Rearranging Formulae

Do the opposite of adding 7 to both sides.

The opposite of subtracting 4 is adding 4.

h is multiplied by 6, so divide both sides by 6.

m is divided by 3, so multiply both sides by 3.

Undo the adding first, then undo the multiplying.

Undo the subtracting first, then undo the multiplying.

1. Add 8 to both sides: m+8=5k.
2. Divide both sides by 5: \frac{m+8}{5}=k.
3. So k=\frac{m+8}{5}.

Add 4x to both sides first, so that the x term is positive.

1. Add 4x to both sides: y+4x=20.
2. Subtract y from both sides: 4x=20-y.
3. Divide both sides by 4: x=\frac{20-y}{4}.

Multiply both sides by 2 first, to clear the fraction.

1. Multiply both sides by 2: 2m=a+b.
2. Subtract b from both sides: 2m-b=a.
3. So a=2m-b.

a is multiplied by m, so do the opposite to both sides.

1. In F=ma, a is multiplied by m.
2. Divide both sides by m: \frac{F}{m}=a.
3. So a=\frac{F}{m}.

Get the x term on its own first, then divide.

1. Subtract c from both sides: y-c=mx.
2. Divide both sides by m: \frac{y-c}{m}=x.
3. So x=\frac{y-c}{m}.

You can divide both sides by 3 first, or multiply out the bracket first.

1. Divide both sides by 3: \frac{y}{3}=x+4.
2. Subtract 4 from both sides: \frac{y}{3}-4=x.
3. So x=\frac{y}{3}-4, which can also be written x=\frac{y-12}{3}.

Take away 12 first, then undo the dividing by 5.

1. Subtract 12 from both sides: C-12=\frac{n}{5}.
2. Multiply all of the left side by 5: 5(C-12)=n.
3. So n=5(C-12), which is the same as n=5C-60.

Move the 2w term to the other side first.

1. Subtract 2w from both sides: P-2w=2l.
2. Divide both sides by 2: \frac{P-2w}{2}=l.
3. So l=\frac{P-2w}{2}, which is the same as l=\frac{P}{2}-w.

Clear the half first, then divide by the other letter.

Part (a)

1. Multiply both sides by 2: 2A=bh.
2. Divide both sides by b: \frac{2A}{b}=h.
3. So h=\frac{2A}{b}.

Part (b)

1. h=\frac{2\times30}{12}=\frac{60}{12}=5.
2. The height is 5 cm.

Check each line of the working: was every term dealt with?

Part (a)

1. Dividing both sides by 6 should give \frac{g}{6}=h+3, because 18\div6=3.
2. Omar divided g and 6h by 6 but did not divide the 18 by 6.

Part (b)

1. Subtract 18 from both sides: g-18=6h.
2. Divide both sides by 6: \frac{g-18}{6}=h.
3. So h=\frac{g-18}{6}, which is the same as h=\frac{g}{6}-3.

When the letter you want is on the bottom of a fraction, multiply both sides by it first.

Part (a)

1. Multiply both sides by n: nT=36.
2. Divide both sides by T: n=\frac{36}{T}.

Part (b)

1. n=\frac{36}{4}=9.
2. Check: \frac{36}{9}=4 hours. 9 people are needed.

Get x squared on its own first. The opposite of squaring is taking the square root.

1. Divide both sides by 6: \frac{S}{6}=x^2.
2. Take the square root of both sides: \sqrt{\frac{S}{6}}=x.
3. So x=\sqrt{\frac{S}{6}}.

Square both sides first to remove the square root.

1. Square both sides: d^2=5a-4.
2. Add 4 to both sides: d^2+4=5a.
3. Divide both sides by 5: \frac{d^2+4}{5}=a.
4. So a=\frac{d^2+4}{5}.

Clear the fraction first, then deal with the t, then the u.

1. Multiply both sides by 2: 2s=(u+v)t.
2. Divide both sides by t: \frac{2s}{t}=u+v.
3. Subtract u from both sides: \frac{2s}{t}-u=v.
4. So v=\frac{2s}{t}-u, which is the same as v=\frac{2s-ut}{t}.

Undo the steps in the right order: clear the half and the m, then undo the squaring.

Part (a)

1. Multiply both sides by 2: 2E=mv^2.
2. Divide both sides by m: \frac{2E}{m}=v^2.
3. Take the square root of both sides: v=\sqrt{\frac{2E}{m}}.

Part (b)

1. \frac{2\times400}{8}=\frac{800}{8}=100.
2. v=\sqrt{100}=10.