Chapter 5.1, Problem 2E

(a)

To determine

Run the program to find the GCF of the numerator and the denominator of each fraction. Write each fraction in simplest form.

Answer to Problem 2E

87

Explanation of Solution

Given :

  $\frac{87}{1653}$

Calculation:

The program that uses Euclidean Algorithm to find GCF’s :

  $\begin{array}{l}10\text{ PRINT"FIND THE GCF OF THE POSITIVE INTEGERS}\text{."}\\ \text{20 INPUT"ENTER THE NUMBERS(LARGER FIRST):";A,B}\\ \text{30 PRINT"THE GCF OF ";A;"AND";B;"IS";}\\ \text{40 IF INT(A/B)=A/B THEN 90}\\ \text{50 LET R = A - B}\ast \text{INT(A/B)}\\ \text{60 LET A = B}\\ 70\text{ LET B = R}\\ \text{80 GOTO 40}\\ \text{90 PRINT B}\\ \text{95 END}\end{array}$

Run the program :

FIND THE GCF OF THE POSITIVE INTEGERS.

THE GCF OF 1653 AND 87 IS 87 .

(b)

To determine

Run the program to find the GCF of the numerator and the denominator of each fraction. Write each fraction in simplest form.

Answer to Problem 2E

512

Explanation of Solution

Given :

  $\frac{11,776}{15,872}$

Calculation:

The program that uses Euclidean Algorithm to find GCF’s :

  $\begin{array}{l}10\text{ PRINT"FIND THE GCF OF THE POSITIVE INTEGERS}\text{."}\\ \text{20 INPUT"ENTER THE NUMBERS(LARGER FIRST):";A,B}\\ \text{30 PRINT"THE GCF OF ";A;"AND";B;"IS";}\\ \text{40 IF INT(A/B)=A/B THEN 90}\\ \text{50 LET R = A - B}\ast \text{INT(A/B)}\\ \text{60 LET A = B}\\ 70\text{ LET B = R}\\ \text{80 GOTO 40}\\ \text{90 PRINT B}\\ \text{95 END}\end{array}$

Run the program :

FIND THE GCF OF THE POSITIVE INTEGERS.

THE GCF OF 15872 AND 11776 IS 512 .

(c)

To determine

Run the program to find the GCF of the numerator and the denominator of each fraction. Write each fraction in simplest form.

Answer to Problem 2E

396

Explanation of Solution

Given :

  $\frac{2772}{5940}$

Calculation:

The program that uses Euclidean Algorithm to find GCF’s :

  $\begin{array}{l}10\text{ PRINT"FIND THE GCF OF THE POSITIVE INTEGERS}\text{."}\\ \text{20 INPUT"ENTER THE NUMBERS(LARGER FIRST):";A,B}\\ \text{30 PRINT"THE GCF OF ";A;"AND";B;"IS";}\\ \text{40 IF INT(A/B)=A/B THEN 90}\\ \text{50 LET R = A - B}\ast \text{INT(A/B)}\\ \text{60 LET A = B}\\ 70\text{ LET B = R}\\ \text{80 GOTO 40}\\ \text{90 PRINT B}\\ \text{95 END}\end{array}$

Run the program :

FIND THE GCF OF THE POSITIVE INTEGERS.

THE GCF OF 5940 AND 2772 IS 396 .

(d)

To determine

Run the program to find the GCF of the numerator and the denominator of each fraction. Write each fraction in simplest form.

Answer to Problem 2E

1

Explanation of Solution

Given :

  $\frac{2048}{40,387}$

Calculation:

The program that uses Euclidean Algorithm to find GCF’s :

  $\begin{array}{l}10\text{ PRINT"FIND THE GCF OF THE POSITIVE INTEGERS}\text{."}\\ \text{20 INPUT"ENTER THE NUMBERS(LARGER FIRST):";A,B}\\ \text{30 PRINT"THE GCF OF ";A;"AND";B;"IS";}\\ \text{40 IF INT(A/B)=A/B THEN 90}\\ \text{50 LET R = A - B}\ast \text{INT(A/B)}\\ \text{60 LET A = B}\\ 70\text{ LET B = R}\\ \text{80 GOTO 40}\\ \text{90 PRINT B}\\ \text{95 END}\end{array}$

Run the program :

FIND THE GCF OF THE POSITIVE INTEGERS.

THE GCF OF 40387 AND 2048 IS 1 .