Step 1a

The given fraction is \$430/13\$

Explanation: The given fraction is \$430/13\$, which is an improper fraction.

Now, we have to convert this improper fraction into a mixed fraction.

Step 1b

In the first step, divide the numerator by the denominator.

Hence, the numerator is 430, and the denominator is 13.

Explanation: In this step, we must divide the numerator by the denominator.

Here, the dividend is 430, and the divisor is 13. 430 is not divisible by 13, but since 13 x 33 = 429. We go for subtracting 430 - 429 = 1.

We get the quotient as 33 and the remainder as 1.

Step 1c

Moving to the next step, the quotient becomes the whole number, and the remainder becomes the new numerator while the denominator remains the same.

Explanation: In this step, the denominator is 13, and the quotient is 33, with a remainder of 1.

Step 1d

Now, we combine the whole number and fraction parts and get a mixed fraction represented as a \$33 1/13\$.

Explanation: Finally, by combining a whole number and a fraction, we get a mixed fraction represented as \$33 1/13\$.

Step 2a

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 2b

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 2c

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 3a

To reduce the fraction \$78/126\$, we need to find the greatest common divisor (GCD):

Factors for 78 :1, 2, 3, 6, 13, 26, 39, 78

Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

Explanation: In this step,To simplify the fraction 78/126, we need to determine the greatest common divisor (GCD) of the numerator and denominator.

The factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78. The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.

Step 3b

The greatest common factor of 78 and 126 is 6. Divide both the numerator and the denominator by the GCD.

\$78/126\$ = \$78/126 \div 6/6\$

Explanation: In this step, to find the GCD of 78 and 126, which is 6. Then, divide the numerator and denominator by 6.

Therefore,\$78/126\$ = \$78/126 ÷ 6/6\$.

Step 3c

After performing division, the fraction we get \$13/21\$.

So, \$78/126\$ reduces to \$13/21\$.

Explanation: After dividing, \$78/126\$ simplifies to \$13/21\$.