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Answer :
To convert [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex] to equivalent fractions with a denominator of 105, we can follow these steps:
1. Identify the Least Common Denominator (LCD):
The LCD given for these fractions is 105.
2. Convert [tex]\(\frac{13}{15}\)[/tex] to have a denominator of 105:
- First, find out how many times 15 goes into 105. To do this, divide 105 by 15:
[tex]\[
105 \div 15 = 7
\][/tex]
- Multiply both the numerator and the denominator of [tex]\(\frac{13}{15}\)[/tex] by 7:
[tex]\[
\frac{13}{15} = \frac{13 \times 7}{15 \times 7} = \frac{91}{105}
\][/tex]
3. Convert [tex]\(\frac{6}{7}\)[/tex] to have a denominator of 105:
- Similarly, find out how many times 7 goes into 105. Divide 105 by 7:
[tex]\[
105 \div 7 = 15
\][/tex]
- Multiply both the numerator and the denominator of [tex]\(\frac{6}{7}\)[/tex] by 15:
[tex]\[
\frac{6}{7} = \frac{6 \times 15}{7 \times 15} = \frac{90}{105}
\][/tex]
In summary, the equivalent fractions are:
[tex]\[
\frac{13}{15} = \frac{91}{105}, \quad \text{and} \quad \frac{6}{7} = \frac{90}{105}
\][/tex]
1. Identify the Least Common Denominator (LCD):
The LCD given for these fractions is 105.
2. Convert [tex]\(\frac{13}{15}\)[/tex] to have a denominator of 105:
- First, find out how many times 15 goes into 105. To do this, divide 105 by 15:
[tex]\[
105 \div 15 = 7
\][/tex]
- Multiply both the numerator and the denominator of [tex]\(\frac{13}{15}\)[/tex] by 7:
[tex]\[
\frac{13}{15} = \frac{13 \times 7}{15 \times 7} = \frac{91}{105}
\][/tex]
3. Convert [tex]\(\frac{6}{7}\)[/tex] to have a denominator of 105:
- Similarly, find out how many times 7 goes into 105. Divide 105 by 7:
[tex]\[
105 \div 7 = 15
\][/tex]
- Multiply both the numerator and the denominator of [tex]\(\frac{6}{7}\)[/tex] by 15:
[tex]\[
\frac{6}{7} = \frac{6 \times 15}{7 \times 15} = \frac{90}{105}
\][/tex]
In summary, the equivalent fractions are:
[tex]\[
\frac{13}{15} = \frac{91}{105}, \quad \text{and} \quad \frac{6}{7} = \frac{90}{105}
\][/tex]
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