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Sagot :
Sure! Let's solve the problem step-by-step.
We need to calculate the product of the two fractions:
[tex]\[ \left(\frac{-13}{26}\right) \times \left(\frac{6}{44}\right) \][/tex]
### Step 1: Simplify each fraction if possible
First, let’s simplify both fractions.
#### Fraction 1: [tex]\(\frac{-13}{26}\)[/tex]
- The numerator is [tex]\(-13\)[/tex] and the denominator is [tex]\(26\)[/tex].
- We can see that the numerator [tex]\(-13\)[/tex] and the denominator [tex]\(26\)[/tex] share a common factor of [tex]\(13\)[/tex].
Divide both numerator and denominator by their greatest common divisor (GCD), which is [tex]\(13\)[/tex]:
[tex]\[ \frac{-13}{26} = \frac{-13 \div 13}{26 \div 13} = \frac{-1}{2} = -0.5 \][/tex]
#### Fraction 2: [tex]\(\frac{6}{44}\)[/tex]
- The numerator is [tex]\(6\)[/tex] and the denominator is [tex]\(44\)[/tex].
- We can see that both the numerator [tex]\(6\)[/tex] and the denominator [tex]\(44\)[/tex] share a common factor of [tex]\(2\)[/tex].
Divide both numerator and denominator by their GCD, which is [tex]\(2\)[/tex]:
[tex]\[ \frac{6}{44} = \frac{6 \div 2}{44 \div 2} = \frac{3}{22} \approx 0.13636 \][/tex]
Now we have the simplified fractions:
- [tex]\(\frac{-1}{2}\)[/tex]
- [tex]\(\frac{3}{22}\)[/tex]
### Step 2: Multiply the simplified fractions
Now, multiply the simplified fractions together:
[tex]\[ \left(\frac{-1}{2}\right) \times \left(\frac{3}{22}\right) = \frac{(-1) \times 3}{2 \times 22} = \frac{-3}{44} \][/tex]
So, the result of the multiplication is:
[tex]\[ \frac{-3}{44} \][/tex]
### Step 3: Simplify the result if possible
Check if [tex]\(\frac{-3}{44}\)[/tex] can be simplified further. Since the greatest common divisor (GCD) of 3 and 44 is 1, the fraction is already in its simplest form.
Therefore, the final simplified result is:
[tex]\[ \frac{-3}{44} \approx -0.06818 \][/tex]
Thus, the detailed step-by-step solution yields:
- First fraction: [tex]\(-0.5\)[/tex]
- Second fraction: [tex]\(0.13636\)[/tex]
- Result of the multiplication: [tex]\(-0.06818\)[/tex]
- Numerator after multiplication: [tex]\(-3\)[/tex]
- Denominator after multiplication: [tex]\(44\)[/tex]
So,
[tex]\(\left(\frac{-13}{26}\right) \times \left(\frac{6}{44}\right) = \frac{-3}{44} = -0.06818\)[/tex].
We need to calculate the product of the two fractions:
[tex]\[ \left(\frac{-13}{26}\right) \times \left(\frac{6}{44}\right) \][/tex]
### Step 1: Simplify each fraction if possible
First, let’s simplify both fractions.
#### Fraction 1: [tex]\(\frac{-13}{26}\)[/tex]
- The numerator is [tex]\(-13\)[/tex] and the denominator is [tex]\(26\)[/tex].
- We can see that the numerator [tex]\(-13\)[/tex] and the denominator [tex]\(26\)[/tex] share a common factor of [tex]\(13\)[/tex].
Divide both numerator and denominator by their greatest common divisor (GCD), which is [tex]\(13\)[/tex]:
[tex]\[ \frac{-13}{26} = \frac{-13 \div 13}{26 \div 13} = \frac{-1}{2} = -0.5 \][/tex]
#### Fraction 2: [tex]\(\frac{6}{44}\)[/tex]
- The numerator is [tex]\(6\)[/tex] and the denominator is [tex]\(44\)[/tex].
- We can see that both the numerator [tex]\(6\)[/tex] and the denominator [tex]\(44\)[/tex] share a common factor of [tex]\(2\)[/tex].
Divide both numerator and denominator by their GCD, which is [tex]\(2\)[/tex]:
[tex]\[ \frac{6}{44} = \frac{6 \div 2}{44 \div 2} = \frac{3}{22} \approx 0.13636 \][/tex]
Now we have the simplified fractions:
- [tex]\(\frac{-1}{2}\)[/tex]
- [tex]\(\frac{3}{22}\)[/tex]
### Step 2: Multiply the simplified fractions
Now, multiply the simplified fractions together:
[tex]\[ \left(\frac{-1}{2}\right) \times \left(\frac{3}{22}\right) = \frac{(-1) \times 3}{2 \times 22} = \frac{-3}{44} \][/tex]
So, the result of the multiplication is:
[tex]\[ \frac{-3}{44} \][/tex]
### Step 3: Simplify the result if possible
Check if [tex]\(\frac{-3}{44}\)[/tex] can be simplified further. Since the greatest common divisor (GCD) of 3 and 44 is 1, the fraction is already in its simplest form.
Therefore, the final simplified result is:
[tex]\[ \frac{-3}{44} \approx -0.06818 \][/tex]
Thus, the detailed step-by-step solution yields:
- First fraction: [tex]\(-0.5\)[/tex]
- Second fraction: [tex]\(0.13636\)[/tex]
- Result of the multiplication: [tex]\(-0.06818\)[/tex]
- Numerator after multiplication: [tex]\(-3\)[/tex]
- Denominator after multiplication: [tex]\(44\)[/tex]
So,
[tex]\(\left(\frac{-13}{26}\right) \times \left(\frac{6}{44}\right) = \frac{-3}{44} = -0.06818\)[/tex].
Answer:
hello
Step-by-step explanation:
-13/26 x 6/44
=-1/2 x 3/22
=3/44
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