Step 1a

To find \$17/20\$of 120, multiply 120 by \$17/20\$: \$120 \times 17/20\$

Now, multiply the numerators and denominators: \$(120 \times 17)/20\$ = \$2040/20\$.

Explanation: In this step,to find \$17/20\$of 120, we need to multiply 120 by \$17/20\$: \$120 \times 17/20\$

Now, multiply the numerators and denominators: \$(120 \times 17)/20\$ = \$2040/20\$.

Step 1b

Simplify the fraction: \$2040/120\$ = 102

So, \$17/20\$ of 120 is 102.

Explanation: To simplify the fraction \$2040/120\$, we can divide the numerator and denominator by their greatest common factor, 120.

Therefore, \$17/20\$ of 120 is equal to 102.

Step 2a

Compare these fractions directly to find a common denominator.

To make the two fractions comparable, find a common denominator. In this case, the least common multiple (LCM) of 5 and 7 is 35.

Explanation: In order to compare two fractions, it is important to have a common denominator.

In this particular case, the least common multiple (LCM) of 5 and 7 is 35, which will allow us to make the two fractions comparable.

Step 2b

\$3/5\$, multiply both the numerator and denominator by 7, i.e., \$3/5\$ = \$(3 \times 7)/(5 \times 7)\$ = \$21/35\$

\$4/7\$, multiply both the numerator and denominator by 5, i.e., \$4/7\$ = \$(4 \times 5)/(7 \times 5)\$ = \$20/35\$

Explanation: In this step, we will convert \$3/5\$ and \$4/7\$ into equivalent fractions with the same denominator. To do this, we need to multiply both the numerator and denominator of \$3/5\$ by 7.

This gives us \$21/35\$.

Similarly, we need to multiply both the numerator and denominator of \$4/7\$ by 5, which gives us \$20/35\$.

Step 2c

Compare the numerators: Numerator of \$3/5\$ = 21

Numerator of \$4/7\$ = 20

So, 21 is greater than 20, and \$3/5\$ is greater than \$4/7\$.

Explanation: After comparing the numerators, we find that \$3/5\$ is greater than \$4/7\$ because its numerator is 21, while the numerator of \$4/7\$ is 20.

Step 3a

The first step to changing \$4 12/5\$ into a decimal is to change it to an improper fraction.

Explanation: In this step, change fractions into decimals first, we have to change mixed fractions into improper fractions.

Step 3b

Multiply 4 by 5 and add its product to 12 in the numerator to get: \$(20 + 12)/5 = 32/5\$

Explanation: In this step, we need to multiply the denominator(5) with a whole number (4) and add its product to the numerator(12) then we get, \$32/5\$

Step 3c

Convert fractions to decimals using the division method: \$32/5 = 6.4\$

Explanation: To obtain a decimal using the division method, divide the numerator, which is 32, by the denominator, which is 5. The result of the division is 6.4.

Step 4a

Convert fractions to decimals using the division method: \$75/90 = 0.833\$

Explanation: To obtain a decimal using the division method, divide the numerator, which is 75, by the denominator, which is 90. The result of the division is 0.833.