Let's break down each part of the question step-by-step and simplify the expressions as required.
### 4. [tex]\(\frac{150}{15} - \frac{60}{35}\)[/tex]
First, simplify the individual fractions:
- [tex]\(\frac{150}{15}\)[/tex] equals [tex]\(10.0\)[/tex]
- [tex]\(\frac{60}{35}\)[/tex] equals [tex]\(1.7142857142857142\)[/tex]
Now, subtract the second fraction from the first:
- [tex]\(10.0 - 1.7142857142857142 = 8.285714285714286\)[/tex]
### 5. [tex]\(5 \cdot \frac{13}{2} \div \frac{12}{2}\)[/tex]
First, simplify the fractions inside the expression:
- [tex]\(\frac{13}{2}\)[/tex] equals [tex]\(6.5\)[/tex]
- [tex]\(\frac{12}{2}\)[/tex] equals [tex]\(6.0\)[/tex]
Now, proceed with the division and then the multiplication:
- [tex]\(5 \cdot \frac{6.5}{6.0} = 5 \cdot 1.0833333333333333 = 5.416666666666666\)[/tex]
### 6. [tex]\(\frac{30}{12} \div \frac{29}{42}\)[/tex]
First, simplify the fractions inside the expression:
- [tex]\(\frac{30}{12}\)[/tex] equals [tex]\(2.5\)[/tex]
- [tex]\(\frac{29}{42}\)[/tex] equals [tex]\(0.6904761904761905\)[/tex]
Now, proceed with the division:
- [tex]\(\frac{2.5}{0.6904761904761905} = 3.6206896551724137\)[/tex]
### 7. [tex]\(7 \cdot \frac{6}{2} \div \frac{1}{2}\)[/tex]
First, simplify the fractions inside the expression:
- [tex]\(\frac{6}{2}\)[/tex] equals [tex]\(3.0\)[/tex]
- [tex]\(\frac{1}{2}\)[/tex] equals [tex]\(0.5\)[/tex]
Now, proceed with the division and then the multiplication:
- [tex]\(7 \cdot \frac{3.0}{0.5} = 7 \cdot 6 = 42.0\)[/tex]
### 8. [tex]\(\frac{10}{12} \div \frac{1}{3}\)[/tex]
First, simplify the fractions inside the expression:
- [tex]\(\frac{10}{12}\)[/tex] equals [tex]\(0.8333333333333334\)[/tex]
- [tex]\(\frac{1}{3}\)[/tex] equals [tex]\(0.3333333333333333\)[/tex]
Now, proceed with the division:
- [tex]\(\frac{0.8333333333333334}{0.3333333333333333} = 2.5000000000000004\)[/tex]
### 9. [tex]\(\frac{4}{6} \div \frac{5}{13}\)[/tex]
First, simplify the fractions inside the expression:
- [tex]\(\frac{4}{6}\)[/tex] equals [tex]\(0.6666666666666666\)[/tex]
- [tex]\(\frac{5}{13}\)[/tex] equals [tex]\(0.38461538461538464\)[/tex]
Now, proceed with the division:
- [tex]\(\frac{0.6666666666666666}{0.38461538461538464} = 1.7333333333333332\)[/tex]
### Summary of Results:
1. [tex]\(10.0 - 1.7142857142857142 = 8.285714285714286\)[/tex]
2. [tex]\(5 \cdot \frac{13}{2} \div \frac{12}{2} = 5.416666666666666\)[/tex]
3. [tex]\(\frac{30}{12} \div \frac{29}{42} = 3.6206896551724137\)[/tex]
4. [tex]\(7 \cdot \frac{6}{2} \div \frac{1}{2} = 42.0\)[/tex]
5. [tex]\(\frac{10}{12} \div \frac{1}{3} = 2.5000000000000004\)[/tex]
6. [tex]\(\frac{4}{6} \div \frac{5}{13} = 1.7333333333333332\)[/tex]
