Practicing the **Bridges in Mathematics Grade 4 Home Connections Answer Key** **Unit 3 Module 4 **will help students analyze their level of preparation.

## Bridges in Mathematics Grade 4 Home Connections Answer Key Unit 3 Module 4

**Bridges in Mathematics Grade 4 Home Connections Unit 3 Module 4 Session 2 Answer Key**

**Equal, Not Equal**

Question 1.

Fill in the bubble to show the equation that is correct.

1\(\frac{1}{4}\) + 1\(\frac{1}{4}\) = 2\(\frac{3}{4}\)

5\(\frac{2}{8}\) – 3\(\frac{1}{8}\) = 2\(\frac{3}{8}\)

4\(\frac{3}{12}\) + 2\(\frac{9}{12}\) = 6\(\frac{11}{12}\)

\(\frac{3}{10}\) + \(\frac{32}{100}\) = \(\frac{62}{100}\)

Answer:

The correct answer is \(\frac{3}{10}\) + \(\frac{32}{100}\) = \(\frac{62}{100}\).

Explanation:

Now let us check the given options.

1. 1\(\frac{1}{4}\) + 1\(\frac{1}{4}\) = 2\(\frac{3}{4}\)

\(\frac{5}{4}\) + \(\frac{5}{4}\)

Now add

\(\frac{10}{4}\) = 2\(\frac{2}{4}\)

That is 2\(\frac{2}{4}\) is not equal to 2\(\frac{3}{4}\).

Hence The correct answer is \(\frac{3}{10}\) + \(\frac{32}{100}\) = \(\frac{62}{100}\).

Question 2.

Fill in the bubble to show the equation that is not correct.

\(\frac{6}{10}\) + \(\frac{15}{100}\) = \(\frac{75}{100}\)

\(\frac{7}{8}\) – \(\frac{3}{8}\) = \(\frac{1}{3}\)

\(\frac{5}{12}\) + \(\frac{7}{12}\) = \(\frac{12}{12}\)

\(\frac{10}{12}\) – \(\frac{4}{12}\) = \(\frac{1}{2}\)

Answer:

The correct answer is \(\frac{7}{8}\) – \(\frac{3}{8}\) = \(\frac{1}{3}\).

Explanation:

From the given options let us check the below one

\(\frac{7}{8}\) – \(\frac{3}{8}\) = \(\frac{1}{3}\)

\(\frac{(7-3)}{8}\) = \(\frac{4}{8}\)

= \(\frac{1}{2}\)

\(\frac{1}{2}\) is not equal to \(\frac{1}{3}\)

Hence the given option is not correct.

Question 3.

Fill in the bubbles to show the more than one.) comparison statements that are correct. (There is more than one.)

0.3 < 0.03

\(\frac{2}{8}\) = \(\frac{1}{4}\)

0.6 > 0.49

0.7 = 0.70

Answer:

The correct answer is \(\frac{2}{8}\) = \(\frac{1}{4}\)

0.6 > 0.49 and 0.7 = 0.70

Explanation:

\(\frac{2}{8}\) = \(\frac{2}{8}\) is correct.

0.6 is greater than 0.49

0.7 is equal to 0.7

Question 4.

Fill in the bubbles to show the comparison statements that are not correct. (There is more than one.)

0.05 = 2

0.25 > 0.3

0.4 = \(\frac{60}{100}\)

\(\frac{60}{10}\) < \(\frac{60}{100}\)

Answer:

The answers that are not correct are 0.05 = 2, 0.25 > 0.3 and \(\frac{60}{10}\) < \(\frac{60}{100}\).

Explanation:

Let us check the first option

\(\frac{5}{100}\) = 0.05. So this option is not correct

0.25 is not greater than 0.3

\(\frac{60}{10}\) < \(\frac{60}{100}\)

6 < 0.6 is not correct.

Question 5.

Put the fractions and decimal numbers in the correct places on the number line:

Answer:

I have placed the fractions and decimal numbers in the correct places on the given number line.

Explanation:

Question 6.

Fill in the table below with a base ten model, decimal, or fraction. The first one has been done for you.

Answer:

I have filled the table below with a base ten model, decimal, or fraction.

Explanation:

Question 7.

Daniel collects baseball cards and keeps them in a special binder. Each page holds 9 baseball cards in a 3 × 3 array. The first page is \(\frac{4}{9}\) full. The second page is \(\frac{1}{3}\) full. If Daniel put all the cards onto just one page, what fraction of that page would be full? Use numbers, labeled sketches, or words to model and solve the problem.

Answer:

The fraction of that page would be \(\frac{7}{9}\) full.

Explanation:

Given,

Daniel collects baseball cards and keeps them in a special binder.

The first page is four ninths full \(\frac{4}{9}\) × 9 = 4

Thus, there are 4 cards on the first page.

