Answer :
Sure! Let's break down the problem step by step for each part:
1. Simplify the Fractions:
- [tex]\(\frac{32}{40}\)[/tex]:
To simplify this fraction, we find the greatest common divisor (GCD) of 32 and 40, which is 8.
So, [tex]\(\frac{32}{40} = \frac{32 \div 8}{40 \div 8} = \frac{4}{5}\)[/tex].
- [tex]\(\frac{15}{3}\)[/tex]:
The GCD of 15 and 3 is 3.
So, [tex]\(\frac{15}{3} = \frac{15 \div 3}{3 \div 3} = \frac{5}{1} = 5\)[/tex].
2. Find the Product:
- [tex]\(324.6 \times 0.12\)[/tex]:
When we multiply these numbers together, we get the product 38.952.
3. Find the Quotient:
- [tex]\(2.8 \div 68.88\)[/tex]:
Converting these decimals to fractions gives us [tex]\(\frac{28}{10}\)[/tex] for 2.8 and [tex]\(\frac{6888}{100}\)[/tex] for 68.88.
Dividing these fractions results in the quotient approximately equal to 0.0407.
4. Find the Difference:
- First Problem: [tex]\(3 \frac{2}{5} - 1 \frac{1}{3}\)[/tex]
Start with the whole numbers: [tex]\(3 - 1 = 2\)[/tex].
Now the fractions: [tex]\(\frac{2}{5} - \frac{1}{3}\)[/tex].
To subtract these, we need a common denominator. The least common denominator of 5 and 3 is 15.
Convert each fraction: [tex]\(\frac{2}{5} = \frac{6}{15}\)[/tex] and [tex]\(\frac{1}{3} = \frac{5}{15}\)[/tex].
Now subtract: [tex]\(\frac{6}{15} - \frac{5}{15} = \frac{1}{15}\)[/tex].
Combine the whole number and the fraction: [tex]\(2 + \frac{1}{15}\)[/tex], which is approximately 2.0667.
- Second Problem: [tex]\(5 \frac{2}{5} - 4 \frac{1}{4}\)[/tex]
Start with the whole numbers: [tex]\(5 - 4 = 1\)[/tex].
Now the fractions: [tex]\(\frac{2}{5} - \frac{1}{4}\)[/tex].
The least common denominator of 5 and 4 is 20.
Convert each fraction: [tex]\(\frac{2}{5} = \frac{8}{20}\)[/tex] and [tex]\(\frac{1}{4} = \frac{5}{20}\)[/tex].
Now subtract: [tex]\(\frac{8}{20} - \frac{5}{20} = \frac{3}{20}\)[/tex].
Combine the whole number and the fraction: [tex]\(1 + \frac{3}{20}\)[/tex], which is approximately 1.15.
That's the step-by-step solution! Let me know if there's anything you'd like me to explain further.
1. Simplify the Fractions:
- [tex]\(\frac{32}{40}\)[/tex]:
To simplify this fraction, we find the greatest common divisor (GCD) of 32 and 40, which is 8.
So, [tex]\(\frac{32}{40} = \frac{32 \div 8}{40 \div 8} = \frac{4}{5}\)[/tex].
- [tex]\(\frac{15}{3}\)[/tex]:
The GCD of 15 and 3 is 3.
So, [tex]\(\frac{15}{3} = \frac{15 \div 3}{3 \div 3} = \frac{5}{1} = 5\)[/tex].
2. Find the Product:
- [tex]\(324.6 \times 0.12\)[/tex]:
When we multiply these numbers together, we get the product 38.952.
3. Find the Quotient:
- [tex]\(2.8 \div 68.88\)[/tex]:
Converting these decimals to fractions gives us [tex]\(\frac{28}{10}\)[/tex] for 2.8 and [tex]\(\frac{6888}{100}\)[/tex] for 68.88.
Dividing these fractions results in the quotient approximately equal to 0.0407.
4. Find the Difference:
- First Problem: [tex]\(3 \frac{2}{5} - 1 \frac{1}{3}\)[/tex]
Start with the whole numbers: [tex]\(3 - 1 = 2\)[/tex].
Now the fractions: [tex]\(\frac{2}{5} - \frac{1}{3}\)[/tex].
To subtract these, we need a common denominator. The least common denominator of 5 and 3 is 15.
Convert each fraction: [tex]\(\frac{2}{5} = \frac{6}{15}\)[/tex] and [tex]\(\frac{1}{3} = \frac{5}{15}\)[/tex].
Now subtract: [tex]\(\frac{6}{15} - \frac{5}{15} = \frac{1}{15}\)[/tex].
Combine the whole number and the fraction: [tex]\(2 + \frac{1}{15}\)[/tex], which is approximately 2.0667.
- Second Problem: [tex]\(5 \frac{2}{5} - 4 \frac{1}{4}\)[/tex]
Start with the whole numbers: [tex]\(5 - 4 = 1\)[/tex].
Now the fractions: [tex]\(\frac{2}{5} - \frac{1}{4}\)[/tex].
The least common denominator of 5 and 4 is 20.
Convert each fraction: [tex]\(\frac{2}{5} = \frac{8}{20}\)[/tex] and [tex]\(\frac{1}{4} = \frac{5}{20}\)[/tex].
Now subtract: [tex]\(\frac{8}{20} - \frac{5}{20} = \frac{3}{20}\)[/tex].
Combine the whole number and the fraction: [tex]\(1 + \frac{3}{20}\)[/tex], which is approximately 1.15.
That's the step-by-step solution! Let me know if there's anything you'd like me to explain further.
