All the solutions provided in **McGraw Hill My Math Grade 4 Answer Key PDF Chapter 10 Lesson 6 Use Place Value and Models to Add **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 10 Lesson 6 Use Place Value and Models to Add

**Math in My World**

**Example 1**

Denny walked \(\frac{3}{10}\) mile to the post office. Then he walked \(\frac{5}{100}\) mile to the grocery store. How far did he walk in all? Write the answer as a fraction with a denominator of 100 and as a decimal.

Use a model to show \(\frac{3}{10}\) + \(\frac{5}{100}\).

1. Write \(\frac{3}{10}\) as a fraction with a denominator of 100.

The decimal models show that \(\frac{3}{10}\) = \(\frac{30}{100}\).

2. Add like fractions.

3. Write the sum as a decimal.

Think of \(\frac{35}{100}\) as thirty-five hundredths. So, \(\frac{35}{100}\) = 0.35.

So, \(\frac{3}{10}\) + \(\frac{5}{100}\) = \(\frac{35}{100}\), or _______________.

Denny walked \(\frac{35}{100}\), or 0.35, mile in all.

Answer: In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{3}{10}\) by 10. Then, it becomes \(\frac{30}{100}\)

Now, \(\frac{30}{100}\) + \(\frac{5}{100}\) = \(\frac{35}{100}\)

\(\frac{35}{100}\) = 0.35 in decimal

**Example 2**

Find \(\frac{4}{10}\) + \(\frac{22}{100}\). Write the sum as a fraction with a denominator of 100 and as a decimal.

1. Write \(\frac{4}{10}\) as a fraction with a denominator of 100.

The decimal models show that \(\frac{4}{10}\) = \(\frac{40}{100}\).

2. Add like fractions.

3. Write the sum as a decimal.

Think of \(\frac{62}{100}\) as sixty-two hundredths. So, \(\frac{62}{100}\) = 0.62.

So, \(\frac{4}{10}\) + \(\frac{22}{100}\) = \(\frac{62}{100}\) or _____________.

Check:

The models show that \(\frac{4}{10}\) + \(\frac{22}{100}\) = \(\frac{62}{100}\) or 0.62

Answer: In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{4}{10}\) by 10. Then, it becomes \(\frac{40}{100}\)

Now, \(\frac{40}{100}\) + \(\frac{22}{100}\) = \(\frac{62}{100}\)

\(\frac{62}{100}\) = 0.62 in decimal

**Talk Math**

In Example 2, why was \(\frac{4}{10}\) written as \(\frac{40}{100}\)?

Answer: For calculating sum of two fractions, we need like fractions. In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{4}{10}\) by 10. Then, it becomes \(\frac{40}{100}\). Now, as the denominators are same, we can simply perform addition of numerators.

**Guided Practice**

**Add. Write each sum as a fraction with a denominator of 100 and as a decimal.**

Question 1.

\(\frac{5}{10}\) + \(\frac{1}{100}\) = _______________

Answer: \(\frac{51}{100}\) = 0.51

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{5}{10}\) by 10. Then, it becomes \(\frac{50}{100}\)

Now, \(\frac{50}{100}\) + \(\frac{1}{100}\) = \(\frac{51}{100}\)

\(\frac{51}{100}\) = 0.51 in decimal

Question 2.

\(\frac{7}{10}\) + \(\frac{13}{100}\) = ________________

Answer: \(\frac{83}{100}\) = 0.83

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{7}{10}\) by 10. Then, it becomes \(\frac{70}{100}\)

Now, \(\frac{70}{100}\) + \(\frac{13}{100}\) = \(\frac{83}{100}\)

\(\frac{83}{100}\) = 0.83 in decimal

**Independent Practice**

**Shade the models to find each sum. Write the sum as a fraction with a denominator of 100.**

Question 3.

