Example 1: Find \(\frac{48}{100} + \frac{4}{10}\).
Solution:
Step 1: Fractions to be added need to have the same denominators. Let’s use equivalent fractions to do that. Here, we will find the equivalent fraction of \(\frac{4}{10}\).
\(\frac{48}{100} + \frac{4}{10} = \frac{48}{100} + \frac{4 \times 10}{10 \times 10} = \frac{48}{100} + \frac{40}{100}\)
Step 2: Add the numerators.
\(\frac{48 + 40}{100} = \frac{88}{100}\)
Therefore, \(\frac{48}{100} + \frac{4}{10} = \frac{88}{100}\)
Example 2: Find 0.309 + 0.41 + 0.1.
Solution:
Step 1: Write the decimal numbers as fractions.
\(0.309 + 0.41 + 0.1 = \frac{309}{1000} + \frac{41}{100} + \frac{1}{10}\)
Step 2: Fractions to be added need to have the same denominators. Let’s use equivalent fractions to do that,
\(\frac{309}{1000} + \frac{41}{100} + \frac{1}{10} = \frac{309}{1000} + \frac{41 \times 10}{100 \times 10} + \frac{1 \times 100}{10 \times 100} = \frac{309}{1000} + \frac{410}{1000} + \frac{100}{1000}\)
Step 3: Add the numerators.
\(\frac{309 + 410 + 100}{1000} + \frac{819}{1000}\)
Step 4: Write the sum as a decimal number.
\(\frac{819}{1000} = 0.819\)
Therefore, 0.309 + 0.41 + 0.1 = 0.819
Example 3:
Andrew has three nickels, a dime, and a rare half-dollar coin. Find the total amount of money using fractions.
Solution:
1 cent is one-hundredth of a dollar. A nickel is worth 5 cents.
Value of 1 nickel \(¢5 = $5 \times \frac{1}{100} = $\frac{5}{100}\)
Value of 3 nickels \( = $3 \times \frac{5}{100} = $\frac{15}{100}\)
Value of a dime is ten cents or a tenth of a dollar.
Value of 1 dime\( = ¢10 = $10 \times \frac{1}{100} = $\frac{1}{10}\)
Value of half-dollar coin \( = $\frac{1}{2}\)
Total amount \( = $\frac{15}{100} + $\frac{1}{10} + $\frac{1}{2}\)
\( = $\frac{15}{100} + $\frac{1 \times 10}{10 \times 10} + $\frac{1 \times 50}{2 \times 50}\)
\( = $\frac{15}{100} + $\frac{10}{100} + $\frac{50}{100}\)
\( = $(\frac{15 + 10 + 50}{100})\)
\( = $\frac{75}{100}\)
Therefore, Andrew has \(\frac{75}{100}\)dollars or 75 cents.
Example 4:
Tina bought three chocolates whose prices are $0.35, $0.25, and $0.2. Find the amount of money she paid for these chocolates.
Solution:
To find the total amount she spent on chocolate, we need to find $0.35 + $0.25 + $0.2 by following these steps.
Step 1: Write the decimal numbers as fractions.
\(0.35 + 0.25 + 0.2 = \frac{35}{100} + \frac{25}{100} + \frac{2}{10}\)
Step 2: Fractions to be added need to have the same denominators. Let’s use equivalent fractions to do that,
\(\frac{35}{100} + \frac{25}{100} + \frac{2}{10} = \frac{35}{100} +\frac{25}{100} + \frac{2 \times 10}{10 \times 10} = \frac{35}{100} + \frac{25}{100} + \frac{20}{100}\)
Step 3: Add the numerators.
\(\frac{35 + 25 + 20}{100 = \frac{80}{100}\)
Step 4: Write the sum as a decimal number.
\(\frac{80}{100} = 0.8\)
Example 5:
Observe the model and write the equivalent decimal number.
Solution:
Let’s express the picture using actual numbers.
\(5 + \frac{3}{10} + \frac{43}{100}\)
Now, let’s add these fractions to get the final sum.
\(5 + \frac{3}{10} + \frac{43}{100} = 5 + \frac{30}{100} + \frac{43}{100}\)
\( = 5 + \frac{30+43}{100}\)
\( = 5 + \frac{73}{100}\)
= 5 + 0.73
= 5.73
