Unit 6, Lesson 9

Dealing with Negative Numbers

Grade 7

Practice

Problem 1

Solve each equation.

\(4a=\text-28\)

\(b-\text-6=\text-2\)

\(\text-c+4=\text-9\)

\(\text-3d+7=1\)

\(25e+\text-11=\text-86\)

Problem 2

Here is an equation \(2x+9=\text-15\). Write three different equations that have the same solution as \(2x+9=\text-15\). Explain or show your reasoning.

Problem 3

ForLesson 3: Reasoning about Equations with Tape Diagrams

Select all the equations that represent the diagram.

Tape diagram, 3 equal parts each marked x + 5, total 18.

\(x+5=18\)
\(18\div3=x+5\)
\(3(x+5)=18\)
\(x+5 = \frac13\boldcdot 18\)
\(3x+5=18\)

Problem 4

ForLesson 2: Reasoning about Contexts with Tape Diagrams

There are 88 seats in a theater. The seating in the theater is split into 4 identical sections. Each section has 14 red seats and some blue seats.

Draw a tape diagram to represent the situation.
What unknown amounts can be found by using the diagram or reasoning about the situation?

Problem 5

ForLesson 4: Reasoning about Equations and Tape Diagrams (Part 1)

Match each story to an equation.

A stack of nested paper cups is 8 inches tall. The first cup in the stack is 4 inches tall, and each of the other cups in the stack adds \(\frac14\) inch to the height of the stack.
A baker uses 4 cups of flour. She uses \(\frac14\) cup to flour the counters and the rest to make 8 identical muffins.
Elena has an 8-foot piece of ribbon. She cuts off a piece that is \(\frac14\) of a foot long and cuts the remainder into 4 pieces of equal length.

\(\frac14 + 4x=8\)
\(4+\frac14x=8\)

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