Refer to ourÂ Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 1.6 Answer Key Dividing Rational Numbers.

## Texas Go Math Grade 7 Lesson 1.6 Answer Key Dividing Rational Numbers

**Texas Go Math Grade 7 Lesson 1.6 Explore Activity 1 Answer KeyÂ **

A diver needs to descend to a depth of 100 feet below sea level. She wants to do it in 5 equal descents. How far should she travel in each descent?

A. To solve this problem, you can set up a division problem: \(\frac{-100}{}\) =?

B. Rewrite the division problem as a multiplication problem. Think: Some number multiplied by 5 equals -100.

_______ Ã— ? = -100

C. Remember the rules for integer multiplication. If the product is negative, one of the factors must be negative. Since ________ Â¡s positive, the unknown factor must be [Positive/negative.]

D. You know that 5 Ã— _________ = 100. So, using the rules for integer multiplication you can say that 5 Ã— ____ 100.

The diver should descend ________ feet in each descent.

**Reflect**

Question 1.

What do you notice about the quotient of two rational numbers with different signs?

Answer:

The quotient of two rational numbers with different signs will have a negative sign.

**Texas Go Math Grade 7 Pdf Lesson 1.6 Answer Key Question 2.**

What do you notice about the quotient of two rational numbers with the same sign? Does it matter if both signs are positive or both are negative?

Answer:

The quotient of two rational numbers with the same sign will have a positive sign. It does not matter if both signs are positive or both signs are negative.

**Write two equivalent expressions for each quotient.**

Question 3.

\(\frac{14}{-7}\) __________, __________

Answer:

\(\frac{-14}{7}\), – (\(\frac{14}{7}\))

Question 4.

\(\frac{-32}{-8}\) __________, ___________

Answer:

\(\frac{32}{8}\), -(\(\frac{-32}{8}\))

**Your Turn**

**Find each quotient.**

Question 5.

\(\frac{2.8}{-4}\) = ____________

Answer:

The quotient will be negative because signs are different.

Write a decimal as fraction: \(\frac{\frac{28}{10}}{-4}\)

Write complex fraction as division: \(\frac{28}{10}\) Ã· (-4)

Rewrite using multiplication:

\(\frac{28}{10} \times \frac{-1}{4}=\frac{-28}{40}\)

= \(\frac{-7}{10}\)

Question 6.

\(\frac{-\frac{5}{8}}{-\frac{6}{7}}\) = ____________

Answer:

The quotient will be positive because the signs are the same.

Write complex fractions as division:

–\(\frac{5}{8}\) Ã· (-\(\frac{6}{7}\))

Rewrite using multiplication:

–\(\frac{5}{8}\) Ã— (-\(\frac{7}{6}\)) = \(\frac{35}{48}\)

**Texas Go Math Grade 7 Pdf Dividing Rational Numbers Question 7.**

– \(\frac{5.5}{0.5}\) = ___________

Answer:

The quotient will be negative because signs are different.

Write decimal numbers as fractions:

\(-\frac{\frac{55}{10}}{\frac{5}{10}}\)

Write complex fractions as division:

–\(\frac{55}{10}\) Ã· \(\frac{5}{10}\)

Rewrite using multiplication:

–\(\frac{55}{10}\) Ã— \(\frac{10}{5}\) = -11

**Texas Go Math Grade 7 Lesson 1.6 Guided Practice Answer KeyÂ **

**Find each quotient. (Explore Activity 1 and 2, Example 1)**

Question 1.

\(\frac{0.72}{-0.9}\) = ____________

Answer:

The quotient will be negative because signs are different.

Write decimal numbers as fraction:

\(\frac{\frac{72}{100}}{\frac{-9}{10}}\)

Write complex fraction as division:

\(\frac{72}{100}\) Ã· \(\frac{-9}{10}\)

Rewrite using multiplication:

\(\frac{72}{100}\) Ã— \(\frac{10}{-9}\) = \(\frac{8}{-10}\)

= –\(\frac{4}{5}\)

Question 2.

\(\left(-\frac{\frac{1}{5}}{\frac{7}{5}}\right)\) = ____________

Answer:

The quotient will be negative because signs are different.

Write complex fraction as division:

–\(\frac{1}{5}\) Ã· \(\frac{7}{5}\)

Rewrite using multiplication:

–\(\frac{1}{5}\) Ã— \(\frac{5}{7}\) = –\(\frac{1}{7}\)

Question 3.

\(\frac{56}{-7}\) = _____________

Answer:

The quotient will be negative because the signs are different.

