This **question aims** to interpret the equation as having **two** operations:** product and sum.**

- What do we do first when we have a
**math problem**involving**more than one operation**—such as**addition**and**subtraction**or**subtraction**and**multiplication**? What do we do for the expression**10 – 5 X 2 = ?** - Do we
**subtract first****(10 – 5 = 5)**and**then multiply****(5 X 2 = 10)?** - Or do we start by
**multiplying**(5 X 2 = 10) and**then subtracting****(10 – 10 = 0)?**

In a situation like this, we follow **PEMDAS**.

**P**arentheses**E**xponents**M**ultiplication and**D**ivision*(from left to right)***A**ddition and**S**ubtraction*(from left to right)*

In the above example, we are dealing with **multiplication and subtraction.** **Multiplication is the step before subtraction**, so we first multiply $5\times 2$ and then subtract the sum from $10$, leaving $0$.

**Example**

$5+(8-2)\times 2\div 6-1=?$

**Start with the parentheses:** $8 – 2 = 6$. (Although the subtraction is usually done in the last step since it is in the parentheses, we do it first.) That leaves $5+6\times 2\div 6-1=?$.

**Then Exponents**, as there is no exponent in the equation, this step is not required in this example.

**Then multiplication and division**, starting from the left: $6\times 2=12$, we are left with $5+12\div 6-1=?$

**Then moving to the right:** $12\div 6=2$, so the problem $5+2-1=?$

**Then addition and subtraction**, starting from the left:$5+2=7$, leaving $7-1=?$.

**Finally, move to the right:** $7-1=6$.

**Expert Answer**

The** given equation** is $5+1\times 10$.

When an **expression contains both a sum and a product** without parentheses, we must always perform the product before completing the sum. So this is equivalent to placing **parentheses around the product.**

\[=5+(1\times 10)\]

Let’s evaluate the **product** using the fact that the **product** of $1$ and $10$ is $10$.

\[=5+10\]

Next, we evaluate the **sum** using the fact that the **sum** of $5$ and $10$ is $15$.

\[=15\]

So the** answer to the equation** is $15$.

**Numerical Result**

**The answer to the equation $5+1\times 10$ is $15$.**

**Example**

**How to interpret the equation $5+1\times 20=$? Is the answer $25$ or $120$?**

**Solution**

The **given equation** is $5+1\times 20$.

When an expression contains both a **sum and a product** without any parentheses, we must always perform the product before** the sum**. So this is equivalent to placing **parentheses around the product.**

\[=5+(1\times 20)\]

Let’s evaluate the **product** using the fact that the product of $1$ and $20$ is $20$.

\[=5+20\]

Next, we evaluate the** sum** using the fact that the **sum** of $5$ and $20$ is $25$.

\[=25\]

So the **answer to the equation** is $25$.