Question

MATHEMATICS 5 QUARTER 1 - Week 7 October 25 – 29, 2021 → Please refer to Mathematics 5 Module, pages 29 - 33. Week 7 Lessons: a. Solve Word Problems Involving Multiplication Without or With Addition or Subtraction of Fractions and Whole Numbers b. Showing the Reciprocal of Fraction 1. Read and solve each simple problem.(Answer only).
1) In a class of 50 pupils, 3/5 of them are girls. How many are boys: 2) Jack had 360 oranges for sale. He sold 4/9 of them. How many oranges were left? 3) Three-seventh of the workers in a factory are women. The rest are men. If there are 33women, how men are there?​

Answer 1

Given:

1) No. of pupils in a class = 50

Fraction of girls in the class = $\frac{3}{5}$ of pupils

2) No. of oranges for sale = 360

Fraction of oranges sold = $\frac{4}{9}$ of oranges

3) Fraction of women workers in the factory = $\frac{3}{7}$ of workers

No. of women workers = 33

To find:

1) No. of boys in the class.

2) No. of oranges remaining.

3) No. of men workers in the factory.

Solution:

1) There are 50 students out of which $\frac{3}{5}$ of them are girls.

No. of girls = $\frac{3}{5}$ of total students = $\frac{3}{5}*50=30$

Hence, there are 30 girls in the class. To find the no. of boys in the class, subtract the no. of girls from the total no. of students in class.

No. of boys = No. of students - No. of girls

No. of boys = $50-30=20$

Hence, 20 of the students in the class are boys.

2) Jack had 360 oranges and $\frac{4}{9}$ of them were sold.

No. of oranges that are sold = $360*\frac{4}{9}=160$

Hence, Jack sold 160 oranges. To find the remaining no. of oranges, subtract the no. of oranges sold from the total no. of oranges he had initially.

No. of oranges remaining = Total no. of oranges - No. of oranges sold

No. of oranges remaining = $360-160=200$

Hence, 260 oranges were left that were not sold.

3) In the factory there are men and women workers. There are 33 women workers. Let $x$ be the no. of men workers. If there were $\frac{3}{7}$ women workers, then let the no. of workers in the factory be $1$.

No. of workers in factory = No. of women workers + No. of men workers

$1=\frac{3}{7}+x$

$x=1-\frac{3}{7}$

Taking LCM as 7 from the fractions

$x=\frac{1}{1}*\frac{7}{7}- \frac{3}{7} *\frac{1}{1}$

$x=\frac{7-3}{7}=\frac{4}{7}$

Hence, $\frac{4}{7}$ of the workers are men.

It is given that $\frac{3}{7}$ of the workers are women. Let $y$ be the no. of workers. Then, three-seventh of the  $y$ workers are women which totals to 33.

$\frac{3}{7}*y=33$

$y=\frac{7}{3}*33$   (∵ reciprocal of $\frac{3}{7}$)

∴ $y=77$

Thus, there are 77 men workers in the factory.

The answers are:

1) 20 of the students in the class are boys.

2) 260 oranges were left that were not sold.

3) There are 77 men workers in the factory.