Formulae - WJECSubstitution of negative numbers

A formula may be given using letters:

P = 3A + 2T

• 3A means 3 × A
• 2T means 2 × T

Example 1

Use the formula D = 2B + 4C to find the value of D when B = 5 and C = 3.

1. Write in the meaning of 2B (2 × B) and 4C (4 × C):

D = 2 × B + 4 × C.

2. Replace the letters with the values you are given:

D = 2 × 5 + 4 × 3.

3. Remember BIDMAS (multiply first then add):

D = 10 + 12.

D = 22.

Example 2

Use the formula Y = 2Z + 4W when Z = 7 and W = -2.

1. Write in the meanings of 2Z and 4W:

Y = 2 × Z + 4 × W.

2. Replace the letters with the values you are given:

Y = 2 × 7 + 4 × -2.

3. Do the multiplication sums. Don’t forget the rules with negative numbers. In this case, a positive multiplied by a negative make a negative:

Y = 14 + -8.

4. Complete the sum. Don’t forget a plus and a minus make a minus:

Y = 14 - 8.

Y = 6.

Example 3 - Higher tier

Use the formula Q = 2R - 3S to find the value of R when Q = -30 and S = 4.

1. Replace the known letters:

-30 = 2 × R - 3 × 4.

2. Multiply:

-30 = 2 × R - 12.

3. Add 12 to both sides:

-30 + 12 = 2 × R.

-18 = 2 × R.

4. Divide both sides by 2:

-18 ÷ 2 = R.

R = -9.

Example 4 - Higher tier

In equations and formulae, division is usually presented as a fraction, eg: