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Sagot :
To solve the fraction operation [tex]\(\frac{3}{8} + \left( -\frac{15}{52} \right) \)[/tex] and express the result as a mixed number, follow these steps:
1. Find a Common Denominator:
To add the fractions, we need a common denominator. The denominators are 8 and 52. The least common multiple (LCM) of 8 and 52 is 104.
2. Express Each Fraction with a Common Denominator:
Convert both fractions to have the denominator 104.
For [tex]\(\frac{3}{8}\)[/tex]:
[tex]\[ \frac{3}{8} = \frac{3 \times 13}{8 \times 13} = \frac{39}{104} \][/tex]
For [tex]\(-\frac{15}{52}\)[/tex]:
[tex]\[ -\frac{15}{52} = -\frac{15 \times 2}{52 \times 2} = -\frac{30}{104} \][/tex]
3. Add the Fractions:
Now, add the two fractions together:
[tex]\[ \frac{39}{104} + \left(-\frac{30}{104}\right) = \frac{39 - 30}{104} = \frac{9}{104} \][/tex]
4. Convert to a Mixed Number:
Since [tex]\(\frac{9}{104}\)[/tex] is a proper fraction (where the numerator is less than the denominator), it cannot be expressed as a mixed number with a whole part different from zero.
Nevertheless, for completeness:
- A mixed number format includes a whole number part and a fractional part. Since the whole number part is zero:
[tex]\[ 0 \frac{9}{104} \rightarrow (0, \frac{9}{104}) \][/tex]
5. Simplify the Fraction (if needed):
The fraction [tex]\(\frac{9}{104}\)[/tex] is already in its simplest form because there are no common factors, other than 1, between 9 (numerator) and 104 (denominator).
6. Final Answer:
The sum of [tex]\(\frac{3}{8} + \left( -\frac{15}{52} \right) \)[/tex] is:
[tex]\[ \frac{9}{104}, \text{ or in mixed number form: } 0 \frac{9}{104} \][/tex]
Therefore, the solution to [tex]\(\frac{3}{8} + \left( -\frac{15}{52} \right)\)[/tex] as a mixed number in lowest terms is [tex]\(\left(0, \frac{9}{104}\right)\)[/tex].
1. Find a Common Denominator:
To add the fractions, we need a common denominator. The denominators are 8 and 52. The least common multiple (LCM) of 8 and 52 is 104.
2. Express Each Fraction with a Common Denominator:
Convert both fractions to have the denominator 104.
For [tex]\(\frac{3}{8}\)[/tex]:
[tex]\[ \frac{3}{8} = \frac{3 \times 13}{8 \times 13} = \frac{39}{104} \][/tex]
For [tex]\(-\frac{15}{52}\)[/tex]:
[tex]\[ -\frac{15}{52} = -\frac{15 \times 2}{52 \times 2} = -\frac{30}{104} \][/tex]
3. Add the Fractions:
Now, add the two fractions together:
[tex]\[ \frac{39}{104} + \left(-\frac{30}{104}\right) = \frac{39 - 30}{104} = \frac{9}{104} \][/tex]
4. Convert to a Mixed Number:
Since [tex]\(\frac{9}{104}\)[/tex] is a proper fraction (where the numerator is less than the denominator), it cannot be expressed as a mixed number with a whole part different from zero.
Nevertheless, for completeness:
- A mixed number format includes a whole number part and a fractional part. Since the whole number part is zero:
[tex]\[ 0 \frac{9}{104} \rightarrow (0, \frac{9}{104}) \][/tex]
5. Simplify the Fraction (if needed):
The fraction [tex]\(\frac{9}{104}\)[/tex] is already in its simplest form because there are no common factors, other than 1, between 9 (numerator) and 104 (denominator).
6. Final Answer:
The sum of [tex]\(\frac{3}{8} + \left( -\frac{15}{52} \right) \)[/tex] is:
[tex]\[ \frac{9}{104}, \text{ or in mixed number form: } 0 \frac{9}{104} \][/tex]
Therefore, the solution to [tex]\(\frac{3}{8} + \left( -\frac{15}{52} \right)\)[/tex] as a mixed number in lowest terms is [tex]\(\left(0, \frac{9}{104}\right)\)[/tex].
Answer:
hello
Step-by-step explanation:
3/8 +(-15/52)
=13x3/8x13 - 2x15/52x2
=39/104 - 30/104
=9/104
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