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## Texas Go Math Grade 5 Lesson 4.1 Answer Key Division Patterns with Decimals

**Unlock the Problem**

The Healthy Wheat Bakery uses 560 pounds of flour to make 1,000 loaves of bread. Each loaf contains the same amount of flour. How many pounds of flour are used in each loaf of bread?

You can use place value patterns to help you find quotients. Dividing by 10, 100, or 1,000 is the same as multiplying by 0.1, 0.01, or 0.001.

- Underline the sentence that tells you what you are trying to find.
- Circle the numbers you need to use.

**Use place-value patterns**

Divide. 560 ÷ 1,000

Look for a pattern in these products and quotients.

So, __________ pound of flour is used in each loaf of bread.

Explanation:

So, 0.560 pound of flour is used in each loaf of bread.

Question 1.

As you divide by 10,100, and 1,000, how does the position of the decimal point change in the quotients?

Answer:

Move the decimal point to the left for as many places (steps) as there are zeros in the factor 10, 100, or 1000.

Explanation:

28 ÷ 10=2.8 — Move the decimal point one step to the left.

28÷ 100 = 0.28 –Move the decimal point two steps to the left. You need to write zeros in front of the number.

28 ÷ 1000 = 0.028 — Move the decimal point three steps to the left. You need to write zeros in front of the number.

**Try This! Complete the pattern.**

A.

32.6 ÷ 1 = __________

32.6 ÷ 10 = __________

32.6 ÷ 100 = __________

Answer:

32.6 ÷ 1 = 32.6

32.6 ÷ 10 = 3.26

32.6 ÷ 100 =0.326

Explanation:

Move the decimal point to the left for as many places (steps) as there are zeros in the factor 10, 100, or 1000..

B.

150.2 ÷ 1 = __________

150.2 ÷ 10 = __________

150.2 ÷ 100 = _________

Answer:

150.2 ÷ 1 = 150.2

150.2 ÷ 10 = 15.02

150.2 ÷ 100 = 1.502

Explanation:

Move the decimal point to the left for as many places (steps) as there are zeros in the factor 10, 100, or 1000.

**Math Talk**

**Mathematical Processes**

Explain how you can determine where to place the decimal point in the quotient 47.3 ÷ 100.

Answer:0 .473

Explanation:

Move the decimal point two steps to the left. You need to write zeros in front of the number.

**Example**

Liang used 25.5 pounds of tomatoes to make a large batch of salsa. He used one-tenth as many pounds of onions as pounds of tomatoes. He used one-hundredth as many pounds of green peppers as pounds of tomatoes. How many pounds of each ingredient did Liang use?

Tomatoes: 25.5 pounds

Onions: 25.5 pounds ÷ _________

Think: 25.5 ÷ 1 =

25.5 ÷ 10 = ______

Green Peppers: 25.5 pounds ÷ _________

Think ________ ÷ 1 = _________

_________ ÷ 10 = _________

_________ ÷ 100 = _________

So, Liang used 25.5 pounds of tomatoes, _________ pounds of onions, and _________ pound of green peppers.

Answer:

Tomatoes: 25.5 pounds

Onions: 25.5 pounds ÷ 10

Think: 25.5 ÷ 1 =25.5

25.5 ÷ 10 =2.55

Green Peppers: 25.5 pounds ÷ 100

Think 25.5 ÷ 1 = 25.5

25.5 ÷ 10 =2.55

25.5÷ 100 = 0.255

So, Liang used 25.5 pounds of tomatoes, 2.55 pounds of onions, and 0.255 pound of green peppers.

Explanation:

Move the decimal point two steps to the left. You need to write zeros in front of the number

**Math Talk**

**Mathematical Processes**

Explain what happens to the value of a number when you divide by 10, 100, or 1,000.

Answer:

The decimal point will move to the left.

Explanation:

The place value changes. You need to write zeros in front of the number.

**Share and Show**

**Complete the pattern.**

Question 1.

456 ÷ 1 = 456

456 ÷ 10 = 45.6

456 ÷ 100 = 4.56

456 + 1000 = __________

Think: The dividend is being divided by 10, 100, and 1,000 so the decimal point will move to the _________ one place for each equation.

Answer: 0.456

Explanation:

The dividend is being divided by 10, 100, and 1,000 so the decimal point will move to the left one place for each equation.

Question 2.

1,225 ÷ 1 = ________

1,225 ÷ 10 = ________

1,225 ÷ 100 = ________

1,225 ÷ 1,000 = ______

Answer:

1,225 ÷ 1 = 1225

1,225 ÷ 10 = 122.5

1,225 ÷ 100 =12.25

1,225 ÷ 1,000 =1.225

Explanation:

Move the decimal point to the left for as many places (steps) as there are zeros in the factor 10, 100, or 1000.

Question 3.

