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.
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- 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: $7-1=6$.
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 $25$.