Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Module 3 Answer Key Proportional Relationships.

## Texas Go Math Grade 8 Module 3 Answer Key Proportional Relationships

**Essential Question**

How can you use proportional relationships to solve real-world problems?

**Texas Go Math Grade 8 Module 3 Are You Ready? Answer Key**

**Complete these exercises to review skills you will need for this chapter.**

**Write each fraction as decimal.**

Question 1.

\(\frac{3}{8}\)

Answer:

To express \(\frac{3}{8}\) as a decimal, we write the fraction as a division problem.

Therefore, \(\frac{3}{8}\) = 0.375

Question 2.

\(\frac{0.3}{0.4}\)

Answer:

First, multiply the numerator and the denominator by 10 so that the denominator is a whole number.

\(\frac{0.3 \times 10}{0.4 \times 10}\) = \(\frac{3}{4}\)

Now write the fraction as a division problem, place a decimal point in the quotient and divide as whole numbers:

0.75

Question 3.

\(\frac{0.13}{0.2}\)

Answer:

First multiply the numerator and the denominator by 10 so that the denominator is a whole number.

\(\frac{0.13 \times 10}{0.2 \times 10}\) = \(\frac{1.3}{2}\)

Now write the fraction as a division problem. place a decimal point in the quotient and divide as whole numbers:

0.65

Question 4.

\(\frac{0.39}{0.75}\)

Answer:

First, multiply the numerator and the denominator by 100 so that the denominator is a whole number.

\(\frac{0.39 \times 100}{0.75 \times 100}\) = \(\frac{39}{75}\)

Now write the fraction as a division problem, place a decimal point in the quotient and divide as whole numbers:

0.52

Question 5.

\(\frac{4}{5}\)

Answer:

Write the fraction as a division problem, place a decimal point in the quotient and divide as whole numbers

\(\frac{4}{5}\) = 0.8

Question 6.

\(\frac{0.1}{2}\)

Answer:

First, we multiply the numerator and the denominator by a power of 10 so that we get whole numbers.

\(\frac{0.1}{2}\) = \(\frac{0.1 \cdot 10}{2 \cdot 10}\) = \(\frac{1}{20}\)

To express \(\frac{1}{20}\) as a decimal, we write the fraction as a division problem.

Therefore,

\(\frac{0.1}{2}\) = 0.05

Question 7.

\(\frac{3.5}{14}\)

Answer:

First, we multiply the numerator and the denominator by a power of 10 so that we get whole numbers.

\(\frac{3.5}{14}\) = \(\frac{3.5 \cdot 10}{14 \cdot 10}\) = \(\frac{35}{140}\)

To express \(\frac{35}{140}\) as a decimal, we write the fraction as a division problem.

Therefore, \(\frac{3.5}{14}\) = 0.25

Question 8.

\(\frac{7}{14}\)

Answer:

To express \(\frac{7}{14}\) as a decimal, we write the fraction as a division problem.

\(\frac{7}{14}\) = 0.5

Question 9.

\(\frac{0.3}{10}\)

Answer:

First, we multiply the numerator and the denominator by a power of 10 so that we get whole numbers.

\(\frac{0.3}{10}\) = \(\frac{0.3 \cdot 10}{10 \cdot 10}\) = \(\frac{3}{100}\)

To express \(\frac{3}{100}\) as a decimal, we write the fraction as a division problem.

\(\frac{0.3}{10}\) = 0.03

**Solve each proportion for x.**

Question 10.

\(\frac{20}{18}\) = \(\frac{10}{x}\) ______

Answer:

\(\frac{20}{18}\) = \(\frac{10}{x}\) Given

\(\frac{20 \div 2}{18 \div 2}\) = \(\frac{10}{x}\) Divide 20 ÷ 2 = 10, so divide the numerator and denominator by 2

\(\frac{10}{9}\) = \(\frac{10}{x}\)

x = 9 compare

Question 11.

