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Sagot :
Certainly! Let's solve each part of the problem step-by-step:
### Part 2: Simplify [tex]\(\frac{-2}{3} + \frac{5}{6} + \left(-\frac{3}{5}\right) + \frac{7}{15}\)[/tex]
First, let's find a common denominator for all the fractions. The common denominator for 3, 6, 5, and 15 is 30. We will convert each fraction to have this common denominator:
1. [tex]\(\frac{-2}{3} = \frac{-2 \times 10}{3 \times 10} = \frac{-20}{30}\)[/tex]
2. [tex]\(\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}\)[/tex]
3. [tex]\(\left(-\frac{3}{5}\right) = \frac{-3 \times 6}{5 \times 6} = \frac{-18}{30}\)[/tex]
4. [tex]\(\frac{7}{15} = \frac{7 \times 2}{15 \times 2} = \frac{14}{30}\)[/tex]
Now, we sum these fractions:
[tex]\[ \frac{-20}{30} + \frac{25}{30} + \frac{-18}{30} + \frac{14}{30} \][/tex]
Combine the numerators over the common denominator:
[tex]\[ \frac{-20 + 25 - 18 + 14}{30} = \frac{1}{30} \][/tex]
So, the simplified expression is:
[tex]\[ \frac{1}{30} \][/tex]
### Part 3: Product of two numbers is [tex]\(\frac{16}{}\)[/tex]. One of them is [tex]\(\frac{26}{}\)[/tex], find the other
We are given that the product of two numbers is 16, and one of the numbers is 26. We need to find the other number [tex]\( x \)[/tex].
Let [tex]\( x \)[/tex] be the unknown number. According to the problem:
[tex]\[ 26x = 16 \][/tex]
To find [tex]\( x \)[/tex], we divide both sides by 26:
[tex]\[ x = \frac{16}{26} \][/tex]
Simplify the fraction [tex]\(\frac{16}{26}\)[/tex]:
[tex]\[ x = \frac{8}{13} \][/tex]
Thus, the other number is:
[tex]\[ \frac{8}{13} \][/tex]
### Summary:
Step 1: Simplifying [tex]\(\frac{-2}{3} + \frac{5}{6} + \left(-\frac{3}{5}\right) + \frac{7}{15}\)[/tex] we get:
[tex]\[ \frac{1}{30} \][/tex]
Step 2: Finding the other number when the product of both numbers is 16 and one of the numbers is 26, the other number is:
[tex]\[ \frac{8}{13} \][/tex]
So, the final results are:
[tex]\[ \frac{1}{30} \text{ and } \frac{8}{13} \][/tex]
### Part 2: Simplify [tex]\(\frac{-2}{3} + \frac{5}{6} + \left(-\frac{3}{5}\right) + \frac{7}{15}\)[/tex]
First, let's find a common denominator for all the fractions. The common denominator for 3, 6, 5, and 15 is 30. We will convert each fraction to have this common denominator:
1. [tex]\(\frac{-2}{3} = \frac{-2 \times 10}{3 \times 10} = \frac{-20}{30}\)[/tex]
2. [tex]\(\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}\)[/tex]
3. [tex]\(\left(-\frac{3}{5}\right) = \frac{-3 \times 6}{5 \times 6} = \frac{-18}{30}\)[/tex]
4. [tex]\(\frac{7}{15} = \frac{7 \times 2}{15 \times 2} = \frac{14}{30}\)[/tex]
Now, we sum these fractions:
[tex]\[ \frac{-20}{30} + \frac{25}{30} + \frac{-18}{30} + \frac{14}{30} \][/tex]
Combine the numerators over the common denominator:
[tex]\[ \frac{-20 + 25 - 18 + 14}{30} = \frac{1}{30} \][/tex]
So, the simplified expression is:
[tex]\[ \frac{1}{30} \][/tex]
### Part 3: Product of two numbers is [tex]\(\frac{16}{}\)[/tex]. One of them is [tex]\(\frac{26}{}\)[/tex], find the other
We are given that the product of two numbers is 16, and one of the numbers is 26. We need to find the other number [tex]\( x \)[/tex].
Let [tex]\( x \)[/tex] be the unknown number. According to the problem:
[tex]\[ 26x = 16 \][/tex]
To find [tex]\( x \)[/tex], we divide both sides by 26:
[tex]\[ x = \frac{16}{26} \][/tex]
Simplify the fraction [tex]\(\frac{16}{26}\)[/tex]:
[tex]\[ x = \frac{8}{13} \][/tex]
Thus, the other number is:
[tex]\[ \frac{8}{13} \][/tex]
### Summary:
Step 1: Simplifying [tex]\(\frac{-2}{3} + \frac{5}{6} + \left(-\frac{3}{5}\right) + \frac{7}{15}\)[/tex] we get:
[tex]\[ \frac{1}{30} \][/tex]
Step 2: Finding the other number when the product of both numbers is 16 and one of the numbers is 26, the other number is:
[tex]\[ \frac{8}{13} \][/tex]
So, the final results are:
[tex]\[ \frac{1}{30} \text{ and } \frac{8}{13} \][/tex]
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