## Envision Math 6th Grade Textbook Answer Key Topic 1 Reteaching

**Reteaching**

**Set A, pages 4–6**

Write different forms of the number 82,700,360,000,000 and tell the place and value of the digit 6.

Word form: eighty-two trillion, seven hundred billion, three hundred sixty million

Expanded form: (8 × 10,000,000,000,000) + (2 × 1,000,000,000,000) + (7 × 100,000,000,000) + (3 × 100,000,000) + (6 × 10,000,000)

The 6 is in the ten millions place.

Its value is 6 × 10,000,000 = 60,000,000.

Remember to start at the right and work your way left to each period when finding the place and value of a whole number digit. Periods are groups of three digits separated by commas.

In 1 through 6, what is the place and value of the underlined digit?

Question 1.

327,018

Answer:

Question 2.

19,345

Answer:

Question 3.

71,329,684

Answer:

Question 4.

6,291,378

Answer:

Question 5.

632,109,874

Answer:

Question 6.

7,263

Answer:

**Set B, pages 8–9**

Use > or < to compare the two whole numbers.

728,316 ◯ 728,361

Compare the digits in each place.

So, 728,316 < 728,361.

Remember when you compare two whole numbers, line them up so their place values align and then compare their digits from left to right.

Use < or > to compare 1 through 4.

Question 1.

69,354 _____ 69,435

Answer:

69,354 69,435

Explanation:

Question 2.

27,461,398 ______ 27,164,398

Answer:

27,461,398 27,164,398

Explanation:

Question 3.

eighteen trillion ______ 18,000,001

Answer:

eighteen trillion 18,000,001

Explanation:

Question 4.

527 thousand ______ 527,001

Answer:

527 thousand 527,001

Explanation:

**Set C, pages 10–12**

Evaluate 6^{3}.

6 is the base and 3 is the exponent.

6 is used as a factor 3 times.

6 × 6 × 6 = 216

Write 29,654 in expanded form using

exponents. (2 × 10^{4}) = (9 × 10^{3}) = (6 × 10^{2}) = (5 × 10^{1}) = (4 × 100)

Remember that any base number, except zero, with an exponent of 0 has a value of 1.

Evaluate 1 through 3.

Question 1.

9^{2}

Answer:

81

Explanation:

Question 2.

99^{1}

Answer:

99

Explanation:

Question 3.

3,105^{0}

Answer:

1

Explanation:

Question 4.

Write6,209inexpandedform using exponents.

Answer:

(6 × 10^{3}) + (2 × 10^{2}) + (9 × 10^{0})

Explanation:

**Set D, pages 14-16**

Write the place and value of the underlined digit in 2.0795.

The 7 is in the hundredths place.

Its value is 7 × 0.01 = 0.07.

Remember to pay attention to the decimal point and zeros when determining the place and value of a decimal digit.

What is the place of the underlined digit?

Question 1.

17.903

Answer:

thousandths

Explanation:

Question 2.

28.1

Answer:

tenths

Explanation:

Question 3.

68.0009

Answer:

ten thousandths

Explanation:

Question 4.

94.002

Answer:

ones

Explanation:

**Set E, pages 18-19**

Use <, >, or = to compare the two decimals.

37.106 ◯ 37.110

Compare the digits in each place. The digits are the same until the hundredths place.

37.106

37.110

0 < 1,

so 37.106 < 37.110.

Remember that when you compare decimals, line up their decimal points and then compare their digits from left to right.

Use <, >, or = to compare the two decimals.

Question 1.

95.17 _____ 95.71

Answer:

95.17 95.71

Explanation:

Question 2.

0.74 ______ 0.7400

Answer:

0.74 0.7400

Explanation:

Question 3.

37 _____ 0.37

Answer:

37 0.37

Explanation:

Question 4.

224.9 ______ 224.92

Answer:

224.9 224.92

**Set F, pages 20-21**

Elise, Jasmine, Fatima, and Nola want to jump rope at recess. In how many ways can the girls be paired to twirl the rope?

Make an organized list. Choose one of the girls. Find the possible pairs, keeping that girl fixed. Repeat with each girl. Then cross out any repeated pairs.

6 possible pairs of girls can twirl the rope.

Remember to keep each item fixed and find all the possible combinations for that item.

Question 1.

Heyden’s mom bought peaches, pears, bananas, apples, and grapes. How many ways can Heyden combine the fruit so he has two different pieces of fruit in his lunch, without repeating any combinations?

Answer:

10

Explanation:

Question 2.

How many three-letter combinations can be made from the letters in the word “MATH”?

Answer:

24

Explanation: