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Texas Go Math Grade 5 Lesson 3.6 Answer Key Decimal Multiplication.

## Texas Go Math Grade 5 Lesson 3.6 Answer Key Decimal Multiplication

**Investigate**

Materials; color pencils

The distance from Charlene’s house to her school is 0.8 mile.

Charlene rides her bike 7 tenths of the distance and walks the rest of the way.

How far does Charlene ride her bike to school?

You can use a decimal square to multiply decimals.

Multiply. 0.7 × 0.8

A. Draw a square with 10 equal columns.

What decimal value does each column represent? ___0.1_______

B. Using a color pencil, shade columns on the grid to represent the distance to Charlene’s school.

The distance to the school is 0.8 mile.

How many columns did you shade?____8______

C. Divide the square into 10 equal rows.

What decimal value does each row represent? ___0.1_______

D. Using a different color, shade rows that overlap the shaded columns to represent the distance to school that Charlene rides her bike.

- What part of the distance to school does Charlene ride her bike? _____0.56_____
- How many rows of the shaded columns did you shade? _____7_____

E. Count the number of squares that you shaded twice.

There are _____56_____ squares. Each square represents ____0.01______.

Record the value of the squares as the product. 0.7 × 0.8 = ___0.56_______

So, Charlene rides her bike for ___0.56______ mile.

Answer:

Charlene rides her bike for 0.56 miles,

Explanation:

A. Drawn a square with 10 equal columns as shown above,

The decimal value does each column represent is 0.1,

B. Using a color pencil, shade columns on the grid

to represent the distance to Charlene’s school,

The distance to the school is 0.8 mile, So columns shaded are 8,

C. Divided the square into 10 equal rows,

The decimal value does each row represent is 0.1,

D. Using a different color, shade rows that overlap

the shaded columns to represent the distance to school that Charlene rides her bike.

- The distance to school does Charlene ride her bike 0.56,
- Number of rows of the shaded columns did he shade is 7.

**Make Connections**

You can use decimal squares to multiply decimals greater than 1.

Multiply. 0.3 × 1.4

STEP 1:

Shade columns to represent 1.4. How many tenths are in 1.4?

STEP 2:

Shade rows that overlap the shaded columns to represent 0.3.

How many rows of the shaded columns did you shade? _____0.42_______

STEP 3:

Count the number of squares that you shaded twice. Record the product at the right.

0.3 × 1.4 = ______0.42_______

Answer:

The shaded columns is

Explanation:

Multiplying 0.3 × 1.4

STEP 1:

Shaded columns to represent 1.4,

STEP 2:

Shaded rows that overlap the shaded columns to represent 0.3,

Therefore rows of the shaded columns shaded are 0.42.

**Math Talk**

**Mathematical Processes**

Explain why the product is less than only one of the decimal factors.

Answer:

We are finding a fractional amount of a quantity,

Explanation:

When multiplying a number by a decimal less than one,

the product will be smaller than the number being multiplied.

This is because we are finding a fractional amount of a quantity.

For example, 0.1 x 0.8 = 0.08, because the question is asking us to

find one tenth of eight tenths.

**Share and Show**

.**Multiply. Use the decimal model.**

Question 1.

0.8 × 0.4 = ______0.32_______

Answer:

0.8 X 0.4 = 0.32,

Explanation:

Multiplying 0.8 × 0.4

STEP 1:

Shaded columns represents 0.8,

STEP 2:

Shaded rows that overlap the shaded columns to represent 0.4,

Therefore rows of the shaded columns shaded are 0.32.

Question 2.

0.1 × 0.7 = _____0.07_______

Answer:

0.1 X 0.7 = 0.07,

Explanation:

Multiplying 0.1 × 0.7

STEP 1:

Shaded columns represents 0.1,

STEP 2:

Shaded rows that overlap the shaded columns to represent 0.7,

Therefore rows of the shaded columns shaded are 0.32.

Question 3.