\(\frac{56}{-7}\) = -8

Question 4.

\(\frac{251}{4} \div\left(-\frac{3}{8}\right)\) = ____________

Answer:

The quotient will be negative because the complex fraction is negative.

Rewrite using multiplication:

– \(\frac{251}{4}\) Ã— \(\frac{8}{3}\) = –\(\frac{502}{3}\)

**Texas Go Math Grade 7 Answer Key Pdf Lesson 1.6 Question 5.**

\(\frac{75}{-\frac{1}{5}}\) = ____________

Answer:

The quotient will be negative because the signs are different

Write complex fractions as division:

-75 Ã· \(\frac{1}{5}\)

Rewrite using multiplication:

-75 Ã— 5 = -375

Question 6.

\(\frac{-91}{-13}\) = ____________

Answer:

The quotient will be positive because the signs are the same.

\(\frac{-91}{-13}\) = \(\frac{91}{13}\)

= 7

Question 7.

\(\frac{-\frac{3}{7}}{\frac{9}{4}}\) = _____________

Answer:

The quotient will be negative because the signs are different.

Write complex fraction as division:

–\(\frac{3}{7}\) Ã· \(\frac{9}{4}\)

Rewrite using multiplication:

–\(\frac{3}{7}\) Ã— \(\frac{4}{9}\) = –\(\frac{4}{21}\)

Question 8.

–\(\frac{12}{0.03}\) = ____________

Answer:

The quotient will be negative because the fraction has a negative sign.

Write decimal numbers as fraction:

–\(\frac{12}{\frac{3}{100}}\)

Write complex fraction as division:

-12 Ã· \(\frac{3}{100}\)

Rewrite using multiplication:

-12 Ã— \(\frac{100}{3}\) = -400

Question 9.

A water pail in your backyard has a small hole in it. You notice that it has drained a total of 3.5 liters in 4 days. What is the average change in water volume each day? (Example 1)

Answer:

Use a negative number to represent spiLLage of water

Find \(\frac{-3.5}{4}\).

The quotient will be negative because signs are different.

Write decimal numbers as fraction:

\(-\frac{\frac{35}{10}}{4}\)

Write complex fraction as division:

– \(\frac{35}{10}\) Ã· 4

Rewrite using multiplication:

–\(\frac{35}{10}\) Ã— \(\frac{1}{4}\) = – \(\frac{35}{40}\)

= –\(\frac{7}{8}\)

The average change in water volume each day is –\(\frac{7}{8}\) liters.

Question 10.

The price of one share of ABC Company declined a total of $45.75 in 5 days. What was the average change of the price of one share per day? (Example 1)

Answer:

Use a negative number to represent decline in share price.

Find \(\frac{-45.75}{5}\)

The quotient will be negative because signs are different

Write decimal numbers as fraction:

\(-\frac{\frac{4575}{100}}{5}\)

Write complex fraction as division:

–\(\frac{4575}{100}\) Ã· 5

Rewrite using multiplication:

–\(\frac{915}{100}\) Ã— \(\frac{1}{5}\) = –\(\frac{915}{100}\)

= –\(\frac{183}{25}\)

The average change of the price of one share per day is –\(\frac{183}{25}\)

Question 11.

To avoid a storm, a passenger jet pilot descended 0.44 mile in 0.8 minute. What was the planeâ€™s average change of altitude per minute? (Example 1)

Answer:

Use a negative number to represent descent

Find \(\frac{-0.44}{0.8}\).

UL

The quotient will be negative because signs are different.

Write decimal numbers as fraction:

\(\frac{1}{2}\)

Write complex fraction as division:

–\(\frac{44}{100}\) Ã· \(\frac{8}{10}\)

Rewrite using multiplication:

–\(\frac{44}{100}\) Ã— \(\frac{10}{8}\) = –\(\frac{11}{20}\)

The average change of altitude per minute is –\(\frac{11}{20}\) miles.

**Essential Question Check-In**

Question 12.

Explain how you would find the sign of the quotient \(\frac{32 \div(-2)}{-16 \div 4}\).

Answer:

I would first find the sign of the numerator and denominator separately, and then the sign of the whole fraction.

Numerator: Negative, because signs are different

Denominator: Negative, because signs are different.

Whole fraction: Positive, because signs are the same.

**Texas Go Math Grade 7 Lesson 1.6 Independent Practice Answer KeyÂ Â **

Question 13.

