 # How do I interpret this equation 5+1×10=? Is the answer 15 or 60?

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

1. 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 = ?
2. Do we subtract first (10 – 5 = 5) and then multiply (5 X 2 = 10)?
3. Or do we start by multiplying (5 X 2 = 10) and then subtracting (10 – 10 = 0)?

In a situation like this, we follow PEMDAS.

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (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: $7-1=6$.

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 $25$.