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## Texas Go Math Grade 5 Lesson 3.1 Answer Key Multiplication Patterns with Decimals

**Essential Question**

How can patterns help you place the decimal point in a product?

**Unlock the Problem**

Cindy is combining equal-sized rectangles from different fabric patterns to make a postage-stamp quilt.

Each rectangle has an area of 0.75 of a square inch. If she uses 1,000 rectangles to make the quilt,

what will be the area of the quilt?

Use the pattern to find the product.

The quilt will have an area of __1,000 X 0.75= 750____ square inches.

Question 1.

As you multiply by 10, 100, and 1,000,

how does the position of the decimal point change in the product?

Answer:

Unit,tenths,hundreths,thousandths,

Explanation:

When the multiplier is 10, 100 or 1000,

we move the decimal point to the right by as many places as number of zeroes

after 1 in the multiplier. 1. To multiply a decimal by 10,

move the decimal point in the multiplicant by one place to the right.

Place value patterns can be used to find the product of a number and the decimals 0.1 and 0.01.

Example

Jorge is making a scale model of the Willis Tower in Chicago for a theater set.

The height of the tower is 1,353 feet. If the model is \(\frac{1}{100}\)

of the actual size of the building, how tall is the model?

Jorge’s model of the Willis Tower is __13.53_ feet tall.

Question 2.

As you multiply by 0.1 and 0.01, how does the position of

the decimal point change in the product?

Answer:

Unit,tenths,hundreths,thousandths,

Explanation:

When the multiplier is 10, 100 or 1000,

we move the decimal point to the right by as many places as number of zeroes

after 1 in the multiplier. 1. To multiply a decimal by 10,

moved the decimal point in the multiplicant by one place to the right.

**Share and Show**

Complete the pattern.

Question 1.

1 × $17.04 = $17.04,

Think: The decimal point moves one place to the _right__ for each equation.

10 × $17.04 = $170.40,

Think: Money is expressed in hundredths. 170.4 = 170.40.

100 × $17.04 = $1,704

1,000 × $17.04 = _$17,040___

Answer:

The decimal point moves one place to the right for each equation,

Money is expressed in hundredths. 170.4 = 170.40.

100 × $17.04 = $1,704

1,000 × $17.04 = $17,040.

Explanation:

right,

Money is expressed in hundredths. 170.4 = 170.40.

100 × $17.04 = $1,704

1,000 × $17.04 = $17,040.

Question 2.

1 × 3.19 = _3.19__

10 × 3.19 = __30.19_

100 × 3.19 = __300.19_

1,000 × 3.19 = _3,000.19___

Answer:

1 X 3.19 = 3.19,

10 X 3.19 = 30.19,

100 X 3.19 = 300.19,

1,000 X 3.19 = 3,000.19,

Explanation:

The value of unit is 1 so 1 X 3.19 = 3.19

The decimal point moves one place to the right for each equation,

10 X 3.19 = 30.19 (hundreths),

100 X 3.19=300.19 (thousandths),

1,000 X 3.19 = 3,000.19 (ten thousandths) place.

Question 3.

45.6 × 1 = _45.6__

45.6 × 10 = _456___

45.6 × 100 = __4,560__

45.6 × 1,000 = _45,600___

Answer:

45.6 X 1 = 45.6,

45.6 X 10 =456,

45.6 X 100 = 4,560,

45.6 X 1,00 = 45,600,

Explanation:

The value of unit is 1 so 45.6 X 1 = 45.6,

The decimal point moves one place to the right for each equation,

45.6 X 10 = 456 (hundreths),

100 X 3.19= (thousandths),

1,000 X 3.19 = 3,000.19 (ten thousandths) place.

Question 4.

1 × 6,391 = _6,391__

0.1 × 6,391 = _639.1__

0.01 × 6,391 = __63.91_

Answer:

1 X 6,391 = 6,391,

0.1 X 6,391 = 639.1,

0.01 X 6,391 = 63.91,

**Math Talk**

**Mathematical Processes**

Explain how you know that when you multiply the product of 10 × 34.1 by 0.1,

the result will be 34.1.

**Problem Solving**

Algebra Find the value of n.

