Answer:
(a) $1.98
(b) $6.30
Step-by-step explanation:
(a)
The new value =
1.80 + The value of the percentage increase =
1.80 + (10% × 1.80) =
1.80 + 10% × 1.80 =
(1 + 10%) × 1.80 =
(100% + 10%) × 1.80 =
110% × 1.80 =
110 ÷ 100 × 1.80 =
110 × 1.80 ÷ 100 =
198 ÷ 100 =
1.98
Calculate the actual change (the absolute difference) between the two values
The actual change =
The new value - 1.80 =
1.98 - 1.80 =
0.18
Proof of calculation.
Calculate the percentage increased value...
... and see if we get as a result...
... the actual change (the absolute difference).
Calculate the percentage increased value:
The value of the percentage increase =
10% × 1.80 =
10 ÷ 100 × 1.80 =
10 × 1.80 ÷ 100 =
18 ÷ 100 =
0.18
So we have proven that the calculations are correct.
For positive numbers
The actual change =
The value of the percentage increase
The answer:
1.80 increased by 10% = 1.98
The actual change:
1.98 - 1.80 = 0.18
(b)
Calculate the New value
The new value =
42.0 + The value of the percentage increase =
4.20 + (50% × 4.20) =
4.20 + 50% × 4.20 =
(1 + 50%) × 4.20 =
(100% + 50%) × 4.20 =
150% × 4.20 =
150 ÷ 100 × 4.20 =
150 × 4.20 ÷ 100 =
63,000 ÷ 100 =
630
(but its as a dollar so its 6.30)
Calculate the actual change (the absolute difference) between the two values
The actual change =
The new value - 4.20 =
6.30 - 4.20 =
2.10
Proof of calculation.
Calculate the percentage increased value...
... and see if we get as a result...
... the actual change (the absolute difference).
Calculate the percentage increased value:
The value of the percentage increase =
50% × 4.20 =
50 ÷ 100 × 4.20 =
50 × 4.20 ÷ 100 =
21,000 ÷ 100 =
210
(but its as a dollar so its 2.10)
So we have proven that the calculations are correct.
For positive numbers
The actual change =
The value of the percentage increase
The answer:
4.20 increased by 50% = 6.30
The actual change:
6.30 - 4.20 = 2.10
. You get the fraction 
. While this is technically the answer, you can simplify this down to 
. Because 421 is a prime number, this can not be simplified any further. Therefore, the solution is