0.4 × 1.6 = _____0.64_______

Answer:

Explanation:

Multiplying 0.4 × 1.6

STEP 1:

Shaded columns represents 0.4,

STEP 2:

Shaded rows that overlap the shaded columns to represent 1.6,

Therefore rows of the shaded columns shaded are 0.64.

**Problem Solving**

**Sense or Nonsense?**

Question 4.

**Use Diagrams** Randy and Stacy used area models to find 0.3 of 0.5.

Both Randy’s and Stacy’s models are shown below.

Whose model makes sense? Whose model is nonsense?

Explain your reasoning below each model. Then record the correct answer.

0.3 × 0.5 = __0.15__________

Answer:

Randy’s model makes sense, Stacy’s model is nosense,

0.3 X 0.5 = 0.15,

Explanation:

Given Randy and Stacy used area models to find 0.3 of 0.5.

Both Randy’s and Stacy’s models are shown above,

Randy’s model makes sense which matches with 0.5,

Stacy’s model is nosense as it doesnot match with 0.3.

the correct answer is 0.3 X 0.5 = 0.15.

Question 5.

**H.O.T. Multi-Step** A large bottle contains 1.2 liters of olive oil.

A medium-sized bottle has 0.6 times the amount of olive oil as the large bottle.

How much more olive oil does the large bottle contain than the medium-sized bottle?

Answer:

0.48 liters more olive oil does the large bottle contain than the medium-sized bottle,

Explanation:

Given a large bottle contains 1.2 liters of olive oil,

A medium-sized bottle has 0.6 times the amount of olive oil as the large bottle,

therefore medium-sized bottle contains 1.2 liters X 0.6 = 0.72 liters,

Now more olive oil does the large bottle contain than the medium-sized bottle is

1.2 liters – 0.72 liters = 0.48 liters.

**Daily Assessment Task**

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

Question 6.

**Representations** Farmer Green grows 0.9 tons of grain each year.

Seven-tenths of the grain grown are barley. Which model shows

the amount of barley grown each year?

Answer:

Model (A) shows the amount of barley grown each year,

Explanation:

Given Farmer Green grows 0.9 tons of grain each year.

Seven-tenths of the grain grown are barley,

So farmer grows each year is 0.9 X 100 = 90 grains in that

seven-tenth is 90 X 7÷ 10 = 63, Now the model showing

the amount of barley grown each year is 63 matches with (A).

Question 7.

**Use Diagrams** What multiplication problem is modeled by the diagram?

(A) 1.3 × 0.3 = 1.03

(B) 0.7 × 0.3 = 1.03

(C) 1.1 × 0.3 = 0.3

(D) 0.3 × 1.1 = 0.33

Answer:

(C) 1.1 × 0.3 = 0.3,

Explanation:

Given multiplication problem modeled by the diagram as

frame 1- 10 X 10 = 100 ÷ 100 = 1,

and frame 2 as 1 X 10 ÷ 100 = 0.1,

therefore result matches with (C) 1.1 × 0.3 = 0.3.

Question 8.

**Multi-Step** An outdoor swimming race is 1.6 miles long.

Simon swims 8 tenths of the course, and his friend

Sheila swims 9 tenths of the course.

How much farther did Sheila swim?

(A) 0.16 mile

(B) 0.72 mile

(C) 0.1 mile

(D) 0.2 mile

Answer:

(C) 0.1 mile,

Explanation:

Given an outdoor swimming race is 1.6 miles long,

Simon swims 8 tenths of the course means 8÷ 10 = 0.8 and

his friendSheila swims 9 tenths of the course so 9 ÷ 10 = 0.9,

So much farther did Sheila swims is 0.9 – 0.8 = 0.1 which matches with (C).

**Texas Test Prep**

Question 9.

Alex is 1.3 meters tall. His brother, Raul, is 0.6 times as tall as Alex. How tall is Raul?

(A) 1.9 meters

(B) 0.7 meter

(C) 0.78 meter

(D) 7.8 meters

Answer:

(C) 0.78 meter,

Explanation:

Given Alex is 1.3 meters tall. His brother Raul is 0.6 times as tall as Alex.

Therefore Raul is 1.3 X 0.6 = 0.78 meters matches with (C).