Question 5.

n × $3.25 = $325.00

n = _$100__

Answer:

n = $100,

Explanation:

Given n X $3.25 = $325.00,

n = $325.00 ÷ $3.25,

n = ($325.00 X $100) / $325.00,

n = $100.

Question 6.

0.1 × n = 89.5

n = __895_

Answer:

n = 895,

Explanation:

n = 89.5 ÷ 0.1,

n = (89.5 X 10) / 1,

n = 895.

Question 7.

1,000 × n = 630

n = _0.63__

Answer:

n = 0.63,

Explanation:

1,000 X n = 630,

n = (630 ÷ 1,000),

n = 0.63.

Question 8.

**Multi-Step** A glacier in Alaska moved more than 29.9 meters a day.

About how much farther would it move in 1,000 days than it would move in 100 days?

Answer:

In 1,000 days glacier in Alaska moves 29,900 meters,

Explanation:

A glacier in Alaska moved more than 29.9 meters a day.

It would move in 100 days is 2,990 meters,

Farther would it move in 1,000 days is 29,900 meters.

Question 9.

**H.O.T.** Analyze Three friends are selling items at an arts and crafts fair.

Josey makes $45.75 selling jewelry. Mark makes 100 times as much as

Josey makes by selling his custom furniture. Chance makes a tenth of the money

Mark makes by selling paintings. How much money does each friend make?

Answer:

Money does each friend makes is

Josey makes $45.75 by selling jewelry,

Mark makes $4,575 by selling custom furniture,

Chance makes $457.5 y selling paintings,

Explanation:

Analyzed three friends are selling items at an arts and crafts fair.

Josey makes $45.75 selling jewelry. Mark makes 100 times as much as

Josey makes by selling his custom furniture. Therefore Mark makes

$45.75 X 100 = $4,575, Chance makes a tenth of the money

Mark makes by selling paintings. So Chance makes

$4,575 X 0.1 = $457.5.

Money does each friend makes is

Josey makes $45.75 by selling jewelry,

Mark makes $4,575 by selling custom furniture,

Chance makes $457.5 y selling paintings.

**Problem Solving**

**H.O.T.** What’s the Error?

Question 10.

Kirsten is making lanyards for a convention. She needs to make 1,000 lanyards and

knows that 1 lanyard uses 1.75 feet of cord. How much cord will Kirsten need?

Kirsten’s work is shown below.

1 × 1.75 = 1.75

10 × 1.75 = 10.75

100 × 1.75 = 100.75

1,000 × 1.75 = 1,000.75

So, Kirsten needs _1,000.75__ feet of cord to make 1,000 lanyards.

Answer:

Explanation:

Given Kirsten is making lanyards for a convention. She needs to make 1,000 lanyards and

knows that 1 lanyard uses 1.75 feet of cord.

Kirsten’s work is shown as

1 × 1.75 = 1.75,

10 × 1.75 = 10.75,

100 × 1.75 = 100.75,

1,000 × 1.75 = 1,000.75 which is error free,

therefore, Kirsten needs _1,000.75__ feet of cord to make 1,000 lanyards.

Question 11.

Communicate how Kirsten could have solved the problem without writing out the pattern needed.

Answer:

Kirsten solved the problem by using decimal place values multiplied by

whole number value,

Explanation:

Kristen could have solved the problem without writing out the pattern needed as

1,000 X 1.75 feet moves one place to the right for each to ten thousandths place as

1,000.75 feet.

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

Question 12.

Connect When a number is multiplied by 1,000, the result is 320.

When the number is multiplied by 100, the result is 32.

What is the result when the number is multiplied by 10?

(A) 3.2

(B) 3,200

(C) 16

(D) 160

Answer:

(A) 3.2,

Explanation:

Connected when a number is multiplied by 1,000 the result is 320.

Let the number be n,

n X 1,000 = 320,

n = 320 ÷ 1,000,

n = 0.32,

When the number n is multiplied by 100, the result is 32.

so 0.32 X 100 = 32 matches with the result 100,

therefore, the result when the number is multiplied by 10 is

0.32 X 10 = 3.2 matches with (A).

Question 13.

Use Math Language When a number is multiplied by 1,000, the result is 8,510.

When the number is multiplied by 10, the result is 85.1.