\(\frac{2}{10}\) + \(\frac{37}{100}\) = ______________

Answer: \(\frac{57}{100}\) = 0.57

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{2}{10}\) by 10. Then, it becomes \(\frac{20}{100}\)

Now, \(\frac{20}{100}\) + \(\frac{37}{100}\) = \(\frac{57}{100}\)

\(\frac{57}{100}\) = 0.57 in decimal

Question 4.

\(\frac{7}{10}\) + \(\frac{11}{100}\) = ________________

Answer: \(\frac{81}{100}\) = 0.81

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{7}{10}\) by 10. Then, it becomes \(\frac{70}{100}\)

Now, \(\frac{70}{100}\) + \(\frac{11}{100}\) = \(\frac{81}{100}\)

\(\frac{81}{100}\) = 0.81 in decimal

**Add. Write each sum as a fraction with a denominator of 100 and as a decimal.**

Question 5.

\(\frac{6}{10}\) + \(\frac{24}{100}\) = _________________

Answer: \(\frac{84}{100}\) = 0.84

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{6}{10}\) by 10. Then, it becomes \(\frac{60}{100}\)

Now, \(\frac{60}{100}\) + \(\frac{24}{100}\) = \(\frac{84}{100}\)

\(\frac{84}{100}\) = 0.84 in decimal

Question 6.

\(\frac{5}{10}\) + \(\frac{21}{100}\) = _________________

Answer: \(\frac{71}{100}\) = 0.71

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{5}{10}\) by 10. Then, it becomes \(\frac{50}{100}\)

Now, \(\frac{50}{100}\) + \(\frac{21}{100}\) = \(\frac{71}{100}\)

\(\frac{71}{100}\) = 0.71 in decimal

Question 7.

\(\frac{3}{10}\) + \(\frac{65}{100}\) = _________________

Answer: \(\frac{95}{100}\) = 0.95

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{3}{10}\) by 10. Then, it becomes \(\frac{30}{100}\)

Now, \(\frac{30}{100}\) + \(\frac{65}{100}\) = \(\frac{95}{100}\)

\(\frac{95}{100}\) = 0.95 in decimal

Question 8.

\(\frac{1}{10}\) + \(\frac{52}{100}\) = _________________

Answer: \(\frac{62}{100}\) = 0.62

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{1}{10}\) by 10. Then, it becomes \(\frac{10}{100}\)

Now, \(\frac{10}{100}\) + \(\frac{52}{100}\) = \(\frac{62}{100}\)

\(\frac{62}{100}\) = 0.62 in decimal

Question 9.

\(\frac{8}{10}\) + \(\frac{17}{100}\) = _________________

Answer: \(\frac{97}{100}\) = 0.97

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{8}{10}\) by 10. Then, it becomes \(\frac{80}{100}\)

Now, \(\frac{80}{100}\) + \(\frac{17}{100}\) = \(\frac{97}{100}\)

\(\frac{97}{100}\) = 0.97 in decimal

Question 10.

\(\frac{2}{10}\) + \(\frac{42}{100}\) = _________________

Answer: \(\frac{62}{100}\) = 0.62

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{2}{10}\) by 10. Then, it becomes \(\frac{20}{100}\)

Now, \(\frac{20}{100}\) + \(\frac{42}{100}\) = \(\frac{62}{100}\)

\(\frac{62}{100}\) = 0.62 in decimal

Question 11.

\(\frac{6}{10}\) + \(\frac{19}{100}\) = _________________

Answer: \(\frac{79}{100}\) = 0.79

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{6}{10}\) by 10. Then, it becomes \(\frac{60}{100}\)

Now, \(\frac{60}{100}\) + \(\frac{19}{100}\) = \(\frac{79}{100}\)

\(\frac{79}{100}\) = 0.79 in decimal

Question 12.

\(\frac{3}{10}\) + \(\frac{35}{100}\) = _________________

Answer: \(\frac{65}{100}\) = 0.65

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{3}{10}\) by 10. Then, it becomes \(\frac{30}{100}\)

Now, \(\frac{30}{100}\) + \(\frac{35}{100}\) = \(\frac{65}{100}\)

\(\frac{65}{100}\) = 0.65 in decimal

**Problem Solving**

**For Exercises 13 and 14, write each answer as a fraction with a denominator of 100 and as a decimal.**

Question 13.

