Algebra essentials, Year 7: more practice

"n squared": n multiplied by itself

HintThe little raised 2 tells you how many times n appears in the multiplication.

The whyn² means n × n. It is not 2 × n, which is written 2n.

No — a and b are different letters, so the terms are unlike

HintAsk whether a and b stand for the same number.

The whyOnly like terms, with the same letter part, can be added. 3a + 2b has to stay as it is, but 3a + 2a = 5a.

Multiply by 4

HintThink of what would undo it and give you the number you started with.

The whyMultiplying by 4 undoes dividing by 4: (20 ÷ 4) × 4 = 20. Addition and subtraction undo each other in the same way.

23

HintReplace each letter with its number, then multiply before you add.

The why2a + 3b = 2 × 4 + 3 × 5 = 8 + 15 = 23. Each term is a multiplication, so it is done before the addition.

3n − 4

HintWork through the words in order, one operation at a time.

The whyMultiplying n by 3 gives 3n, and taking away 4 gives 3n − 4. Writing 3(n − 4) would mean subtracting 4 first.

The top left (the second quadrant)

HintNegative x means west of the vertical axis; positive y means above the horizontal axis.

The whyThe four quadrants are numbered anticlockwise from the top right. A point such as (−3, 2) is 3 left and 2 up, so it sits in the top left.

10y − 15

HintThe 5 multiplies every term inside the bracket, including the one with the minus sign.

The why5 × 2y = 10y and 5 × (−3) = −15. Check with y = 2: 5(4 − 3) = 5 and 10 × 2 − 15 = 5.

An expression — it has no equals sign

HintCheck whether there is a symbol joining two sides.

The whyAn equation states that two things are equal, such as 4x + 7 = 19. An expression like 4x + 7 only describes a value, so you simplify or evaluate it, not solve it.

26 cm

HintSubstitute 6.5 for s and multiply; the answer is a length, so it needs units.

The whyP = 4 × 6.5 = 26 cm. The 4 and s are multiplied because no sign is written between them.

38

HintReplace n with 8, multiplying before subtracting.

The why5 × 8 − 2 = 40 − 2 = 38. Only the position number is substituted: you do not need the first seven terms.