Which sentence follows the same pattern?

(A) When multiplied by 100, the result is 8.51.

(B) When multiplied by 100, the result is 851.

(C) When multiplied by 1, the result is 85.1.

(D) When multiplied by 1, the result is 851.

Answer:

(B) When multiplied by 100, the result is 851,

Explanation:

Using Math Language, When a number is multiplied by 1,000, the result is 8,510,

So (n X 8,510 = 1,000),

n= 8,510 ÷ 1,000,

n = 8.51,

So the number when multiplied with 100 the result will be 851 and

So when the number is multiplied by 10, the result is 85.1,(8.51 X 10 = 85.1),

therefore the sentence that follows the same pattern is

(B) When multiplied by 100, the result is 851.

Question 14.

**Multi-Step** When a number is multiplied by 1,000 and

then by 0.1, the result is 6,810. What is the original number?

(A) 0.681

(B) 681

(C) 6.81

(D) 68.1

Answer:

(D) 68.1,

Explanation:

Given when a number is multiplied by 1,000 and

then by 0.1, the result is 6,810. Let the number be

n so that n X 1,000 X 0.1 = 6,810,

n X 100 = 6,810,

n = 6,810 ÷ 100,

n = 68.1 matches with (D).

**Texas Test Prep**

Question 15.

A box of crackers costs $0.26 per ounce. If the box contains 10 ounces,

what is the cost of the box of crackers?

(A) $0,026

(B) $2.60

(C) $0.260

(D) $26.00

Answer:

(B) $2.60,

Explanation:

A box of crackers costs $0.26 per ounce and the box contains 10 ounces,

The cost of the box of crackers is $0.26 X 10 = $2.60 matches with (B).

### Texas Go Math Grade 5 Lesson 3.1 Homework and Practice Answer Key

**Find the value of n.**

Question 1.

n × 43.50 = 435

n = ____10_____

Answer:

n = 10,

Explanation:

Given n x 43.50 = 435,

n = 435 ÷ 43.50,

n = (435 X 10) ÷ 435,

n = 10.

Question 2.

394 × n = 3.94

n = ___0.01______

Answer:

n= 0.01,

Explanation:

Given 394 x n = 3.94,

n = 3.94 ÷ 394,

n = (394 X 0.01) ÷ 394,

n = 0.01.

Question 3.

n × 721 = 72.1

n = ___0.1______

Answer:

n= 0.1,

Explanation:

Given n x 721 = 72.1,

n = 72.1 ÷ 721,

n = (721 X 0.1) ÷ 721 ,

n = 0.1.

Question 4.

n × $5.60 = $506.00

n = ____100_____

Answer:

n = 100,

Explanation:

Given n x $5.60 = $506.00,

n = $506.00 ÷ $5.60,

n = $506.00 ÷ ($560 X 0.01),

n = $506 X 100 ÷ 560,

n = 100.

Question 5.

0.074 × n = 74

n = ___1,000______

Answer:

n = 1,000,

Explanation:

Given 0.074 X n = 74,

n = 435 ÷ 43.50,

n = (435 X 10) ÷ 435,

n = 10.

Question 6.

8,034 × n = 80.34

n = ___0.01______

Answer:

n= 0.01,

Explanation:

Given 8,034 x n = 80.34,

n = 80.34 ÷ 8,034,

n = (8034 X 0.01) ÷ 8034,

n = 0.01.

**Problem Solving**

Question 7.

Jaden sells a painting for 10 times the original price.

He sells the painting for $45.50.

What was the original price of the painting?

Answer:

The original price of the painting is $4.55,

Explanation:

Given Jaden sells a painting for 10 times the original price.

He sells the painting for $45.50,

the original price of the painting is $45.50 ÷ 10,

$45.50 X 0.1 = $4.55.

Question 8.

Marla thinks her dog might not be feeling well. He ate 0.1 times

as much dog food on Wednesday as he ate on Tuesday.

If her dog ate 6 cups of dog food on Tuesday,

how much did he eat on Wednesday?

Answer:

On Wednesday the dog ate 0.1 X 6 cups = 0.6 cups,

Explanation:

Given Marla thinks her dog might not be feeling well.