\(\frac{5}{-\frac{2}{8}}\) = __________

Answer:

The quotient will be negative because the signs are different

Write complex fraction as division: -5 Ã· \(\frac{2}{8}\)

Rewrite using multiplication:

-5 Ã— \(\frac{8}{2}\) = -5 Ã— 4

= -20

**7th Grade Go Math Answer Key Lesson 1.6 Question 14.**

\(5 \frac{1}{3} \div\left(-1 \frac{1}{2}\right)\) = __________

Answer:

Write mixed fractions as proper fractions:

\(\frac{16}{3}\) Ã· (-\(\frac{3}{2}\))

The quotient will be negative because the complex fraction is negative

Rewrite using multiplication:

– \(\frac{16}{3}\) Ã— \(\frac{2}{3}\) = –\(\frac{32}{9}\)

Question 15.

\(\frac{-120}{-6}\) = ___________

Answer:

The quotient will be positive because the signs are the same.

\(\frac{-120}{-6}\) = \(\frac{120}{6}\)

= 20

Question 16.

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

Answer:

The quotient will be positive because the signs are the same.

Write complex fraction as division:

\(\frac{4}{5}\) Ã· \(\frac{2}{3}\)

Rewrite using multiplication:

\(\frac{4}{5}\) Ã— \(\frac{3}{2}\) = \(\frac{6}{5}\)

Question 17.

1.03 Ã· (-10.3) = _____________

Answer:

Write decimal numbers as fractions.

\(\frac{103}{100}\) Ã· (-\(\frac{103}{10}\))

The quotient will be negative because the signs are different.

Rewrite using multiplication:

–\(\frac{103}{100}\) Ã— \(\frac{10}{103}\) = –\(\frac{1}{10}\)

Question 18.

\(\frac{-0.4}{80}\) = ____________

Answer:

The quotient will be negative because signs are different.

Write decimal numbers as fraction:

\(\frac{-\frac{4}{10}}{80}\)

Write complex fraction as division:

–\(\frac{4}{10}\) Ã· 80

Rewrite using multiplication:

–\(\frac{4}{10}\) Ã— \(\frac{1}{80}\) = –\(\frac{1}{200}\)

Question 19.

1 Ã· \(\frac{9}{5}\) = ___________

Answer:

The quotient will be positive because the signs are the same.

Rewrite using multiplication:

1 Ã— \(\frac{5}{9}\) = \(\frac{5}{9}\)

Question 20.

\(\frac{\frac{-1}{4}}{\frac{23}{24}}\) = _____________

Answer:

The quotient will be negative because the signs are different

Write complex fractions as division:

–\(\frac{1}{4}\) Ã· \(\frac{23}{24}\)

Rewrite using multipLication:

–\(\frac{1}{4}\) Ã— \(\frac{24}{23}\) = –\(\frac{6}{23}\)

**Lesson 1.6 Go Math 7th Grade Dividing Rational Numbers Answer Key Question 21.**

\(\frac{-10.35}{-2.3}\) = ___________

Answer:

The quotient will be positive because the signs are the same.

Write decimal numbers as fractions:

\(\frac{-\frac{1035}{100}}{-\frac{23}{10}}\)

Write complex fractions as division:

\(\frac{1035}{100}\) Ã· \(\frac{23}{10}\)

Rewrite using muLtiplication:

\(\frac{1035}{100}\) Ã— \(\frac{10}{23}\) = \(\frac{45}{10}\)

= \(\frac{9}{2}\)

Question 22.

Alex usually runs for 21 hours a week, training for a marathon. If he is unable to run for 3 days, describe how to find out how many hours of training time he loses, and write the appropriate integer to describe how it affects his time.

Answer:

If Alex runs 21 hours for a week, that means he runs \(\frac{21}{7}\) = 3 hours per day. If he is unable to run for 3 days, that means he loses 3 Ã— 3 = 9 hours.

Question 23.

The running back for the Bulldogs football team carried the ball 9 times for a total loss of 15\(\frac{3}{4}\) yards. Find the average change in field position on each run.

Answer:

Use negative number to represent loss of yards

Find \(\frac{-15 \frac{3}{4}}{9} .\)

Write mixed fractions as proper fractions:

\(\frac{-\frac{63}{4}}{9}\)

The quotient will be negative because the signs are different.

Write complex fraction as division:

–\(\frac{63}{4}\) Ã· 9

Rewrite using multiplication:

–\(\frac{63}{4}\) Ã— \(\frac{1}{9}\) = –\(\frac{7}{4}\)

Averange change in field position on each run is –\(\frac{7}{4}\) yards.

