Sure, I can help you solve these math problems step by step. Let's break each expression down:
1. [tex]\( \frac{3}{7} - \frac{3}{7} \times \frac{2}{5} \)[/tex]:
- First, calculate [tex]\( \frac{3}{7} \times \frac{2}{5} \)[/tex]:
[tex]\[ \frac{3}{7} \times \frac{2}{5} = \frac{3 \times 2}{7 \times 5} = \frac{6}{35} \][/tex]
- Then subtract this result from [tex]\( \frac{3}{7} \)[/tex]:
[tex]\[ \frac{3}{7} - \frac{6}{35} \][/tex]
To subtract these fractions, find a common denominator, which is 35:
[tex]\[ \frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35} \][/tex]
Now subtract:
[tex]\[ \frac{15}{35} - \frac{6}{35} = \frac{15 - 6}{35} = \frac{9}{35} \][/tex]
- So the answer is [tex]\( \frac{9}{35} \)[/tex].
2. [tex]\( \frac{4}{3} \times \frac{2}{5} + \frac{2}{3} \times e - \frac{2}{5} \)[/tex]:
- First, calculate [tex]\( \frac{4}{3} \times \frac{2}{5} \)[/tex]:
[tex]\[ \frac{4}{3} \times \frac{2}{5} = \frac{4 \times 2}{3 \times 5} = \frac{8}{15} \][/tex]
- Then calculate [tex]\( \frac{2}{3} \times e \)[/tex]:
[tex]\[ \frac{2}{3} \times e = \frac{2e}{3} \][/tex]
- Now combine these results and subtract [tex]\( \frac{2}{5} \)[/tex]:
[tex]\[ \frac{8}{15} + \frac{2e}{3} - \frac{2}{5} \][/tex]
- To combine these, find a common denominator (which is 15 for the numerical fractions):
[tex]\[ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \][/tex]
So, the expression becomes:
[tex]\[ \frac{8}{15} - \frac{6}{15} + \frac{2e}{3} = \frac{2}{15} + \frac{2e}{3} \][/tex]
Keep the final mixed form as:
[tex]\[ \frac{2}{15} + \frac{2e}{3} \][/tex]
- This cannot be further simplified numerically without knowing [tex]\( e \)[/tex], so we leave it as is.
3. [tex]\( 17 \times \frac{9}{16} \)[/tex]:
- Multiply directly:
[tex]\[ 17 \times \frac{9}{16} = \frac{17 \times 9}{16} = \frac{153}{16} \][/tex]
4. [tex]\( \frac{63}{64} \times 25 \)[/tex]:
- Multiply directly:
[tex]\[ \frac{63}{64} \times 25 = \frac{63 \times 25}{64} = \frac{1575}{64} \][/tex]
5. [tex]\( \frac{1}{17} \times \frac{1}{9} \)[/tex]:
- Multiply directly:
[tex]\[ \frac{1}{17} \times \frac{1}{9} = \frac{1 \times 1}{17 \times 9} = \frac{1}{153} \][/tex]
6. [tex]\( \frac{1}{5} \times 27 + \frac{3}{5} \times 41 \)[/tex]:
- First, multiply each fraction separately:
[tex]\[ \frac{1}{5} \times 27 = \frac{27}{5} \][/tex]
[tex]\[ \frac{3}{5} \times 41 = \frac{3 \times 41}{5} = \frac{123}{5} \][/tex]
- Then add these results together:
[tex]\[ \frac{27}{5} + \frac{123}{5} = \frac{27 + 123}{5} = \frac{150}{5} = 30 \][/tex]
I hope these detailed steps help you understand how to solve each math problem!
