Solve 220÷(15×8): Order of Operations Division Problem

Q: Why do I need to do the multiplication first?

The parentheses tell you to calculate $ 15 \times 8 $ first! Without parentheses, you'd go left to right, but parentheses override normal order and must be calculated first.

Q: How do I convert the improper fraction to a mixed number?

Divide the numerator by the denominator: $ 11 ÷ 6 = 1 $ remainder $ 5 $. So $ \frac{11}{6} = 1\frac{5}{6} $.

Q: What's the easiest way to find the GCD of 220 and 120?

List factors or use division: 220 = 120 × 1 + 100, then 120 = 100 × 1 + 20, then 100 = 20 × 5 + 0. The GCD is 20!

Q: Can I leave my answer as an improper fraction?

Yes! $ \frac{11}{6} $ is mathematically correct. However, mixed numbers like $ 1\frac{5}{6} $ are often easier to understand and preferred in many contexts.

Q: How can I check if my fraction is fully simplified?

Make sure the numerator and denominator have no common factors other than 1. Since 11 is prime and doesn't divide 6, $ \frac{11}{6} $ is fully simplified!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Division is also multiplication by the reciprocal

00:07 Therefore when opening the parentheses, it will end up as divided by C

00:11 We will use this formula in our exercise

00:16 We will solve according to the order of operations from left to right

00:19 We will write division as a fraction

00:27 Division is also multiplication by the reciprocal

00:33 We will divide 8 and 220 by 4

00:41 Make sure to multiply numerator by numerator and denominator by denominator

00:45 We will divide 55 and 15 by 3

00:54 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$220:(15\times8)=$

2

Step-by-step solution

To solve the given expression $220 : (15 \times 8)$ , follow these steps:

Step 1: Calculate the multiplication inside the parentheses: $15 \times 8$ .
Step 2: Divide 220 by the result obtained from Step 1.

Let us perform the calculations:

Step 1: Calculate the multiplication.
$15 \times 8 = 120$ .

Step 2: Divide 220 by 120.
So, $220 \div 120 = \frac{220}{120}$ .

To simplify $\frac{220}{120}$ :

Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 20.

The division yields:
$\frac{220}{120} = \frac{11 \times 20}{6 \times 20} = \frac{11}{6}$ .

This fraction $\frac{11}{6}$ can be expressed as a mixed number by dividing 11 by 6:

- 11 divided by 6 equals 1 with a remainder of 5, so:

$1\frac{5}{6}$ .

Thus, the solution to the problem is $1 \frac{5}{6}$ .

3

Final Answer

$1\frac{5}{6}$

Key Points to Remember

Essential concepts to master this topic

Parentheses First: Always calculate expressions inside parentheses before division
Simplification: Reduce $\frac{220}{120}$ by dividing both by GCD 20
Check: Convert back: $1\frac{5}{6} = \frac{11}{6} \times 120 = 220$ ✓

Common Mistakes

Avoid these frequent errors

Calculating left to right without following order of operations
Don't solve 220÷15×8 = 14.67×8 = 117.33! This ignores parentheses and gives a completely wrong answer. Always calculate what's inside parentheses first, then perform the division.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why do I need to do the multiplication first?

+

The parentheses tell you to calculate $15 \times 8$ first! Without parentheses, you'd go left to right, but parentheses override normal order and must be calculated first.

How do I convert the improper fraction to a mixed number?

+

Divide the numerator by the denominator: $11 ÷ 6 = 1$ remainder $5$ . So $\frac{11}{6} = 1\frac{5}{6}$ .

What's the easiest way to find the GCD of 220 and 120?

+

List factors or use division: 220 = 120 × 1 + 100, then 120 = 100 × 1 + 20, then 100 = 20 × 5 + 0. The GCD is 20!

Can I leave my answer as an improper fraction?

+

Yes! $\frac{11}{6}$ is mathematically correct. However, mixed numbers like $1\frac{5}{6}$ are often easier to understand and preferred in many contexts.

How can I check if my fraction is fully simplified?

+

Make sure the numerator and denominator have no common factors other than 1. Since 11 is prime and doesn't divide 6, $\frac{11}{6}$ is fully simplified!

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Solve 220÷(15×8): Order of Operations Division Problem

Order of Operations with Mixed Number Results

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