### Texas Go Math Grade 5 Lesson 3.6 Homework and Practice Answer Key

**Multiply. Use the decimal model.**

Question 1.

0.6 × 0.9 = ___0.54______

Answer:

0.6 X 0.9 =

Explanation:

Multiplying 0.6 × 0.7

STEP 1:

Shaded columns represents 0.6,

STEP 2:

Shaded rows that overlap the shaded columns to represent 0.7,

Therefore rows of the shaded columns shaded are 0.54.

Question 2.

0.5 × 1.7 = ___0.85_______

Answer:

Explanation:

Multiplying 0.5 × 1.7

STEP 1:

Shaded columns represents 0.5,

STEP 2:

Shaded rows that overlap the shaded columns to represent 1.7,

Therefore rows of the shaded columns shaded are 0.85.

Question 3.

0.2 × 0.8 = ____0.16________

Answer:

0.2 X 0.8 = 0.16,

Explanation:

Multiplying 0.2 × 0.8

STEP 1:

Shaded columns represents 0.2,

STEP 2:

Shaded rows that overlap the shaded columns to represent 0.8,

Therefore rows of the shaded columns shaded are 0.16.

Question 4.

0.3 × 0.7 = _____0.21_______

Answer:

Explanation:

Multiplying 0.3 × 0.7

STEP 1:

Shaded columns represents 0.3,

STEP 2:

Shaded rows that overlap the shaded columns to represent 0.7,

Therefore rows of the shaded columns shaded are 0.21.

Question 5.

0.7 × 1.2 = _____0.84________

Answer:

0.7 X 1.2 = 0.84,

Explanation:

Multiplying 0.7 × 1.2

STEP 1:

Shaded columns represents 0.7,

STEP 2:

Shaded rows that overlap the shaded columns to represent 1.2,

Therefore rows of the shaded columns shaded are 0.84.

Question 6.

0.4 × 0.6 = ______0.24_______

Answer:

0.4 X 0.6 = 0.24,

Explanation:

Multiplying 0.4 × 0.6

STEP 1:

Shaded columns represents 0.4,

STEP 2:

Shaded rows that overlap the shaded columns to represent 0.6,

Therefore rows of the shaded columns shaded are 0.24.

Question 7.

0.8 × 0.8 = ______0.64_______

Answer:

0.8 X 0.8 = 0.64,

Explanation:

Multiplying 0.8 × 0.8

STEP 1:

Shaded columns represents 0.8,

STEP 2:

Shaded rows that overlap the shaded columns to represent 0.8,

Therefore rows of the shaded columns shaded are 0.64.

Question 8.

0.4 × 1.9 = ___0.76__________

Answer:

0.4 X 1.9 = 0.76,

Explanation:

Multiplying 0.4 × 1.9

STEP 1:

Shaded columns represents 0.4,

STEP 2:

Shaded rows that overlap the shaded columns to represent 1.9,

Therefore rows of the shaded columns shaded are 0.76.

Question 9.

0.9 × 0.7 = _____0.63________

Answer:

0.9 X 0.7 = 0.63,

Explanation:

Multiplying 0.9 × 0.7

STEP 1:

Shaded columns represents 0.9,

STEP 2:

Shaded rows that overlap the shaded columns to represent 0.7,

Therefore rows of the shaded columns shaded are 0.63.

**Problem Solving**

Question 10.

Nicole draws a mural on her wall. She begins by drawing a line that is 0.5 meter long.

She traces 2 tenths of the line with a purple pencil.

What is the length of the purple part of the line? Use the decimal model to solve.

Answer:

Explanation:

Given Nicole draws a mural on her wall. She begins by drawing a line that is 0.5 meter long.

She traces 2 tenths of the line with a purple pencil.

So, the length of the purple part of the line is 0.5 X 0.2 = 0.10,

Shown using the decimal model to solve the given length of the

purple part of the line.

Question 11.

Vanesh uses 1.6 gallons of paint for his bedroom walls.

For his study, he uses 0.7 times

the amount of paint as he uses for his bedroom.

