Simplify This Algebraic Expression: (78 - (39 - 47) - (95 + 3:3/5))?

Q: Why do I solve parentheses first even if subtraction comes before them?

Parentheses always come first in PEMDAS! Even though subtraction appears earlier in the expression, you must complete all operations inside parentheses before doing anything else.

Q: How do I divide by a fraction like 3/5?

To divide by a fraction, multiply by its reciprocal! So $ 3 \div \frac{3}{5} $ becomes $ 3 \times \frac{5}{3} = 5 $. Flip the fraction and multiply!

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

The colon (:) means division, just like ÷. So $ 3:\frac{3}{5} $ is the same as $ 3 \div \frac{3}{5} $. Both symbols mean 'divide'!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Negative times positive is always negative

00:09 Negative times negative is always positive

00:16 Negative times positive is always negative

00:24 Division is also multiplication by the reciprocal

00:35 Let's reduce what we can

00:40 Use the distribution law and split 78 into 70 plus 8

00:44 Use the distribution law and split 39 into 30 and 9

00:48 Use the distribution law and split 47 into 40 plus 7

00:53 Use the distribution law and split 95 into 90 and 5

01:08 Use the substitution law and arrange the exercise to make it easier to solve

01:12 Collect the tens

01:16 Collect the ones

01:31 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

$78-(39-47)-(95+3:\frac{3}{5})=\text{?}$

2

Step-by-step solution

To solve the problem $78-(39-47)-(95+3:\frac{3}{5})$ , follow these steps:

Step 1: First, evaluate the expression within the first parentheses: $39-47 = -8$ . Thus, the expression becomes $78 - (-8) - (95 + 3:\frac{3}{5})$ .
Step 2: Simplifying $78 - (-8)$ gives $78 + 8 = 86$ . The expression is now $86 - (95 + 3:\frac{3}{5})$ .
Step 3: Calculate the division within the second parentheses $3:\frac{3}{5}$ by multiplying 3 by the reciprocal of $\frac{3}{5}$ , resulting in $3 \times \frac{5}{3} = 5$ . Thus, $95 + 5 = 100$ .
Step 4: Substitute back into the problem, yielding $86 - 100$ , which equals $-14$ .

Thus, the solution to the problem is $-14$ .

3

Final Answer

$-14$

Key Points to Remember

Essential concepts to master this topic

Rule: Follow PEMDAS—parentheses first, then division and subtraction left to right
Technique: Convert division by fractions: $3 \div \frac{3}{5} = 3 \times \frac{5}{3} = 5$
Check: Work backwards: -14 + 100 = 86, then 86 - 8 = 78 ✓

Common Mistakes

Avoid these frequent errors

Computing operations left to right without following order of operations
Don't work left to right like 78 - 39 + 47 - 95 - 5 = wrong answer! This ignores parentheses and gives -14 instead of the correct answer. Always solve parentheses completely first, then work left to right for same-level operations.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why do I solve parentheses first even if subtraction comes before them?

+

Parentheses always come first in PEMDAS! Even though subtraction appears earlier in the expression, you must complete all operations inside parentheses before doing anything else.

How do I divide by a fraction like 3/5?

+

To divide by a fraction, multiply by its reciprocal! So $3 \div \frac{3}{5}$ becomes $3 \times \frac{5}{3} = 5$ . Flip the fraction and multiply!

What does the colon (:) symbol mean in math?

+

The colon (:) means division, just like ÷. So $3:\frac{3}{5}$ is the same as $3 \div \frac{3}{5}$ . Both symbols mean 'divide'!

Why does 78 - (-8) become 78 + 8?

+

When you subtract a negative number, it becomes addition! Think of it as 'take away a debt' which actually gives you more. So minus negative equals plus.

How can I check if my final answer of -14 is correct?

+

Work backwards! Start with -14, add 100 to get 86, then subtract 8 to get 78. If you get the original number 78, your answer is right!

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Simplify This Algebraic Expression: (78 - (39 - 47) - (95 + 3:3/5))?

Order of Operations with Division by Fractions

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