Solve 35÷(2×7): Order of Operations with Division and Parentheses

Q: Why do I solve the parentheses first?

The order of operations (PEMDAS) requires you to solve parentheses first! The expression 2×7 in parentheses must be calculated before any division takes place.

Q: How do I know when to write the answer as a mixed number?

When your fraction is improper (numerator larger than denominator), you can convert it to a mixed number. Since $ \frac{5}{2} $ = 2 remainder 1, it becomes $ 2\frac{1}{2} $.

Q: What if I can't see how to factor 35?

Look for common factors! Since 35 = 7×5 and the denominator has 7×2, you can cancel the 7's. This makes division much easier: $ \frac{7×5}{7×2} = \frac{5}{2} $.

Q: Is there another way to write 2½?

Yes! You can write it as the improper fraction $ \frac{5}{2} $ or as the decimal 2.5. All three forms represent the same value.

Division by Products with Fraction Simplification

$35:(2\times7)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve this step by step.

00:09 First, let's write the division as a fraction.

00:13 Now, break down 35 into the factors 7 and 5.

00:23 Next, let's reduce any fractions that we can.

00:31 We'll break down 5 into 4 plus 1.

00:35 Then, split the fraction into two separate fractions for simplicity.

00:41 And that's how we find the solution to this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$35:(2\times7)=$

Step-by-step solution

We write the exercise in fraction form:

$\frac{35}{2\times7}=$

We separate the numerator into a multiplication exercise:

$\frac{7\times5}{2\times7}=$

We simplify the 7 in the numerator and denominator, obtaining:

$\frac{5}{2}=2\frac{1}{2}$

Final Answer

$2\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Always solve parentheses first before dividing
Technique: Factor numerator 35 = 7×5 to simplify with denominator
Check: Verify $2\frac{1}{2} \times 14 = 35$ ✓

Common Mistakes

Avoid these frequent errors

Dividing 35 by 2 and 7 separately
Don't calculate 35÷2÷7 = 2.5 as the answer! This ignores parentheses and gives the wrong result. Always solve parentheses first: 2×7 = 14, then 35÷14 = 2½.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I solve the parentheses first?

The order of operations (PEMDAS) requires you to solve parentheses first! The expression 2×7 in parentheses must be calculated before any division takes place.

How do I know when to write the answer as a mixed number?

When your fraction is improper (numerator larger than denominator), you can convert it to a mixed number. Since $\frac{5}{2}$ = 2 remainder 1, it becomes $2\frac{1}{2}$ .

Can I use a calculator for this problem?

Yes, but be careful with parentheses! Make sure to calculate 2×7 = 14 first, then 35÷14. Many students forget the parentheses and get the wrong answer.

What if I can't see how to factor 35?

Look for common factors! Since 35 = 7×5 and the denominator has 7×2, you can cancel the 7's. This makes division much easier: $\frac{7×5}{7×2} = \frac{5}{2}$ .

Is there another way to write 2½?

Yes! You can write it as the improper fraction $\frac{5}{2}$ or as the decimal 2.5. All three forms represent the same value.

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