Section C: Practice Problems Addition of Tenths and Hundredths

Section Summary

Details

In this section, we learned more ways to add fractions and to solve problems that involve adding, subtracting, and multiplying fractions.

We started by adding tenths and hundredths, using what we know about equivalent fractions. For example, to find the sum of $\frac{4}{10}$ and $\frac{30}{100}$ , we can:

Write $\frac{4}{10}$ as $\frac{40}{100}$ , and then find $\frac{40}{100} + \frac{30}{100}$ , or
Write $\frac{30}{100}$ as $\frac{3}{10}$ , and then find $\frac{4}{10} + \frac{3}{10}$ .

We learned that when adding a few fractions, it may help to rearrange or group them. For instance:

$\frac{6}{100} + \frac{2}{10} + \frac{74}{100}$ can be rearranged as $\frac{6}{100} + \frac{74}{100} + \frac{2}{10}$ .
Next, the hundredths can be added first, giving $\frac{80}{100} + \frac{2}{10}$ .
Then, we can write an equivalent fraction for $\frac{80}{100}$ and find $\frac{8}{10} + \frac{2}{10}$ , or write an equivalent fraction for $\frac{2}{10}$ and find $\frac{80}{100} + \frac{20}{100}$ .

Problem 1 (Lesson 15)

Andre is building a tower out of different foam blocks. These blocks come in three different thicknesses: $\frac{1}{2}$ -foot, $\frac{1}{4}$ -foot, and $\frac{1}{8}$ -foot.

Andre stacks two $\frac{1}{2}$ -foot blocks, two $\frac{1}{4}$ -foot blocks, and two $\frac{1}{8}$ -foot blocks to create a tower. What will the height of the tower be in feet? Explain or show how you know.

Problem 2 (Lesson 16)

Find the value of each of the following sums. Show your reasoning. Use number lines if you find them helpful.

$\frac{1}{10} + \frac{3}{100}$
$\frac{24}{100} + \frac{4}{10}$
$\frac{7}{10} + \frac{13}{100}$

Problem 3 (Lesson 17)

Is the value of each expression greater than, less than or equal to 1? Explain how you know.

$\frac{3}{10} + \frac{7}{100}$
$\frac{13}{10} + \frac{7}{100}$
$\frac{30}{100} + \frac{7}{10}$

Problem 4 (Lesson 18)

Diego and Lin continued to play with their coins.

Diego said that he has exactly 3 coins whose thickness adds up to $\frac{50}{100}$ cm. What coins does Diego have? Explain or show your reasoning.

coin	thickness in cm
1 centavo	$\frac{12}{100}$
10 centavos	$\frac{22}{100}$
1 peso	$\frac{16}{100}$
2 pesos	$\frac{14}{100}$
5 pesos	$\frac{2}{10}$
20 pesos	$\frac{25}{100}$

Problem 5 (Exploration)

A chocolate cake recipe calls for 2 cups of flour. You gather your measuring cups and notice you have these sizes: $\frac{1}{2}$ cup, $\frac{1}{3}$ cup, $\frac{1}{4}$ cup, and $\frac{1}{6}$ cup.

What are the different ways you could use all 4 measuring cups to measure 2 cups of flour?
What are other ways you could use just some of the 4 measuring cups to measure exactly 2 cups of flour?

Problem 6 (Exploration)

A dime is worth $\frac{1}{10}$ of a dollar and a penny is worth $\frac{1}{100}$ of a dollar.

If I have $\frac{89}{100}$ of a dollar, how many different combinations of dimes and pennies could I have? Use equations to show your reasoning.
A nickel is worth $\frac{5}{100}$ of a dollar. How many different combinations of dimes, nickels and pennies could I have if I still have $\frac{89}{100}$ of a dollar? Use equations to show your reasoning.