He ate 0.1 times as much dog food on Wednesday as he ate on Tuesday.

If her dog ate 6 cups of dog food on Tuesday,

On Wednesday the dog ate 0.1 X 6 cups = 0.6 cups.

**Lesson Check**

Fill in the bubble completely to show your answer.

Question 9.

The camp counselors cut ribbons for an art project.

They cut 1,000 pieces of ribbon. Each ribbon is 1.45 feet long.

Which equation correctly shows the number of feet of ribbon cut for the project?

(A) 1,000 × 1.45 = 14.50

(B) 1,000 × 1.45 = 145

(C) 1,000 × 1.45 = 1,450

(D) 1,000 × 1.45 = 14,500

Answer:

(C) 1,000 × 1.45 = 1,450,

Explanation:

The camp counselors cut ribbons for an art project.

They cut 1,000 pieces of ribbon. Each ribbon is 1.45 feet long.

So, the equation correctly shows the number of feet of ribbon cut for the project

is 1,000 X 1.45 = 1,450 matches with (C).

Question 10.

Marbles cost $0.50 per ounce. A box of marbles at the warehouse store

contains 100 ounces of marbles. What is the cost of the box of marbles?

(A) $5

(B) $50

(C) $500

(D) $5,000

Answer:

(B) $50,

Explanation:

Marbles cost $0.50 per ounce, A box of marbles at the warehouse store

contains 100 ounces of marbles.

So, the cost of the box of marbles is $0.50 X 100 = $50 matches with (B).

Question 11.

Which equation correctly shows the next product In the pattern?

1 × 0.67 = 0.67

10 × 0.67 = 6.7

100 × 0.67 = 67

(A) 1,000 × 0.67 = 0.067

(B) 1,000 × 0.67 = 67,000

(C) 1,000 × 0.67 = 6,700

(D) 1,000 × 0.67 = 670

Answer:

(D) 1,000 × 0.67 = 670,

Explanation:

Given 1 × 0.67 = 0.67,

10 × 0.67 = 6.7,

100 × 0.67 = 67,

So, equation correctly shows the next product in the pattern

is 1,000 X 0.67 matches with (D).

Question 12.

Bianca plants a tree at the park that is 0.3 meter tall.

An oak tree nearby is 100 times taller. How tall is the oak tree?

(A) 0.03 meter

(B) 3 meters

(C) 30 meters

(D) 300 meters

Answer:

(C) 30 meters,

Explanation:

Given Bianca plants a tree at the park that is 0.3 meter tall.

An oak tree nearby is 100 times taller. Taller is the oak tree

is 100 X 0.3 = 30 meters which matches with (C).

Question 13.

**Multi-Step** Leo practices his violin 12.5 hours each week.

He also practices singing for 3.5 hours each week.

If he practices the same amount of time each week,

how many hours does Leo practice in 10 weeks?

(A) 125 hours

(B) 160 hours

(C) 16 hours

(D) 1,600 hours

Answer:

(B) 160 hours,

Explanation:

Given Leo practices his violin 12.5 hours each week.

He also practices singing for 3.5 hours each week.

If he practices the same amount of time each week,

Number of hours does Leo practice in 10 weeks is

12.5 hours X 10 = 125 hours in violin,

3.5 hours X 10 = 35 hours in singing,

125 hours + 35 hours = 160 hours matches with (B).

Question 14.

**Multi-Step** Greg ran 3 times as far as Jed. RJ ran 0.1 times as far as Greg.

If Jed ran 25 yards, how far did Greg and RJ run?

(A) Greg: 75 yards; RJ: 7.5 yards

(B) Greg: 7.5 yards; RJ: 75 yards

(C) Greg: 750 yards; RJ: 75 yards

(D) Greg: 7.5 yards; RJ: 0.75 yards

Answer:

(A) Greg: 75 yards; RJ: 7.5 yards,

Explanation:

Given Greg ran 3 times as far as Jed,

RJ ran 0.1 times as far as Greg.

If Jed ran 25 yards,Greg runs 3 X 25 yards = 75 yards and

RJ runs 0.1 X 75 yards = 7.5 yards,

therefore Greg and RJ runs : Greg: 75 yards; RJ: 7.5 yards

matches with (A).