How much paint does Vanesh use to paint his study?

Answer:

Explanation:

Given Vanesh uses 1.6 gallons of paint for his bedroom walls.

For his study, he uses 0.7 times the amount of paint as he uses for

his bedroom is 1.6 X 0.7 = 1.12 gallons of paint Vanesh used to paint his study.

**Lesson Check**

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

Question 12.

Alex’s tablet computer weighs 1.5 pounds. The weight of his calculator is 0.6 times

the weight of his tablet computer. What is the weight of Alex’s calculator?

(A) 2.1 pounds

(B) 1.56 pounds

(C) 0.3 pound

(D) 0.9 pound

Answer:

(D) 0.9 pound,

Explanation:

Given Alex’s tablet computer weighs 1.5 pounds. The weight of his calculator is 0.6 times

the weight of his tablet computer. So the weight of Alex’s

calculator is 1.5 pounds X 0.6 = 0.9 pound matches with (D).

Question 13.

Which equation is represented by the model below?

(A) 0.1 × 0.7 = 0.07

(B) 0.7 × 0.6 = 0.42

(C) 0.6 × 0.2 = 0.12

(D) 6.0 × 7.0 = 42.0

Answer:

(A) 0.1 × 0.7 = 0.07,

Explanation:

Given model above is 0.1 X 0.1 = 0.01,

So each block is 0.1 and we have 7 blocks like that

0.1 X 0.7 = 0.07 which matches with 0.07.

Question 14.

Sasha’s hundredths decimal model shows the product 0.72.

If she shaded 9 columns,

what factor represents the shaded rows?

(A) 0.6

(B) 0.9

(C) 0.7

(D) 0.8

Answer:

(D) 0.8,

Explanation:

Given Sasha’s hundredths decimal model shows the product 0.72.

If she shaded 9 columns factor represents

the shaded rowsis 0.72 ÷ 0.9 = 0.8 matches with (D).

Question 15.

The postman delivers a package and an envelope to Mr. O’Connor.

The package weighs 1.8 pounds. The envelope is 0.8 times the weight of the package.

What is the weight of the envelope?

(A) 1.44 pounds

(B) 1 pound

(C) 1.16 pounds

(D) 1.64 pounds

Answer:

(A) 1.44 pounds,

Explanation:

Given the postman delivers a package and an envelope to Mr. O’Connor.

The package weighs 1.8 pounds. The envelope is 0.8 times the weight of the package.

The weight of the envelope is 1.8 pounds X 0.8 = 1.44 pounds matches with (A).

Question 16.

**Multi-Step** Carter solves 0.5 × 0.5. Liam solves 0.4 × 1.4.

How much greater is Liam’s product than Carter’s product?

(A) 0.31

(B) 0.56

(C) 0.25

(D) 0.81

Answer:

(A) 0.31,

Explanation:

Given Carter solved 0.5 X 0.5 as = 0.25 and Liam solved greater as

0.4 X 1.4 = 0.56, Greater is Liam’s product than Carter’s product is

0.56 – 0.25 = 0.31 matches with (A).

Question 17.

**Multi-Step** Jessica makes punch for her party. She uses 1.6 liters of orange juice.

The amount of cranberry juice she uses is 0.5 times the amount of orange juice, and

the amount of apple juice is 0.5 times the amount of cranberry juice.

What is the total amount of juice in Jessica’s punch?

(A) 2.6 liters

(B) 2.65 liters

(C) 2.8 liters

(D) 1.8 liters

Answer:

(C) 2.8 liters,

Explanation:

Given Jessica makes punch for her party. She uses 1.6 liters of orange juice.

The amount of cranberry juice she uses is 0.5 times the amount of orange juice,

So cranberry juice Jessica makes is 1.6 liters X 0.5 = 0.8 liter + 1.6 liters = 2.4 liters and

the amount of apple juice is 0.5 times the amount of cranberry juice,

So the amount of apple juice is 0.8 liter X 0.5 = 0.4 liter + 2.4 liters = 2.8 liters of

cranberry juice is the total amount of juice in Jessica’s punch.