Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Sure, let’s solve the given mathematical expression step-by-step.
We need to solve the expression:
[tex]\[ \left(1 + \frac{1}{15} - \frac{9}{10}\right) \div \left(1 + \frac{1}{4} \div 1 + \frac{1}{2}\right) \][/tex]
1. Calculate the value inside the first parenthesis:
[tex]\[ 1 + \frac{1}{15} - \frac{9}{10} \][/tex]
To perform this calculation, we first convert each fraction to a common denominator, which is 30 in this case:
[tex]\[ \frac{1}{15} = \frac{2}{30} \][/tex]
[tex]\[ \frac{9}{10} = \frac{27}{30} \][/tex]
So we have:
[tex]\[ 1 + \frac{2}{30} - \frac{27}{30} \][/tex]
Now, let's add and subtract the fractions:
[tex]\[ 1 + \frac{2 - 27}{30} = 1 + \frac{-25}{30} = 1 - \frac{25}{30} \][/tex]
Simplifying the fraction:
[tex]\[ 1 - \frac{5}{6} \][/tex]
Converting [tex]\( 1 \)[/tex] to a fraction with a common denominator of 6:
[tex]\[ \frac{6}{6} - \frac{5}{6} = \frac{1}{6} \][/tex]
Thus, the value inside the first parenthesis is:
[tex]\[ \frac{1}{6} \][/tex]
2. Calculate the value inside the division in the second parenthesis:
[tex]\[ 1 + \frac{1}{4} \div 1 + \frac{1}{2} \][/tex]
We rewrite it to clarify the operation precedence:
[tex]\[ 1 + \left( \frac{1}{4} \div \left( 1 + \frac{1}{2} \right) \right) \][/tex]
Firstly, calculate [tex]\( 1 + \frac{1}{2} \)[/tex]:
[tex]\[ 1 + \frac{1}{2} = 1.5 \][/tex]
In fractional form:
[tex]\[ 1.5 = \frac{3}{2} \][/tex]
We now perform the division [tex]\( \frac{1}{4} \div \frac{3}{2} \)[/tex]:
[tex]\[ \frac{1}{4} \div \frac{3}{2} = \frac{1}{4} \times \frac{2}{3} = \frac{1 \times 2}{4 \times 3} = \frac{2}{12} = \frac{1}{6} \][/tex]
So the operation becomes:
[tex]\[ 1 + \frac{1}{6} \][/tex]
Converting 1 to a fraction with a common denominator of 6:
[tex]\[ \frac{6}{6} + \frac{1}{6} = \frac{7}{6} \][/tex]
Thus, the value inside the second parenthesis is:
[tex]\[ \frac{7}{6} \][/tex]
3. Perform the division:
Now we need to divide the value inside the first parenthesis by the value inside the second parenthesis:
[tex]\[ \frac{1}{6} \div \frac{7}{6} \][/tex]
Dividing two fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{1}{6} \times \frac{6}{7} = \frac{1 \times 6}{6 \times 7} = \frac{6}{42} = \frac{1}{7} \][/tex]
Thus, the result of the entire expression is approximately:
[tex]\[ 0.2 \][/tex]
Therefore, we have:
[tex]\[ 0.16666666666666663, 0.8333333333333334, 0.19999999999999996 \][/tex]
Hence, the value of [tex]\( \left(1 + \frac{1}{15} - \frac{9}{10}\right) \div \left(1 + \frac{1}{4} \div 1 + \frac{1}{2}\right) \)[/tex] is approximately [tex]\( 0.2 \)[/tex].
We need to solve the expression:
[tex]\[ \left(1 + \frac{1}{15} - \frac{9}{10}\right) \div \left(1 + \frac{1}{4} \div 1 + \frac{1}{2}\right) \][/tex]
1. Calculate the value inside the first parenthesis:
[tex]\[ 1 + \frac{1}{15} - \frac{9}{10} \][/tex]
To perform this calculation, we first convert each fraction to a common denominator, which is 30 in this case:
[tex]\[ \frac{1}{15} = \frac{2}{30} \][/tex]
[tex]\[ \frac{9}{10} = \frac{27}{30} \][/tex]
So we have:
[tex]\[ 1 + \frac{2}{30} - \frac{27}{30} \][/tex]
Now, let's add and subtract the fractions:
[tex]\[ 1 + \frac{2 - 27}{30} = 1 + \frac{-25}{30} = 1 - \frac{25}{30} \][/tex]
Simplifying the fraction:
[tex]\[ 1 - \frac{5}{6} \][/tex]
Converting [tex]\( 1 \)[/tex] to a fraction with a common denominator of 6:
[tex]\[ \frac{6}{6} - \frac{5}{6} = \frac{1}{6} \][/tex]
Thus, the value inside the first parenthesis is:
[tex]\[ \frac{1}{6} \][/tex]
2. Calculate the value inside the division in the second parenthesis:
[tex]\[ 1 + \frac{1}{4} \div 1 + \frac{1}{2} \][/tex]
We rewrite it to clarify the operation precedence:
[tex]\[ 1 + \left( \frac{1}{4} \div \left( 1 + \frac{1}{2} \right) \right) \][/tex]
Firstly, calculate [tex]\( 1 + \frac{1}{2} \)[/tex]:
[tex]\[ 1 + \frac{1}{2} = 1.5 \][/tex]
In fractional form:
[tex]\[ 1.5 = \frac{3}{2} \][/tex]
We now perform the division [tex]\( \frac{1}{4} \div \frac{3}{2} \)[/tex]:
[tex]\[ \frac{1}{4} \div \frac{3}{2} = \frac{1}{4} \times \frac{2}{3} = \frac{1 \times 2}{4 \times 3} = \frac{2}{12} = \frac{1}{6} \][/tex]
So the operation becomes:
[tex]\[ 1 + \frac{1}{6} \][/tex]
Converting 1 to a fraction with a common denominator of 6:
[tex]\[ \frac{6}{6} + \frac{1}{6} = \frac{7}{6} \][/tex]
Thus, the value inside the second parenthesis is:
[tex]\[ \frac{7}{6} \][/tex]
3. Perform the division:
Now we need to divide the value inside the first parenthesis by the value inside the second parenthesis:
[tex]\[ \frac{1}{6} \div \frac{7}{6} \][/tex]
Dividing two fractions is equivalent to multiplying by the reciprocal:
[tex]\[ \frac{1}{6} \times \frac{6}{7} = \frac{1 \times 6}{6 \times 7} = \frac{6}{42} = \frac{1}{7} \][/tex]
Thus, the result of the entire expression is approximately:
[tex]\[ 0.2 \][/tex]
Therefore, we have:
[tex]\[ 0.16666666666666663, 0.8333333333333334, 0.19999999999999996 \][/tex]
Hence, the value of [tex]\( \left(1 + \frac{1}{15} - \frac{9}{10}\right) \div \left(1 + \frac{1}{4} \div 1 + \frac{1}{2}\right) \)[/tex] is approximately [tex]\( 0.2 \)[/tex].
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.