The second page is one third full \(\frac{1}{3}\) ×9=3

Thus, there are 3 cards on the second page.

If daniel put all the cards onto just one page, then the total cards on one page= are 3+4=7

The fraction of that page would be \(\frac{7}{9}\) full.

Question 8.

**CHALLENGE** Sienna also collects baseball cards in a binder just like Daniel’s. Her last page was \(\frac{6}{9}\) full, but she gave \(\frac{1}{3}\) of those cards to Daniel.

a. What fraction of Sienna’s last page is full now? Use numbers, labeled sketches, or words to model and solve the problem.

Answer:

\(\frac{4}{9}\) full.

Explanation:

b. Can Daniel fit the cards from his first page, his second page, and the cards Sienna gave him all on one page in his binder? Use labeled sketches, numbers or words to show your thinking.

Answer:

yes, they will be exactly filled in on 1 page.

Explanation:

Yes, Daniel fit the cards from his first page, his second page, and the cards Sienna gave him all on one page in his binder.

**Bridges in Mathematics Grade 4 Home Connections Unit 3 Module 4 Session 3 Answer Key**

**Frankie’s Fractions & Decimals**

Solve the following problems. Use numbers, words, or labeled sketches to show your thinking.

Question 1.

Frankie’s dad made scrambled eggs for the family’s breakfast. He started with a full carton of 12 eggs. He used 8 of the eggs. What fraction of the carton of eggs did he use? Write at least two equivalent fractions.

Answer:

\(\frac{8}{12}\) = \(\frac{4}{9}\) = \(\frac{2}{3}\)

Explanation:

Given,

He started with a full carton of 12 eggs.

He used 8 of the eggs.

The fraction of the carton he used is \(\frac{8}{12}\)

= \(\frac{2}{3}\)

Question 2.

Frankie found a quarter on the sidewalk.

a. What fraction of a dollar did Frankie find? Write at least two equivalent fractions.

Answer:

\(\frac{1}{4}\) or \(\frac{25}{100}\).

Explanation:

The fraction of dollar Frankie found is \(\frac{1}{4}\).

The two equivalent fractions are \(\frac{1}{4}\) or \(\frac{25}{100}\).

b. Write the amount of money Frankie found as a decimal. ________

Answer:

0.25

Explanation:

The amount of money Frankie found as a decimal is 0.25

Question 3.

Frankie ate \(\frac{3}{8}\) of a granola bar. Her friend Pablo ate \(\frac{4}{8}\) of the granola bar.

a. What fraction of the granola bar did they eat in all?

Answer:

\(\frac{7}{8}\)

Explanation:

Frankie ate \(\frac{3}{8}\) of a granola bar.

Her friend Pablo ate \(\frac{4}{8}\)

\(\frac{3}{8}\) + \(\frac{4}{8}\)

\(\frac{7}{8}\)

b. How much of the granola bar is left?

Answer:

The \(\frac{1}{8}\) of the granola bar is left.

Explanation:

Given,

Frankie ate \(\frac{3}{8}\) of a granola bar.

Her friend Pablo ate \(\frac{4}{8}\)

\(\frac{4}{8}\) – \(\frac{3}{8}\)

\(\frac{1}{8}\)

Hence, the \(\frac{1}{8}\) of the granola bar is left.

Question 4.

Write each fraction as an equivalent fraction with 100 in the denominator.

ex

\(\frac{4}{10}\) = \(\frac{40}{100}\)

\(\frac{2}{10}\) = ________ \(\frac{6}{10}\) = ______ \(\frac{9}{10}\) = ________ \(\frac{5}{10}\) = _________

Answer:

\(\frac{20}{100}\), \(\frac{60}{100}\), \(\frac{90}{100}\), \(\frac{50}{100}\)

Explanation:

Given,

\(\frac{2}{10}\) = \(\frac{20}{100}\)

\(\frac{6}{10}\) = \(\frac{60}{100}\)

\(\frac{9}{10}\) = \(\frac{90}{100}\)

\(\frac{5}{10}\) = \(\frac{50}{100}\)

Question 5.

Add or Subtract.

a.

1\(\frac{2}{4}\) + 3\(\frac{2}{4}\) = _______

Answer:

The addition of the given fraction is 5.

Explanation:

Given,

1\(\frac{2}{4}\) + 3\(\frac{2}{4}\)

Convert them into fractions

\(\frac{6}{4}\) + \(\frac{14}{4}\)

Let the L.C.M be 4.

\(\frac{(6 +14)}{4}\)

\(\frac{20}{4}\)

5

b.

\(\frac{1}{5}\) + ________ = \(\frac{3}{5}\)

Answer:

The answer is \(\frac{2}{5}\).

