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Chapter 2: Problem 101

Simplify the given expression. \(\frac{4 \cdot 5-(-19)}{3}\)

Short Answer

Expert verified
The simplified expression is 13.

Step by step solution

01

Solve the Multiplication in the Numerator

The expression given is \( \frac{4 \cdot 5 - (-19)}{3} \). First, we solve the multiplication in the numerator: \(4 \cdot 5 = 20\).
02

Simplify the Expression in the Numerator

Next, take the result from Step 1 and incorporate it back into the numerator, which becomes \(20 - (-19)\). Subtracting a negative is equivalent to adding the positive: \(20 + 19\).
03

Add Values in the Numerator

Now add \(20 + 19 = 39\). The expression is now \(\frac{39}{3}\).
04

Divide the Numerator by the Denominator

Finally, divide \(39\) by \(3\). \(39 \div 3 = 13\). Thus, the simplified expression is \(13\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Multiplication
Let's start with the basics of multiplication. Multiplication is repeated addition. For instance, if you have 4 groups of 5, it means you add 5 to itself 4 times: 5 + 5 + 5 + 5. When simplifying expressions, multiplication often comes first according to the order of operations (PEMDAS/BODMAS). In the exercise given, you multiply 4 and 5, resulting in 20. One way to check your work is using multiplication facts or times tables. The times tables for 4 and 5 can help you quickly find the result without iterating through addition multiple times.
Negative Numbers
Understanding negative numbers can be tricky, but it's essential for simplifying expressions. Negative numbers are values less than zero, symbolized by a minus sign (-). When you perform math operations involving negative numbers, remember:
  • Subtracting a negative is the same as adding its positive. For example, in the expression \( -(-19) \), you can simply convert it to \(+19\).
  • Multiplying two negative numbers results in a positive number.
  • Multiplying a negative and a positive number gives a negative result.
In the original exercise, you deal with subtraction of a negative, which turns into addition because \( 20 - (-19) \) is the same as \( 20 + 19 \).
Division
Division is essentially the opposite of multiplication. It involves splitting a number into equal parts. In this exercise, once you have simplified your numerator to the sum of 20 and 19 (which gives 39), your next step is to divide 39 by 3. When dividing, ensure you understand the key terms:
  • The number being divided is the **dividend** (39 in our example).
  • The number you divide by is the **divisor** (3 here).
  • The result of a division is called the **quotient** (13 here).
Using division facts or division tables can simplify this process significantly. Knowing that 39 divided by 3 equals 13 helps confirm your work effectively.

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