Answer :
To tackle the subtraction of the two fractions [tex]\(-\frac{4}{9}\)[/tex] and [tex]\(-\frac{14}{15}\)[/tex], follow these steps:
1. Identify the Fractions:
- The problem asks you to subtract [tex]\(-\frac{4}{9}\)[/tex] and [tex]\(-\frac{14}{15}\)[/tex].
2. Rewrite the Expression:
- Subtracting these fractions can be seen as: [tex]\(-\frac{4}{9} - (-\frac{14}{15})\)[/tex].
- This is equivalent to adding the opposite: [tex]\(-\frac{4}{9} + \frac{14}{15}\)[/tex].
3. Find a Common Denominator:
- To add fractions, they must have the same denominator. The denominators are 9 and 15.
- The least common denominator (LCD) of 9 and 15 is 45.
4. Convert Each Fraction to Have the Common Denominator:
- Convert [tex]\(-\frac{4}{9}\)[/tex]:
[tex]\[
-\frac{4}{9} = -\frac{4 \times 5}{9 \times 5} = -\frac{20}{45}
\][/tex]
- Convert [tex]\(\frac{14}{15}\)[/tex]:
[tex]\[
\frac{14}{15} = \frac{14 \times 3}{15 \times 3} = \frac{42}{45}
\][/tex]
5. Add the Equivalent Fractions:
- Now, add the two fractions:
[tex]\[
-\frac{20}{45} + \frac{42}{45} = \frac{-20 + 42}{45} = \frac{22}{45}
\][/tex]
6. Simplify if Needed:
- [tex]\(\frac{22}{45}\)[/tex] is already in its simplest form since 22 and 45 have no common factors other than 1.
Thus, the answer to the subtraction [tex]\(-\frac{4}{9} - \frac{14}{15}\)[/tex] is [tex]\(\frac{22}{45}\)[/tex].
1. Identify the Fractions:
- The problem asks you to subtract [tex]\(-\frac{4}{9}\)[/tex] and [tex]\(-\frac{14}{15}\)[/tex].
2. Rewrite the Expression:
- Subtracting these fractions can be seen as: [tex]\(-\frac{4}{9} - (-\frac{14}{15})\)[/tex].
- This is equivalent to adding the opposite: [tex]\(-\frac{4}{9} + \frac{14}{15}\)[/tex].
3. Find a Common Denominator:
- To add fractions, they must have the same denominator. The denominators are 9 and 15.
- The least common denominator (LCD) of 9 and 15 is 45.
4. Convert Each Fraction to Have the Common Denominator:
- Convert [tex]\(-\frac{4}{9}\)[/tex]:
[tex]\[
-\frac{4}{9} = -\frac{4 \times 5}{9 \times 5} = -\frac{20}{45}
\][/tex]
- Convert [tex]\(\frac{14}{15}\)[/tex]:
[tex]\[
\frac{14}{15} = \frac{14 \times 3}{15 \times 3} = \frac{42}{45}
\][/tex]
5. Add the Equivalent Fractions:
- Now, add the two fractions:
[tex]\[
-\frac{20}{45} + \frac{42}{45} = \frac{-20 + 42}{45} = \frac{22}{45}
\][/tex]
6. Simplify if Needed:
- [tex]\(\frac{22}{45}\)[/tex] is already in its simplest form since 22 and 45 have no common factors other than 1.
Thus, the answer to the subtraction [tex]\(-\frac{4}{9} - \frac{14}{15}\)[/tex] is [tex]\(\frac{22}{45}\)[/tex].
