Lesson 2

Truth and Equations

Let's use equations to represent stories and see what it means to solve equations.

Problem 1

Select all the true equations.

A:

\(5 + 0 = 0\)

B:

\(15 \boldcdot 0 = 0\)

C:

\(1.4 + 2.7 = 4.1\)

D:

\(\frac{2}{3} \boldcdot \frac{5}{9} = \frac{7}{12}\)

E:

\(4 \frac{2}{3}=5 - \frac{1}{3}\)

Problem 2

Mai's water bottle had 24 ounces in it. After she drank \(x\) ounces of water, there were 10 ounces left. Select all the equations that represent this situation.

A:

\(24 \div 10 = x\)

B:

\(24 +10 = x\)

C:

\(24 - 10 = x\)

D:

\(x + 10 = 24\)

E:

\(10x = 24\)

Problem 3

Priya has 5 pencils, each \(x\) inches in length. When she lines up the pencils end to end, they measure 34.5 inches. Select all the equations that represent this situation.

A:

\(5 + x = 34.5\)

B:

\(5x = 34.5\)

C:

\(34.5 \div 5 = x\)

D:

\(34.5 - 5 = x\)

E:

\(x = (34.5) \boldcdot 5\)

Problem 4

Match each equation with a solution from the list of values.

A:

\(2a = 4.6\)

B:

\(b + 2 = 4.6\)

C:

\(c \div 2 = 4.6\)

D:

\(d - 2 = 4.6\)

E:

\(e+\frac{3}{8} = 2\)

F:

\(\frac{1}{8}f = 3\)

G:

\(g \div \frac{8}{5} = 1\)

1:

\(\frac{8}{5}\)

2:

\(1 \frac{5}{8}\)

3:

2.3

4:

2.6

5:

6.6

6:

9.2

7:

24

Problem 5

The daily recommended allowance of vitamin C for a sixth grader is 45 mg. 1 orange has about 75% of the recommended daily allowance of vitamin C. How many milligrams are in 1 orange? If you get stuck, consider using the double number line.

Double number line. Vitamin C in mg. Percentage.

(From Unit 3, Lesson 11.)

Problem 6

There are 90 kids in the band. 20% of the kids own their own instruments, and the rest rent them.

  1. How many kids own their own instruments?
  2. How many kids rent instruments?
  3. What percentage of kids rent their instruments?
(From Unit 3, Lesson 12.)

Problem 7

Find each product.

  1. \((0.25) \boldcdot (1.4)\)
  2. \((0.061) \boldcdot (0.43)\)
  3. \((1.017) \boldcdot (0.072)\)
  4. \((5.226) \boldcdot (0.037)\)
(From Unit 5, Lesson 8.)