Step 1a

Given equivalent fraction \$15/30\$ = \$90/?\$

Explanation: In this step, the given fraction is \$15/30\$=\$90/?\$.To find an equivalent fraction of \$15/30\$ with a numerator of 90, multiply both the numerator and denominator by the same number.

Step 1b

To find what number, you can multiply 15 by to get 90.

That number is 6. Number to multiply = \$90/15\$ = 6.

Explanation: To convert \$15/30\$ to an equivalent fraction with a numerator of 90, you need to divide 90 by the current denominator (15), i.e.,\$90/15\$ = 6.

Step 1c

Now, multiply both the numerator and denominator of \$15/30\$ by 6: \$15/30\$ × \$6/6\$ = \$90/180\$

So,\$15/30\$ is equivalent to \$90/180\$ when the numerator is 90.

Explanation: In this step, we multiply 15 and 6 to get 90, and we multiply 30 and 6 to get 180. So, \$15/30\$ is equivalent to \$90/180\$.

Step 2a

To reduce the fraction \$78/126\$, we need to find the greatest common divisor (GCD): Factors for 64 :1, 2, 4, 8, 16, 32, and 64.

Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

Explanation: In this step, To simplify the fraction \$64/96\$, we need to determine the greatest common divisor (GCD) of the numerator and denominator.

The factors of 64 are 1, 2, 4, 8, 16, 32, and 64.The factors of 96 are 1, 2, 4, 6, 8, 12, 16, 24, 32, and 96.

Step 2b

The greatest common factor of 64 and 96 is 32. Divide both the numerator and the denominator by the GCD.

\$64/96\$ = \$64/96 \div 32/32\$

Explanation: In this step, to find the GCD of 64 and 96, which is 32. Then, divide the numerator and denominator by 32.

Therefore,\$64/96\$ = \$64/32 ÷ 96/32\$.

Step 2c

After performing division, the fraction we get \$2/3\$.

So, \$64/96\$ reduces to \$2/3\$.

Explanation: After dividing, \$64/96\$ simplifies to \$2/3\$.