Solve and Simplify the Equation: 35 ÷ (7×5) - (2 + 9 ÷ 3/2)

Q: Why do I multiply by the reciprocal when dividing by a fraction?

Dividing by a fraction is the same as multiplying by its reciprocal. Think of it this way: $ 9 \div \frac{3}{2} $ means 'how many 3/2's fit into 9?' Since 2/3 is the reciprocal of 3/2, we get $ 9 \times \frac{2}{3} = 6 $.

Q: Should I solve what's in parentheses first or do multiplication first?

Always do parentheses first! In $ (2 + 9 \div \frac{3}{2}) $, you must solve everything inside the parentheses before using that result in the subtraction.

Q: What does the colon symbol (:) mean in this problem?

The colon (:) symbol means division, just like ÷. So $ 35:35 $ is the same as $ 35 \div 35 = 1 $.

Q: How do I know which operations to do first?

Follow PEMDAS order:Parentheses firstExponents (none in this problem)Multiplication and Division from left to rightAddition and Subtraction from left to right

Q: Why is my answer negative?

A negative answer is correct here! We get $ 1 - 8 = -7 $ because we're subtracting a larger number (8) from a smaller number (1). Always check your arithmetic - negative results are often correct in these problems.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 Let's solve this problem together.

00:15 First, always solve what's inside the parentheses.

00:22 Remember, a negative times a positive number is always negative.

00:35 Dividing a number by itself? That's always one.

00:43 Think of division as multiplying by the reciprocal.

00:51 Now, move the multiplication up to the top.

00:59 Convert the fraction into a whole number.

01:04 And there you have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$35:(7\cdot5)-(2+9:\frac{3}{2})=\text{?}$

2

Step-by-step solution

To solve this problem, we'll follow these steps according to the order of operations:

Step 1: Simplify the expression $35:(7 \cdot 5)-(2+9:\frac{3}{2})$ .
Step 2: Calculate $7 \cdot 5$ and $9:\frac{3}{2}$ .
Step 3: Simplify the division $35:35$ as well as $9:\frac{3}{2}$ .
Step 4: Evaluate the expression step-by-step.

Now, let's solve the expression:

Step 1: Calculate the multiplication: $7 \cdot 5 = 35$ .

Step 2: Calculate the division: $9:\frac{3}{2} = 9 \times \frac{2}{3} = 6$ . We use the reciprocal of $\frac{3}{2}$ .

Step 3: Substitute back into the original expression: $35:35 - (2 + 6) = 35:35 - 8$ .

Step 4: Simplify the division: $35:35 = 1$ .

Step 5: Calculate the subtraction: $1 - 8 = -7$ .

Therefore, the solution to the problem is $-7$ .

3

Final Answer

7-

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses first, then multiplication and division left to right
Division by Fractions: $9 \div \frac{3}{2} = 9 \times \frac{2}{3} = 6$
Check Work: Verify each step: 35÷35=1, 2+6=8, 1-8=-7 ✓

Common Mistakes

Avoid these frequent errors

Calculating division by fraction incorrectly
Don't divide 9÷3/2 as (9÷3)÷2 = 1.5! This ignores the fraction structure and gives 1.5 instead of 6. Always multiply by the reciprocal: 9×(2/3) when dividing by a fraction.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(5+55)= $$

FAQ

Everything you need to know about this question

Why do I multiply by the reciprocal when dividing by a fraction?

+

Dividing by a fraction is the same as multiplying by its reciprocal. Think of it this way: $9 \div \frac{3}{2}$ means 'how many 3/2's fit into 9?' Since 2/3 is the reciprocal of 3/2, we get $9 \times \frac{2}{3} = 6$ .

Should I solve what's in parentheses first or do multiplication first?

+

Always do parentheses first! In $(2 + 9 \div \frac{3}{2})$ , you must solve everything inside the parentheses before using that result in the subtraction.

What does the colon symbol (:) mean in this problem?

+

The colon (:) symbol means division, just like ÷. So $35:35$ is the same as $35 \div 35 = 1$ .

How do I know which operations to do first?

+

Follow PEMDAS order:

Parentheses first
Exponents (none in this problem)
Multiplication and Division from left to right
Addition and Subtraction from left to right

Why is my answer negative?

+

A negative answer is correct here! We get $1 - 8 = -7$ because we're subtracting a larger number (8) from a smaller number (1). Always check your arithmetic - negative results are often correct in these problems.

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Solve and Simplify the Equation: 35 ÷ (7×5) - (2 + 9 ÷ 3/2)

Order of Operations with Division by Fractions

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