Marisa walked her dog \(\frac{1}{10}\) mile on Saturday and \(\frac{55}{100}\) mile on Sunday. How far did she walk her

dog in all?

Answer: \(\frac{65}{100}\) = 0.65

Number of miles walked by Marisa’ dog on saturday = \(\frac{1}{10}\) mile

Number of miles walked by Marisa’ dog on sunday= \(\frac{55}{100}\) mile

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{1}{10}\) by 10. Then, it becomes \(\frac{10}{100}\)

Now, \(\frac{10}{100}\) + \(\frac{55}{100}\) = \(\frac{65}{100}\)

Therefore, total miles walked by Marisa’s dog = \(\frac{65}{100}\) = 0.65 in decimal

Question 14.

Nevaeh read \(\frac{2}{10}\) of a book. Her older sister read \(\frac{60}{100}\) of the same book. How much of the book did they read altogether?

Answer: \(\frac{80}{100}\) = 0.80 = 0.8

Nevaeh read \(\frac{2}{10}\) of a book

Her older sister read \(\frac{60}{100}\) of the same book.

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{2}{10}\) by 10. Then, it becomes \(\frac{20}{100}\)

Now, \(\frac{20}{100}\) + \(\frac{60}{100}\) = \(\frac{80}{100}\)

Therefore, they read \(\frac{80}{100}\) of the book altogether, which is 0.80 in decimal

Question 15.

**Mathematical PRACTICE** Use Algebra Find the unknown in the number sentence

Answer: 11

\(\frac{3}{10}\) + \(\frac{?}{100}\) = \(\frac{41}{100}\)

\(\frac{?}{100}\) = \(\frac{41}{100}\) – \(\frac{3}{10}\)

Make sure all the values in the denominators are same. In order to make the denominators same for calculation, represent \(\frac{3}{10}\) in the form of denominator 100 by multiplying and dividing it with 10. Then, it becomes \(\frac{30}{100}\)

Now, replace \(\frac{3}{10}\) with \(\frac{30}{100}\) in the equation for calculation

\(\frac{?}{100}\) = \(\frac{41}{100}\) – \(\frac{30}{100}\)

= \(\frac{41 – 30}{100}\)

= \(\frac{11}{100}\)

Therefore, the missing number is 11 in the given equation.

**HOT Problems**

Question 16.

**Mathematical PRACTICE** Explain to a Friend Refer to Exercise 15. Explain to a friend or classmate how you found the unknown.

Answer: To find the unknown number, simplify the steps in the following way.

Step 1: Move \(\frac{3}{10}\) from Left side of the equation to right side, in order to make unknown equation as subject.

\(\frac{?}{100}\) = \(\frac{41}{100}\) – \(\frac{3}{10}\)

Step 2: Make sure all the values in the denominators are same. In order to make the denominators same for calculation, represent \(\frac{3}{10}\) in the form of denominator 100 by multiplying and dividing it with 10. Then, it becomes \(\frac{30}{100}\)

Step 3: Now, replace \(\frac{3}{10}\) with \(\frac{30}{100}\) in the equation for calculation

latex]\frac{?}{100}[/latex] = \(\frac{41}{100}\) – \(\frac{30}{100}\)

= \(\frac{41 – 30}{100}\)

= \(\frac{11}{100}\)

Step 4: Now, compare the both equations on left and right side for the conclusion.

Therefore, the missing number is 11 in the given equation.

Question 17.

**Building on the Essential Question** How does place value help when adding \(\frac{1}{10}\) and \(\frac{1}{100}\)?

Answer: \(\frac{1}{10}\) can be noted as 1 tenth, which is 0.1 and \(\frac{1}{100}\) can be noted as 1 hundredth, which is 0.01.

Place value represents the position of a digit in the number. The digits followed by decimal point are noted in tenth’s place, hundredth’s place, thousandth’s place and so on.

