High School

4. Simplify the following:

(a) [tex]\frac{2}{5} \times \frac{6}{11} \times \frac{15}{18}[/tex]

(b) [tex]\frac{12}{25} \times \frac{15}{28} \times \frac{35}{36}[/tex]

Answer :

Sure! Let's simplify each of the fractions and tackle the reading part step-by-step.

### 4. Simplify the following:

#### (a) [tex]\(\frac{2}{5} \times \frac{6}{11} \times \frac{15}{18}\)[/tex]

1. Multiply the numerators:
[tex]\[
2 \times 6 \times 15 = 180
\][/tex]

2. Multiply the denominators:
[tex]\[
5 \times 11 \times 18 = 990
\][/tex]

3. Form the fraction:
[tex]\[
\frac{180}{990}
\][/tex]

4. Simplify the fraction:
- Find the greatest common divisor (GCD) of 180 and 990. The GCD is 90.
- Divide the numerator and denominator by their GCD:
[tex]\[
\frac{180 \div 90}{990 \div 90} = \frac{2}{11}
\][/tex]

So, the simplified fraction for part (a) is [tex]\(\frac{2}{11}\)[/tex].

#### (b) [tex]\(\frac{12}{25} \times \frac{15}{28} \times \frac{35}{36}\)[/tex]

1. Multiply the numerators:
[tex]\[
12 \times 15 \times 35 = 6300
\][/tex]

2. Multiply the denominators:
[tex]\[
25 \times 28 \times 36 = 25200
\][/tex]

3. Form the fraction:
[tex]\[
\frac{6300}{25200}
\][/tex]

4. Simplify the fraction:
- Find the greatest common divisor (GCD) of 6300 and 25200. The GCD is 6300.
- Divide the numerator and denominator by their GCD:
[tex]\[
\frac{6300 \div 6300}{25200 \div 6300} = \frac{1}{4}
\][/tex]

So, the simplified fraction for part (b) is [tex]\(\frac{1}{4}\)[/tex].

### 5. A book has 400 pages. Shanu reads 1 page per day.

1. Calculate the number of days needed to finish the book:
- Since Shanu reads 1 page per day, it will take:
[tex]\[
\frac{400 \text{ pages}}{1 \text{ page per day}} = 400 \text{ days}
\][/tex]

Shanu will need 400 days to finish the book if she reads 1 page per day.