Explanation:

Given,

\(\frac{1}{5}\) + ________ = \(\frac{3}{5}\)

Let the value to be calculated is x.

\(\frac{1}{5}\) + x = \(\frac{3}{5}\)

x = \(\frac{3}{5}\) – \(\frac{1}{5}\)

x = \(\frac{(3-1)}{5}\)

x = \(\frac{2}{5}\)

c.

\(\frac{4}{10}\) + \(\frac{23}{10}\) = _______

Answer:

\(\frac{27}{10}\).

Explanation:

Given,

\(\frac{4}{10}\) + \(\frac{23}{10}\)

L.C.M is 10

Now add the fractions

\(\frac{27}{10}\)

d.

\(\frac{50}{100}\) – \(\frac{2}{10}\) = _______

Answer:

The answer is 0.3

Explanation:

Given,

\(\frac{50}{100}\) – \(\frac{2}{10}\)

L.C.M of 10 and 100 is 100

\(\frac{(50 – 20)}{100}\)

\(\frac{30}{100}\)

\(\frac{3}{10}\) = 0.3

e.

\(\frac{10}{12}\) + ____ = \(\frac{4}{12}\)

Answer:

The answer is \(\frac{1}{2}\) = 0.5

Explanation:

Given,

\(\frac{10}{12}\) + ____ = \(\frac{4}{12}\)

Let the unknown be x

\(\frac{10}{12}\) + x = \(\frac{4}{12}\)

\(\frac{10}{12}\) – \(\frac{4}{12}\) = x

\(\frac{(10- 4)}{12}\) = x

\(\frac{6}{12}\) = \(\frac{1}{2}\)

x = \(\frac{1}{2}\)

f.

\(\frac{75}{100}\) – \(\frac{5}{10}\) = _______

Answer:

The answer is \(\frac{1}{4}\).

Explanation:

Given,

\(\frac{75}{100}\) – \(\frac{5}{10}\) = _______

The L.C.M of 10 and 100 is 100.

\(\frac{(75 – 50)}{100}\)

\(\frac{25}{100}\) = \(\frac{1}{4}\)

Hence the answer is \(\frac{1}{4}\).

Question 6.

Frankie wrote this equation on her paper during math class: 1\(\frac{2}{3}\) = \(\frac{3}{3}\) + \(\frac{2}{3}\).

a. Is Frankie’s equation true? ___________

Answer:

Yes, Frankie’s equation is true.

Explanation:

Given,

1\(\frac{2}{3}\) = \(\frac{3}{3}\) + \(\frac{2}{3}\).

Now let us prove the given equation

1\(\frac{2}{3}\) = \(\frac{5}{3}\)

\(\frac{3}{3}\) + \(\frac{2}{3}\)

1 + \(\frac{2}{3}\)

Let us add

\(\frac{(3 + 2)}{3}\)

\(\frac{5}{3}\)

Hence \(\frac{5}{3}\) = \(\frac{5}{3}\)

Therefore Frankie’s equation is true.

b. Write three more equations for 1\(\frac{2}{3}\) that are all true and all different. Use only fractions with a denominator of 3 in your equations.

1\(\frac{2}{3}\) = ____________________

1\(\frac{2}{3}\) = ____________________

1\(\frac{2}{3}\) = ____________________

Answer:

The equations are 1 + \(\frac{1}{3}\) + \(\frac{1}{3}\)

1 + \(\frac{2}{3}\)

\(\frac{2}{3}\) + \(\frac{3}{3}\)

Explanation:

Here we need to write three more equations for 1\(\frac{2}{3}\) that are all true and all different.

The first one is 1 + \(\frac{1}{3}\) + \(\frac{1}{3}\) which is equal to 1\(\frac{2}{3}\)

1 + \(\frac{2}{3}\) = 1\(\frac{2}{3}\)

\(\frac{2}{3}\) + \(\frac{3}{3}\) = \(\frac{2}{3}\)

Question 7.

Frankie’s teacher asked each of the students to cut a square of grid paper any size they wanted. Frankie cut out a 10 × 10 grid, and her friend Lori cut out an 8 × 8 grid. Then the teacher said, “Each grid you cut, no matter what size, has a value of 1. Please shade in exactly \(\frac{1}{4}\) of your grid.”

a. Here are the grids Frankie and Lori cut out. Shade in exactly \(\frac{1}{4}\) of each grid.

Answer:

b. How many little squares did you shade in on Frankie’s grid? ____________

How many little squares did you shade in on Lori’s grid? ____________

Answer:

The number of little squares we shaded on Frankie’s grid is 25.

The number of little squares we shaded on Lori’s grid is 16.

c. Why did you need to shade in a different number of squares on each grid, even though you shaded in one-fourth on both of them?

Answer:

We need to shade in a different number of squares on each grid is because the number of little squares shaded is different from each grid