605 ÷ 1 = ________

605 ÷ 10 = ________

605 ÷ 100 = _____

605 ÷ 1,000 = ________

Answer:

605 ÷ 1 =605

605 ÷ 10 = 60.5

605 ÷ 100 =6.05

605 ÷ 1,000 = 0.605

Explanation:

Move the decimal point to the left for as many places (steps) as there are zeros in the factor 10, 100, or 1000.

Question 4.

74.3 ÷ 1 = ________

74.3 ÷ 10 = ________

74.3 ÷ 100 = ________

Answer:

74.3 ÷ 1 = 74.3

74.3 ÷ 10 = 7.43

74.3 ÷ 100 = 0.743

Explanation:

Move the decimal point to the left for as many places (steps) as there are zeros in the factor 10, 100, or 1000.

**Problem Solving**

**H.O.T. Algebra** Find the value of n.

Question 5.

268 ÷ n = 0.268

n = _____________

Answer: 1000

Explanation:

when 268 is divided by 1000

the answer will be 0.268

Question 6.

n ÷ 100 = 0.123

n = _____________

Answer: 12.3

Explanation:

When 12.3 divided by 100

the answer will be 0.123

Question 7.

n ÷ 10 = 4.6

n = ______________

Answer: 46

Explanation:

When 46 is divided 10

the answer will be 4.6

Question 8.

**Write Math** Explain how you know that the quotient 47.3 is equal to the product 47.3 × 0.1.

Answer: Equal

Explanation:

When 47.3 is divided with 10 the answer is 4.73

and the same number is multiplied with 0.1 the answer is 4.73

**Problem Solving**

**Use the table to solve 9-11.**

Question 9.

**Multi-Step** About how much more cornmeal than flour does each muffin contain?

Answer: 40kilograms

Explanation:

As cornmeal is 150 and flour is 110

150 – 110 = 40

Question 10.

**H.O.T.** If each muffin contains the same amount of sugar, how many kilograms of sugar, to the nearest thousandth, are in each corn muffin?

Answer: 0.0667

Explanation:

If each muffin contains the same amount of sugar,

0.0667 kilograms of sugar, to the nearest thousandth, are in each corn muffin

Question 11.

**H.O.T. Multi-Step** The bakery decides to make only 100 corn muffins on Tuesday. How many kilograms of sugar will be needed?

Answer: 0.667

Explanation:

The bakery decides to make only 100 corn muffins on Tuesday.

0.667 kilograms of sugar will be needed

**Daily Assessment Task**

**Fill in the bubble completely to show your answer.**

Question 12.

Orange crayons are usually made in batches of 100. If it takes 22 pounds of wax to make 100 orange crayons, then how much wax will you need to make one orange crayon?

(A) 0.22 pound

(B) 22 pounds

(C) 2 pounds

(D) 0.022 pound

Answer: A

Explanation:

Orange crayons are usually made in batches of 100.

If it takes 22 pounds of wax to make 100 orange crayons,

0.22 pound of wax will be need to make one orange crayon

Question 13.

**Use Symbols** A famous barbecue restaurant in Texas makes 1,000 pounds of barbecue pork each week. The owner has a catering order that requires 100 pounds of barbecue pork. The owner uses 44 pounds of sauce for every 1,000 pounds of barbecue pork. Which equation shows the amount of sauce needed for the catering order?

(A) 44 ÷ 1 = 44 pounds

(B) 44 ÷ 10 = 4.4 pounds

(C) 44 ÷ 100 = 0.44 pound

(D) 44 ÷ 1,000 = 0.044 pound

Answer: B

Explanation:

A famous barbecue restaurant in Texas makes 1,000 pounds of barbecue pork each week.

The owner uses 44 pounds of sauce for every 1,000 pounds of barbecue pork.

44 ÷ 1,000 = 0.044 pound

0.044 x 100 = 4.4

so, 44 ÷ 10 = 4.4 pounds

Question 14.

**Multi-Step** Loretta is trying to build the largest taco in the world. She uses 2,000 pounds of ground beef, one-tenth as many pounds of cheese, one-hundredth as many pounds of lettuce, and one-thousandth as many pounds of hot sauce. How many pounds of lettuce and cheese does she use?

(A) 2,020 pounds

(B) 220 pounds

(C) 2,200 pounds

(D) 20 pounds

Answer: B

Explanation:

Loretta is trying to build the largest taco in the world.

She uses 2,000 pounds of ground beef, one-tenth as many pounds of cheese, 2000 ÷ 10 = 200

one-hundredth as many pounds of lettuce, 2000 ÷ 100 = 20

and one-thousandth as many pounds of hot sauce.

220 pounds of lettuce and cheese she use, 200 + 20 = 220

**Texas Test Prep**

Question 15.

Apply Ella used 37.2 pounds of apples to make applesauce. She used one-tenth as many pounds of sugar as pounds of apples. How many pounds of sugar did Ella use?

(A) 0.372 pound

(B) 3.72 pounds

(C) 372 pounds

(D) 0.0372 pound

Answer: B

Explanation:

Apply Ella used 37.2 pounds of apples to make applesauce.

She used one-tenth as many pounds of sugar as pounds of apples.

