Sure, let’s solve each of these expressions step by step.
### Question 10: [tex]\( 25 \div 5 - 16 \div 8 \)[/tex]
1. Step 1: Perform the division operations separately.
[tex]\[
\frac{25}{5} = 5
\][/tex]
[tex]\[
\frac{16}{8} = 2
\][/tex]
2. Step 2: Subtract the results of the divisions.
[tex]\[
5 - 2 = 3
\][/tex]
So, the result for question 10 is [tex]\( \boxed{3} \)[/tex].
### Question 13: [tex]\( \frac{4}{7} \div \frac{6}{7} \)[/tex] of [tex]\( \frac{8}{9} + \frac{1}{4} \)[/tex]
1. Step 1: Start with the division of fractions. When dividing by a fraction, multiply by its reciprocal.
[tex]\[
\frac{4}{7} \div \frac{6}{7} = \frac{4}{7} \times \frac{7}{6}
\][/tex]
Simplify by multiplying:
[tex]\[
\frac{4 \cdot 7}{7 \cdot 6} = \frac{4}{6} = \frac{2}{3} = 0.6666666666666666
\][/tex]
2. Step 2: Perform the addition inside the parenthesis.
[tex]\[
\frac{8}{9} + \frac{1}{4}
\][/tex]
Find a common denominator to add these fractions:
The least common multiple of 9 and 4 is 36.
Convert the fractions:
[tex]\[
\frac{8}{9} = \frac{8 \times 4}{9 \times 4} = \frac{32}{36}
\][/tex]
[tex]\[
\frac{1}{4} = \frac{1 \times 9}{4 \times 9} = \frac{9}{36}
\][/tex]
Add the fractions:
[tex]\[
\frac{32}{36} + \frac{9}{36} = \frac{41}{36} = 1.1388888888888888
\][/tex]
3. Step 3: Multiply the results from step 1 and step 2.
[tex]\[
0.6666666666666666 \times 1.1388888888888888 = 0.7592592592592592
\][/tex]
So, the result for question 13 is [tex]\( \boxed{0.7592592592592592} \)[/tex].
Thus, the answers are:
1. [tex]\( 25 \div 5 - 16 \div 8 = 3 \)[/tex]
2. [tex]\( \frac{4}{7} \div \frac{6}{7} \)[/tex] of [tex]\( \frac{8}{9} + \frac{1}{4} = 0.7592592592592592 \)[/tex]
