Question

Moussa delivered 3/8 of the newspaper on his route in the 1st hour and 4/5 of the rest in the second hour. What fraction of the newspapers did Moussa deliver in the second hour?

Answer 1

To get the fraction of news papers delivered in the second hour we proceed as follows:
fraction delivered in the first hour=3/8
Remaining fraction is (1-3/8)=5/8
Given that in the second hour he delivered 4/5 of 5/8, then the fraction delivered in the second hour will be:
4/5 of 5/8
=4/5×5/8
=1/2
He delivered 1/2 of the papers in the second hour.

Answer 2

¹/₂

Further explanation

Given:

Moussa delivered:

• $\frac{3}{8}$ of the newspaper on his route in the first hour, and
• $\frac{4}{5}$ of the rest in the second hour.

Question:

What fraction of the newspapers did Moussa deliver in the second hour?

The Process:

Step-1

Let us design a diagram that matches the initial conditions.

$\boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot}$

1 unit represents 1 part of all newspapers delivered by Moussa.

Moussa delivered $\frac{3}{8}$ of the newspaper on his route in the first hour, that is $\boxed{\cdot} \boxed{\cdot} \boxed{\cdot}$ or 3 of 8 units.

The rest of the newspaper after the first hour of delivery is $\boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot}$ or 5 of 8 units.

So, there are $\frac{5}{8}$ of the newspapers left.

Step-2

Next, Moussa delivered $\frac{4}{5}$ of the rest in the second hour.

We saw that the remainder of the newspaper was 5 units, i.e., $\boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot}$.

So, in the second hour, Moussa delivered 4 units of the remaining 5 units, i.e., $\boxed{\cdot} \boxed{\cdot} \boxed{\cdot} \boxed{\cdot}$.

Recall the total number of newspaper units delivered by Moussa is 8 units, while in the second hour 4 units are delivered.

So, we can write the fraction of the newspapers did Moussa deliver in the second hour.

$\boxed{ \ 4 \ of \ 8 \ units \ is \ \frac{4}{8} \ }$

Simplify it. The numerator and denominator are equally divided by 4.

$\boxed{ \ = \frac{4 \div 4}{8 \div 4} \ }$

$\boxed{\boxed{ \ \frac{1}{2} \ }}$

Thus, Moussa delivered $\frac{1}{2}$ of the newspapers in the second hour.

- - - - - - - - - -

Quick Steps

$\boxed{ \ \frac{4}{5} \times \bigg( 1 - \frac{3}{8} \bigg) = \ ? \ }$

$\boxed{ \ = \frac{4}{5} \times \bigg( \frac{8}{8} - \frac{3}{8} \bigg) \ }$

$\boxed{ \ = \frac{4}{5} \times \frac{5}{8} \ }$

$\boxed{ \ Recall \ \frac{a}{b} \times \frac{m}{n} = \frac{a \times m}{b \times n} \ }$

$\boxed{ \ = \frac{4 \times 5}{5 \times 8} \ }$

$\boxed{ \ = \frac{20}{40} \ }$

Simplify it. The numerator and denominator are equally divided by 20.

$\boxed{\boxed{ \ \frac{1}{2} \ }}$

Another way, $\boxed{ \ = \frac{4}{5} \times \frac{5}{8} \ }$

We crossed out 5 with 5 and also 4 with 8.

$\boxed{ \ = \frac{1}{1} \times \frac{1}{2} \ }$

$\boxed{\boxed{ \ \frac{1}{2} \ }}$

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Keywords: Moussa, delivered, 3/8 of the newspaper, on his route, in the first hour, 4/5 of the rest, in the second, what fraction, units, diagram, the numerator and denominator