Question 24.

The 6:00 a.m. temperatures for four consecutive days in the town of Lincoln were -12.1Â°C, -7.8Â°C, -14.3Â°C, and -7.2 Â°C. What was the average 6:00 a.m. temperature for the four days?

Answer:

First we need to add the temperatures up.

12.1 + (- 7.8) + (- 14.3) + (- 7.2) = 19.9 + (- 14.3) + (- 7.2)

= 34.2 + (- 7.2)

= 41.4

Now, we need to divide the result with the count of temperature measurements.

Find \(\frac{-41.4}{4}\).

The quotient will be negative because signs are different.

Write decimal numbers as fraction:

\(\frac{-\frac{414}{10}}{4}\)

Write complex fraction as division:

–\(\frac{414}{10}\) Ã· 4

Rewrite using multiplication:

–\(\frac{414}{10}\) Ã— \(\frac{1}{4}\) = –\(\frac{207}{20}\)

The average 6.00 a.m temperature for four days was –\(\frac{207}{20}\) degrees Celsius.

Question 25.

Multistep A seafood restaurant claims an increase of $1,750.00 over its average profit during a week where it introduced a special of baked clams.

a. If this is true, how much extra profit did it receive per day?

Answer:

Find \(\frac{1750}{7}\).

\(\frac{1750}{7}\) = 250

They received $250 extra profit per day.

b. If it had, instead, lost $150 per day, how much money would it have lost for the week?

Answer:

Find -150 Ã— 7

-150 Ã— 7 = -1050

They would have lost $1050 for the week.

c. If its total loss was $490 for the week, what was its average daily change?

Answer:

Find \(\frac{-490}{7}\)

\(\frac{-490}{7}\) = -70

The average daily change was -$70.

Question 26.

A hot air balloon descended 99.6 meters in 12 seconds. What was the balloonâ€™s average rate of descent in meters per second?

Answer:

Use a negative number to represent descent.

Find \(\frac{-99.6}{12}\)

The quotient will be negative because signs are different.

Write decimal numbers as fraction:

\(-\frac{\frac{996}{10}}{12}\)

Write complex fraction as division:

–\(\frac{996}{10}\) Ã· 12

Rewrite using multiplication:

–\(\frac{996}{10}\) Ã— \(\frac{1}{12}\) = –\(\frac{83}{10}\)

= -8.3

The average rate of descent is 8.3 meters per second

Question 27.

Sanderson is having trouble with his assignment. His work is as follows:

\(\frac{-\frac{3}{4}}{\frac{4}{3}}=-\frac{3}{4} \times \frac{4}{3}=-\frac{12}{12}=-1\)

However, his answer does not match the answer that his teacher gave him. What is Sandersonâ€™s mistake? Find the correct answer.

Answer:

Sanderson jumped over one step. He should have written complex fractions using division.

\(\frac{3}{4}\) Ã· \(\frac{4}{3}\)

And then rewrite it using multiplication.

\(\frac{3}{4}\) Ã— \(\frac{3}{4}\)

**Go Math Answer Key Grade 7 Lesson 1.6 Question 28.**

Science Beginning in 1996, a glacier lost an average of 3.7 meters of thickness each year. Find the total change in its thickness by the end of 2012.

Answer:

First, find out how many years have passed in the period 1996-2012.

2012 – 1996 = 16

Find -3.7 Ã— 16.

-3.7 Ã— 16 = -59.2

The total change in thickness by the end of 2012 is -59.2 inches.

**H.O.T. Focus on Higher Order Thinking**

Question 29.

**Represent Real-World Problems** Describe a real-world situation that can be represented by the quotient -85 Ã· 15. Then find the quotient and explain what the quotient means in terms of the real-world situation.

Answer:

A group of 15 people lost 85 dollars. If every person lost the same amount of dollars, how many dollars have each person lost?

–\(\frac{85}{15}\) = –\(\frac{17}{3}\)

Each person lost –\(\frac{17}{3}\)

Question 30.

**Construct an Argument** Divided 5 by 4. Is your answer a rational number? Explain.

Answer:

Yes, it is a Quotient of dividing 5 by 4 is a fraction, and every fraction is a rational number.

Question 31.

**Critical Thinking** Is the quotient of an integer divided by a nonzero integer always a rational number? Explain.

Answer:

Yes, it is. A quotient of any two integers can be written as a fraction, the denominator being a nonzero integer. Thus, it is a rational. number.