3.72 pounds of sugar used by Ella

37.2 ÷ 10 = 3.72

### Texas Go Math Grade 5 Lesson 4.1 Homework and Practice Answer Key

**Find the value of n.**

Question 1.

456 ÷ n = 4.56

n = _____________

Answer: 100

Explanation:

When 456 is divided by 100

the answer is 4.56

Question 2.

n ÷ 100 = 0.982

n = _____________

Answer: 98.2

Explanation:

When 98.2 is divided by 100

the answer will be 0.982

Question 3.

n ÷ 10 = 32.7

n = ______________

Answer: 327

Explanation:

When 327 is divided by 10

the answer will be 32.7

Question 4.

32 ÷ 1,000 = n

n = ______________

Answer: 0.032

Explanation:

When 32 is divided by 1000

the answer will be 0.032

Question 5.

1,672 ÷ n= 1.672

n = _______________

Answer: 1000

Explanation:

When 1672 is divided by 1000

the answer will be 1.672

Question 6.

24 ÷ 100 = n

n = _______________

Answer: 0.24

Explanation:

When 24 is divided by 100

the answer will be 0.24

Question 7.

9,871 ÷ n = 987.1

n = ______________

Answer: 10

When 9871 is divided by 10

the answer will be 987.4

Question 8.

n ÷ 10 = 5.69

n = ______________

Answer: 56.9

Explanation:

When 56.9 is divided by 10

the answer will be 5.69

Question 9.

n ÷ 1,000 = 0.823

n = _______________

Answer: 823

Explanation:

When 823 is divided by 1000

the answer is 0.823

**Problem Solving**

Question 10.

Mr. Baker drives 24.5 miles to his cousin’s house. He drives one-tenth as many miles to his nephew’s house. How many miles does Mr. Baker drive to his nephew’s house?

Answer: 2.45

Explanation:

Mr. Baker drives 24.5 miles to his cousin’s house.

He drives one-tenth as many miles to his nephew’s house.

24.5÷10 =2.45

Mr. Baker drive to his nephew’s house

Question 11.

Elena sews sequins on a skirt for the dance recital. She sews 100 sequins end-to-end along the length of the skirt. The skirt is 50 centimeters long. What is the length of one sequin?

Answer: 50 centimeters

Explanation:

Elena sews sequins on a skirt for the dance recital.

She sews 100 sequins end-to-end along the length of the skirt.

The skirt is 50 centimeters long.

50 ÷1=50

**Lesson Check**

**Fill in the bubble completely to show your answer.**

Question 12.

An online bookstore ships boxes with a copy of the new bestseller in each box. The total weight of the shipment is 1,200 pounds. If each box weighs 1.2 pounds, how many boxes are shipped?

(A) 10

(B) 10,000

(C) 1,000

(D) 100

Answer: B

Explanation:

An online bookstore ships boxes with a copy of the new bestseller in each box.

The total weight of the shipment is 1,200 pounds.

If each box weighs 1.2 pounds

1000 boxes are shipped

Question 13.

A car dealership uses 1,350 gallons of gasoline to fill the tanks of 100 of their compact cars. How much gas does each tank hold?

(A) 13.5 gallons

(B) 1.35 gallons

(C) 135 gallons

(D) 0.135 gallon

Answer: A

Explanation:

A car dealership uses 1,350 gallons of gasoline to fill the tanks of 100 of their compact cars.

1350 ÷ 100 = 13.50 pounds

Violet sells homemade granola at the Saturday market. Her recipe makes 10 large bags of granola or 100 snack-size bags. Use Violet’s recipe at the right for 14-16.

Question 14.

Which equation shows the number of grams of almonds in one large bag?

(A) 750.2 ÷ 1 = 750.2 grams

(B) 750.2 ÷ 10 = 75.02 grams

(C) 750.2 ÷ 100 = 7.502 grams

(D) 750.2 ÷ 1,000 = 0.7502 gram

Answer: B

Explanation:

Her recipe makes 10 large bags of granola

for 10 large bags she uses 750.2 grams of almonds

750.2 ÷ 10 = 75.02

Question 15.

**Multi-Step** What is the total number of grams of oats and sunflower seeds in one large bag?

(A) 345.05 grams

(B) 750.5 grams

(C) 45.05 grams

(D) 120.07 grams

Answer: A

Explanation:

Her recipe makes 10 large bags of granola

For 10 large bags she uses 3000 grams of oats and 450.5 grams of sunflower seeds

3450.5 ÷ 10 = 345.05

Question 16.

**Multi-Step** How many grams of sunflower seeds are in two snack-size servings of granola?

(A) 4.505 grams

(B) 45.05 grams

(C) 91 grams

(D) 9.01 grams

Answer: D

Explanation:

Her recipe makes 10 large bags of granola or 100 snack-size bags.

for 100 grams of sunflower seeds 450.5 grams of sunflower seeds are used

grams of sunflower seeds are in two snack-size servings of granola

450.5÷100=4.505

4.505×2=9.01