Questions: What is a like unit for fourths and fifths? 1 3/4-3/5 Twelfths Twentieths Thirtieths

What is a like unit for fourths and fifths? 1 3/4-3/5 Twelfths Twentieths Thirtieths
Transcript text: What is a like unit for fourths and fifths? \[ 1 \frac{3}{4}-\frac{3}{5} \] Twelfths Twentieths Thirtieths
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Solution

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Solution Steps

Step 1: Identify the Like Unit for Fourths and Fifths

To find a like unit for fourths and fifths, we need to determine the least common multiple (LCM) of the denominators 4 and 5. The LCM of 4 and 5 is 20. Therefore, the like unit for fourths and fifths is twentieths.

Step 2: Convert the Mixed Number to an Improper Fraction

The expression given is \(1 \frac{3}{4} - \frac{3}{5}\). First, convert the mixed number \(1 \frac{3}{4}\) to an improper fraction:

\[ 1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4} \]

Step 3: Subtract the Fractions

Now, subtract \(\frac{3}{5}\) from \(\frac{7}{4}\). To do this, convert both fractions to have a common denominator, which is 20:

\[ \frac{7}{4} = \frac{7 \times 5}{4 \times 5} = \frac{35}{20} \] \[ \frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20} \]

Now, subtract the fractions:

\[ \frac{35}{20} - \frac{12}{20} = \frac{35 - 12}{20} = \frac{23}{20} \]

Final Answer

The like unit for fourths and fifths is twentieths, and the result of the subtraction is:

\[ \boxed{\frac{23}{20}} \]

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