Maths Olympiad Prep

Library / /206 of 520

Algebra Difficulty 3.1 AMC 10/12 Find the answer

When Qiqi calculated (2)3+6÷(1213)(-2)^3+6÷(\frac{1}{2}-\frac{1}{3}), the steps are as follows:

Original expression =(6)+6÷126÷13=\left(-6\right)+6\div \frac{1}{2}-6\div \frac{1}{3}
=6+1218=-6+12-18
=12=-12

(1)(1) Please point out the two errors in Qiqi's first step: ______, ______;
(2)(2) Please provide the correct solution process.

A number or a short expression. Spacing and $ signs are ignored.

Solution

### Solution:

#### Part 1: Identifying Errors

The two errors in Qiqi's first step are:
1. Misunderstanding the meaning of exponentiation.
2. The fact that division does not distribute over addition.

Therefore, the answer is: misunderstanding the meaning of exponentiation and the fact that division does not distribute over addition\boxed{\text{misunderstanding the meaning of exponentiation and the fact that division does not distribute over addition}}.

#### Part 2: Correct Solution Process

Let's correct the calculation step by step:

Original expression:
\begin{align*}
&= (-2)^3 + 6 \div \left(\frac{1}{2} - \frac{1}{3}\right) \\
&= -8 + 6 \div \left(\frac{3}{6} - \frac{2}{6}\right) \\
&= -8 + 6 \div \frac{1}{6} \\
&= -8 + 6 \times 6 \\
&= -8 + 36 \\
&= 28.
\end{align*}

Thus, the correct solution is 28\boxed{28}.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.