\(\frac{x}{12}\) = \(\frac{30}{72}\) ______

Answer:

\(\frac{x}{12}\) = \(\frac{30}{72}\) Given

\(\frac{x}{12}\) = \(\frac{30 \div 6}{72 \div 6}\) Divide 72 ÷ 6 = 12, so divide the numerator and denominator by 6.

\(\frac{x}{12}\) = \(\frac{5}{12}\)

x = 5 compare

Question 12.

\(\frac{x}{4}\) = \(\frac{4}{16}\) ______

Answer:

\(\frac{x}{4}\) = \(\frac{4}{16}\) Given

\(\frac{x}{4}\) = \(\frac{4 \div 4}{16 \div 4}\) Divide 16 ÷ 4 = 4, so divide the numerator and denominator by 4.

\(\frac{x}{4}\) = \(\frac{1}{4}\)

x = 1 compare

Question 13.

\(\frac{11}{x}\) = \(\frac{132}{120}\) ______

Answer:

\(\frac{11}{x}\) = \(\frac{132}{120}\) Given

\(\frac{11}{x}\) = \(\frac{132 \div 12}{120 \div 12}\) Divide 132 ÷ 12 = 11, so divide the numerator and denominator by 12.

\(\frac{11}{x}\) = \(\frac{11}{10}\)

x = 10 compare

Question 14.

\(\frac{36}{48}\) = \(\frac{x}{4}\) ______

Answer:

\(\frac{36}{48}\) = \(\frac{x}{4}\) Given

\(\frac{36 \div 12}{48 \div 12}\) = \(\frac{x}{4}\) Divide 48 ÷ 12 = 4, so divide the numerator and denominator by 12.

\(\frac{3}{4}\) = \(\frac{x}{4}\)

x = 3 compare

Question 15.

\(\frac{x}{9}\) = \(\frac{21}{27}\) ______

Answer:

\(\frac{x}{9}\) = \(\frac{21}{27}\) Given

\(\frac{x}{9}\) = \(\frac{21 \div 3}{27 \div 3}\) Divide 27 ÷ 3 = 9, so divide the numerator and denominator by 12.

\(\frac{x}{9}\) = \(\frac{7}{9}\)

x = 7 Compare

x = 7

Question 16.

\(\frac{24}{16}\) = \(\frac{x}{2}\) ______

Answer:

\(\frac{24}{16}\) = \(\frac{x}{2}\) Given

\(\frac{24 \div 8}{16 \div 8}\) = \(\frac{x}{2}\) Divide 16 ÷ 8 = 2, so divide the numerator and denominator by 8.

\(\frac{3}{2}\) = \(\frac{x}{2}\)

x = 3 Compare

x = 3

Question 17.

\(\frac{30}{15}\) = \(\frac{6}{x}\) ______

Answer:

\(\frac{30}{15}\) = \(\frac{6}{x}\) Given

\(\frac{30 \div 5}{15 \div 5}\) = \(\frac{6}{x}\) Divide 30 ÷ 5 = 6, so divide the numerator and denominator by 5.

\(\frac{6}{3}\) = \(\frac{6}{x}\)

x = 3 Compare

x = 3

Question 18.

\(\frac{3}{x}\) = \(\frac{18}{36}\) ______

Answer:

\(\frac{3}{x}\) = \(\frac{18}{36}\)

\(\frac{3}{x}\) = \(\frac{18 \div 6}{36 \div 6}\) Divide 18 ÷ 6 = 3, so divide the numerator and denominator by 6.

\(\frac{3}{x}\) = \(\frac{3}{6}\)

x = 6

**Texas Go Math Grade 8 Module 3 Reading Start-Up Answer Key**

**Visualize Vocabulary**

**Use the ✓ words to complete the diagram.**

**Understand Vocabulary**

**Match the term on the left to the definition on the right.**

Answer:

1. (B) A unit rate is: B. A rate in which the second quantity in the comparison is one unit.

2. (A) Constant of proportionality is: A. A constant ratio of two variables related proportionally.

3. (C) A proportional relationship is: C. A relationship between two quantities in which the ration of one quantity to the other quantity is constant.