide:
   $8÷4=2$
3. Step 2: Add:
   $2+7=9$

Answer: $9$

---

Question 16:

Simplify:
$10+(3\times 4)÷6$

Solution:

1. Follow PODMAS: Solve the multiplication first, then division, and finally the addition.
2. Step 1: Perform the multiplication:
   $3\times 4=12$
3. Step 2: Divide:
   $12÷6=2$
4. Step 3: Now, add:
   $10+2=12$

Answer: $12$

---

Question 17:

Simplify:
$14÷(7+7)$

Solution:

1. Follow PODMAS: Solve inside the parentheses first.
2. Step 1: Add inside the parentheses:
   $7+7=14$
3. Step 2: Now, divide:
   $14÷14=1$

Answer: $1$

---

Question 18:

Simplify:
$18-2\times 5$

Solution:

1. Follow PODMAS: Multiplication comes before subtraction.
2. Step 1: Multiply:
   $2\times 5=10$
3. Step 2: Now, subtract:
   $18-10=8$

Answer: $8$

---

Question 19:

Simplify:
$6\times (4+3)$

Solution:

1. Follow PODMAS: Solve inside the parentheses first, then multiply.
2. Step 1: Add inside the parentheses:
   $4+3=7$
3. Step 2: Now, multiply:
   $6\times 7=42$

Answer: $42$

---

Question 20:

Simplify:
$5\times 2+3÷3$

Solution:

1. Follow PODMAS: Do multiplication and division first, then addition.
2. Step 1: Perform the multiplication:
   $5\times 2=10$
3. Step 2: Perform the division:
   $3÷3=1$
4. Step 3: Now, add:
   $10+1=11$

Answer: 11

Let's move on to the intermediate level. Here, the problems will be slightly more complex, combining multiple operations, parentheses, and exponents. I will provide step-by-step explanations for each question to help you understand how to approach these problems.

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Intermediate Level Training:

Question 1:

Simplify:
$3\times (4+5)-2^3$

Solution:

1. Follow PODMAS: Parentheses first, then exponent, multiplication, and subtraction.
2. Step 1: Solve inside the parentheses:
   $4+5=9$
3. Step 2: Solve the exponent:
   $2^3=8$
4. Step 3: Multiply:
   $3\times 9=27$
5. Step 4: Subtract:
   $27-8=19$

Answer: $19$

---

Question 2:

Simplify:
$12+18÷3\times 2^2-7$

Solution:

1. Follow PODMAS: Start with exponent, then division, multiplication, and finally addition/subtraction.
2. Step 1: Solve the exponent:
   $2^2=4$
3. Step 2: Perform the division:
   $18÷3=6$
4. Step 3: Perform the multiplication:
   $6\times 4=24$
5. Step 4: Add and subtract from left to right:
   $12+24=36$, then $36-7=29$

Answer: $29$

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Question 3:

Simplify:
$(8÷2)+3^2\times (4-1)$

Solution:

1. Follow PODMAS: Parentheses first, exponent, division, multiplication, and addition.
2. Step 1: Solve inside the parentheses:
   $4-1=3$
3. Step 2: Solve the exponent:
   $3^2=9$
4. Step 3: Perform the division:
   $8÷2=4$
5. Step 4: Perform the multiplication:
   $9\times 3=27$
6. Step 5: Add:
   $4+27=31$

Answer: $31$

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Question 4:

Simplify:
$20÷(5\times 2)+6\times 3$

Solution:

1. Follow PODMAS: Parentheses first, then division and multiplication, finally addition.
2. Step 1: Solve inside the parentheses:
   $5\times 2=10$
3. Step 2: Perform the division:
   $20÷10=2$
4. Step 3: Perform the multiplication:
   $6\times 3=18$
5. Step 4: Add:
   $2+18=20$

Answer: $20$

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Question 5:

Simplify:
$(2^3\times 5)+(18÷3)-7$

Solution:

1. Follow PODMAS: Handle the exponents first, then multiplication, division, addition, and subtraction.
2. Step 1: Solve the exponent:
   $2^3=8$
3. Step 2: Perform the multiplication:
   $8\times 5=40$
4. Step 3: Perform the division:
   $18÷3=6$
5. Step 4: Add:
   $40+6=46$
6. Step 5: Subtract:
   $46-7=39$

Answer: $39$

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Question 6:

Simplify:
$9\times (3^2-4)+12÷3$

Solution:

1. Follow PODMAS: Solve the exponent first, then parentheses, multiplication, division, and addition.
2. Step 1: Solve the exponent:
   $3^2=9$
3. Step 2: Solve inside the parentheses:
   $9-4=5$
4. Step 3: Perform the multiplication:
   $9\times 5=45$
5. Step 4: Perform the division:
   $12÷3=4$
6. Step 5: Add:
   $45+4=49$

Answer: $49$

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Question 7:

Simplify:
$15÷3+(4\times 2^2)-5$

Solution:

1. Follow PODMAS: Start with the exponent, then parentheses, division, multiplication, and finally addition/subtraction.
2. Step 1: Solve the exponent:
   $2^2=4$
3. Step 2: Solve inside the parentheses:
   $4\times 4=16$
4. Step 3: Perform the division:
   $15÷3=5$
5. Step 4: Add and subtract from left to right:
   $5+16=21$, then $21-5=16$

Answer: $16$

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Question 8:

Simplify:
$(6+8÷2^2)\times 3$

Solution:

1. Follow PODMAS: Handle exponent first, then division, addition, and multiplication.
2. Step 1: Solve the exponent:
   $2^2=4$
3. Step 2: Perform the division:
   $8÷4=2$
4. Step 3: Solve inside the parentheses:
   $6+2=8$
5. Step 4: Now, multiply:
   $8\times 3=24$

Answer: $24$

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Question 9:

Simplify:
$18÷(2+4)+5^2$

Solution:

1. Follow PODMAS: Solve parentheses first, then division and exponent, then addition.
2. Step 1: Solve inside the parentheses:
   $2+4=6$
3. Step 2: Perform the division:
   $18÷6=3$
4. Step 3: Solve the exponent:
   $5^2=25$
5. Step 4: Add:
   $3+25=28$

Answer: $28$

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Question 10:

Simplify:
$(4^2+6)÷(8-4)$

Solution:

1. Follow PODMAS: Solve the exponent and parentheses first, then perform division.
2. Step 1: Solve the exponent:
   $4^2=16$
3. Step 2: Solve inside the parentheses:
   $16+6=22$, and $8-4=4$
4. Step 3: Now, divide:
   $22÷4=5.5$

Answer: $5.5$

$11$