### McGraw Hill My Math Grade 4 Chapter 10 Lesson 6 My Homework Answer Key

**Practice**

**Add. Write each sum as a fraction with a denominator of 100 and as a decimal.**

Question 1.

\(\frac{2}{10}\) + \(\frac{33}{100}\) = ________________

Answer: \(\frac{53}{100}\) = 0.53

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{2}{10}\) by 10. Then, it becomes \(\frac{20}{100}\)

Now, \(\frac{20}{100}\) + \(\frac{33}{100}\) = \(\frac{53}{100}\)

\(\frac{53}{100}\) = 0.53 in decimal

Question 2.

\(\frac{6}{10}\) + \(\frac{25}{100}\) = ________________

Answer: \(\frac{85}{100}\) = 0.85

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{6}{10}\) by 10. Then, it becomes \(\frac{60}{100}\)

Now, \(\frac{60}{100}\) + \(\frac{25}{100}\) = \(\frac{85}{100}\)

\(\frac{85}{100}\) = 0.85 in decimal

Question 3.

\(\frac{4}{10}\) + \(\frac{17}{100}\) = ________________

Answer: \(\frac{57}{100}\) = 0.57

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{4}{10}\) by 10. Then, it becomes \(\frac{40}{100}\)

Now, \(\frac{40}{100}\) + \(\frac{17}{100}\) = \(\frac{57}{100}\)

\(\frac{57}{100}\) = 0.57 in decimal

Question 4.

\(\frac{2}{10}\) + \(\frac{22}{100}\) = ________________

Answer: \(\frac{42}{100}\) = 0.42

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{2}{10}\) by 10. Then, it becomes \(\frac{20}{100}\)

Now, \(\frac{20}{100}\) + \(\frac{22}{100}\) = \(\frac{42}{100}\)

\(\frac{42}{100}\) = 0.42 in decimal

**Problem Solving**

**Mathematical PRACTICE** Use Number Sense Write each answer as a fraction with a denominator of 100 and as a decimal.

Question 5.

An insect’s body is \(\frac{1}{10}\) inch long. The insect’s head is \(\frac{3}{100}\) inch long. What is the combined length of the insect’s body and head?

Answer: \(\frac{13}{100}\) = 0.13

Length of insect’s body = \(\frac{1}{10}\) inch

Length of insect’s head = \(\frac{3}{100}\) inch

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{1}{10}\) by 10. Then, it becomes \(\frac{10}{100}\)

Now, \(\frac{10}{100}\) + \(\frac{3}{100}\) = \(\frac{13}{100}\)

Therefore, total length of insect = \(\frac{13}{100}\) = 0.13 in decimal

Question 6.

Makenna rode her bike \(\frac{6}{10}\) mile in the morning and \(\frac{23}{100}\) mile in the afternoon. How far did she ride her bike in all?

Answer: \(\frac{83}{100}\) = 0.83

Makenna rode her bike \(\frac{6}{10}\) mile in the morning and \(\frac{23}{100}\) mile in the afternoon.

In order to make the denominators of both fractions same for addition, multiply and divide \(\frac{6}{10}\) by 10. Then, it becomes \(\frac{60}{100}\)

Now, \(\frac{60}{100}\) + \(\frac{23}{100}\) = \(\frac{83}{100}\)

Therefore, total distance Makenna rode her bike = \(\frac{83}{100}\) = 0.83 in decimal

**Test Practice**

Question 7.

Which addition expression describes the model at the right?

(A) \(\frac{70}{10}\) + \(\frac{18}{100}\)

(B) \(\frac{7}{10}\) + \(\frac{18}{100}\)

(C) \(\frac{7}{100}\) + \(\frac{18}{100}\)

(D) \(\frac{7}{10}\) + \(\frac{18}{10}\)

Answer: B (\(\frac{7}{10}\) + \(\frac{18}{100}\))

As, there are 7 blue parts colored out of 10, which is \(\frac{7}{10}\). Similarly, there are 18 colored parts out of 100, which is \(\frac{18}{100}\)