Calculating the value of numbers with different operations

Question

Calculate the value of: $$-14 + 49 \times 21 - 63 + 56 \div 35 \div 28 \times 70 - 42 \div 7$$

I noticed the numbers are a factor of $7$, so I took out $7$ as a common factor:

$$7[-2 + (7 \times 3) - 9 + (8 \div 5 \div 4 \times 10) - (6\div 1)]$$ $$ = 7[-2+21-9+4-6]$$ $$ = 7[8]$$ $$ =56$$

The solution said the answer is $950$. I am not sure where I went wrong. Can somebody help please?

Answer 1

You're not allowed to factor $7a \times 7b$ as $7(a\times b)$, or $7a \div 7b$ as $7(a \div b)$.

For instance, the $49 \times 21$ term can be written as $7\times (7\times 21)$, instead.

Answer 2

You need to learn the rules of operator precedence.

1. First, anything in parenthesis.
2. Then exponents.
3. Then multiplication and division.
4. Last, addition and subtraction.

(The first two don't apply to this particular situation).

Computers obey these rules. Try cutting and pasting $$-14 + 49 \times 21 − 63 + 56 \div 35 \div 28 \times 70 − 42 \div 7$$ into Wolfram Alpha. It will answer $950$, just like your answer key. There are more rules, of course, like whether to go from left to right, but just knowing operator precedence is a big step forward.