Question

solve the problems.
1 simplify 18.1 − 1.1(7.4 − 9.6 + 0.5). write your answers in the blanks.
18.1 − 1.1(7.4 − 9.6 + 0.5) = 18.1 − 1.1(\underline{quadquad} + 0.5)
quadquadquadquadquadquadquadquadquadquadquad= 18.1 − 1.1(\underline{quadquad})
quadquadquadquadquadquadquadquadquadquadquad= 18.1 + \underline{quadquad}
quadquadquadquadquadquadquadquadquadquadquad= \underline{quadquad}

Explanation:

Step1: Simplify inner parentheses

First, calculate \(7.4 - 9.6 + 0.5\). Let's do the subtraction first: \(7.4 - 9.6=-2.2\), then add \(0.5\): \(-2.2 + 0.5=-1.7\). Wait, maybe we can use the distributive property? Wait, the original expression is \(18.1 - 1.1(7.4 - 9.6 + 0.5)\). Let's first simplify the expression inside the parentheses: \(7.4 - 9.6 + 0.5\). Let's combine \(7.4 + 0.5 = 7.9\), then \(7.9 - 9.6=-1.7\). But maybe the problem is structured to use the distributive property? Wait, no, the first blank: let's see the original step: \(18.1 - 1.1(\underline{\quad} + 0.5)\). Wait, maybe there's a typo or miswriting. Wait, maybe the inner expression is \(7.4 - 9.6 + 0.5\), so we can group \(7.4 - 9.6\) as \((7.4 - 9.6)\), so the first blank is \(7.4 - 9.6\), then the next step: \(18.1 - 1.1(\underline{\quad})\), where the blank is \((7.4 - 9.6 + 0.5)\) simplified? Wait, maybe I misread. Let's re-express the original problem:

We have \(18.1 - 1.1(7.4 - 9.6 + 0.5)\). Let's first compute the expression inside the parentheses: \(7.4 - 9.6 + 0.5\). Let's calculate \(7.4 + 0.5 = 7.9\), then \(7.9 - 9.6=-1.7\). Then multiply by \(1.1\): \(1.1\times(-1.7)=-1.87\). Then subtract from \(18.1\): \(18.1 - (-1.87)\)? Wait, no, it's \(18.1 - 1.1\times(\text{something})\). Wait, maybe the problem is written as \(18.1 - 1.1(7.4 - 9.6 + 0.5)=18.1 - 1.1(\underline{7.4 - 9.6} + 0.5)\), then the next step: \(18.1 - 1.1(\underline{-2.2 + 0.5})\) (since \(7.4 - 9.6=-2.2\)), then \(18.1 - 1.1(\underline{-1.7})\) (since \(-2.2 + 0.5=-1.7\)), then calculate \(1.1\times(-1.7)=-1.87\), then \(18.1 - (-1.87)=18.1 + 1.87 = 19.97\)? Wait, no, \(18.1 - 1.1\times(-1.7)=18.1 + 1.87 = 19.97\)? Wait, maybe I made a mistake. Wait, let's do it step by step:

1. Simplify inside the parentheses: \(7.4 - 9.6 + 0.5\)
- \(7.4 - 9.6 = -2.2\)
- \(-2.2 + 0.5 = -1.7\)
2. Multiply by \(1.1\): \(1.1\times(-1.7)=-1.87\)
3. Subtract from \(18.1\): \(18.1 - (-1.87)=18.1 + 1.87 = 19.97\)? Wait, no, \(18.1 - 1.1\times(-1.7)=18.1 + 1.87 = 19.97\). But maybe the problem is structured differently. Let's check the blanks:

First blank: \(7.4 - 9.6\) (since the expression inside is \(7.4 - 9.6 + 0.5\), so grouped as \((7.4 - 9.6) + 0.5\))

Second blank: \((7.4 - 9.6 + 0.5)\) simplified? Wait, \(7.4 - 9.6=-2.2\), so \(-2.2 + 0.5=-1.7\), so the second blank is \(-1.7\) (or \(7.4 - 9.6 + 0.5=-1.7\))

Then, \(18.1 - 1.1\times(-1.7)=18.1 + 1.87 = 19.97\)? Wait, no, \(1.1\times(-1.7)=-1.87\), so \(18.1 - (-1.87)=18.1 + 1.87 = 19.97\). But maybe I messed up the sign. Wait, the original expression is \(18.1 - 1.1(\text{negative number})\), so subtracting a negative is adding a positive.

Wait, let's do it step by step with the blanks:

1. \(18.1 - 1.1(\underline{7.4 - 9.6} + 0.5)\) (first blank: \(7.4 - 9.6\))
2. Calculate \(7.4 - 9.6=-2.2\), so now: \(18.1 - 1.1(\underline{-2.2} + 0.5)\) (second blank: \(-2.2\))
3. Then \(-2.2 + 0.5=-1.7\), so: \(18.1 - 1.1(\underline{-1.7})\) (third blank: \(-1.7\))
4. Now multiply \(1.1\times(-1.7)=-1.87\)
5. Then \(18.1 - (-1.87)=18.1 + 1.87 = 19.97\) (fourth blank: \(1.87\)? Wait, no, \(18.1 - 1.1\times(-1.7)=18.1 + (1.1\times1.7)=18.1 + 1.87 = 19.97\))

Wait, maybe the problem has a different structure. Let's assume the first blank is \(7.4 - 9.6\), the second blank is \(-2.2 + 0.5\) (which is \(-1.7\)), then the next step is \(18.1 - 1.1\times(-1.7)\), then \(18.1 + 1.87\), then \(19.97\).

But maybe the intended steps are:

Step 1: \(18.1 - 1.1((7.4 - 9.6) + 0.5)\) (first blank: \(7.4 - 9.6\))

Step 2: \(18.1 - 1.1(-2.2 + 0.5)\) (second blank: \(-2.2\))

Step 3: \(18.1 - 1.1(-1.7)\) (third blank: \(-1.7\))

Step 4: \(18.1 + 1.87\) (since \(1.1\times1.7 = 1.87\), and subtracting a negative is adding)

Step 5: \(19.97\)

So the blanks would be:

First blank: \(7.4 - 9.6\)

Second blank: \(-2.2 + 0.5\) (or \(-1.7\))

Then the result is \(19.97\)

But maybe the problem is simpler. Let's check the arithmetic again:

\(7.4 - 9.6 = -2.2\)

\(-2.2 + 0.5 = -1.7\)

\(1.1\times(-1.7) = -1.87\)

\(18.1 - (-1.87) = 18.1 + 1.87 = 19.97\)

So the steps:

1. \(18.1 - 1.1(\underline{7.4 - 9.6} + 0.5)\)

2. \(18.1 - 1.1(\underline{-2.2 + 0.5})\)

3. \(18.1 - 1.1(\underline{-1.7})\)

4. \(18.1 + \underline{1.87}\)

5. \(=\underline{19.97}\)

Answer:

First blank: \(7.4 - 9.6\), Second blank: \(-2.2 + 0.5\) (or \(-1.7\)), Third blank: \(-1.7\), Fourth blank: \(1.87\), Final answer: \(19.97\) (Note: The blanks may vary based on the problem's intended grouping, but the final simplified value is \(19.97\))