Le Rocquier School Quick Explainers Beta

Maths

Tick the topics and the support you need, then start. In each topic: read the idea, watch the video, then try the questions. The answers stay hidden until you click Show answers.

1 Negative numbersNumbers below zero, and how to add and take away with them 2:15

Negative numbers are numbers below zero, like the temperature on a very cold day: −3°C.

On a number line, zero is in the middle. Negatives are on the left, positives are on the right. Further right means bigger, so −2 is bigger than −5.

  • Adding: move right.
  • Taking away: move left.
  • Adding a negative is the same as taking away: 3 + (−5) = 3 − 5
  • Taking away a negative is the same as adding: 1 − (−3) = 1 + 3

Two minus signs next to each other make a plus.

Have a go

Draw a number line if it helps.

  1. Which is bigger: −7 or −2?
  2. 3 − 8 =
  3. −6 + 4 =
  4. 5 + (−3) =
  5. −2 − (−6) =
  6. It is −4°C in the morning. By lunch it is 9 degrees warmer. What is the temperature at lunch?
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  1. −2 (it is further right)
  2. −5
  3. −2
  4. 2 (same as 5 − 3)
  5. 4 (same as −2 + 6)
  6. 5°C
2 Multiplying and dividing negativesSame signs or different signs? 1:14

When you multiply or divide with negative numbers, do it in two steps:

  1. Work out the numbers, ignoring the signs.
  2. Then choose the sign.
  • Same signs → answer is positive. −3 × −4 = 12
  • Different signs → answer is negative. 3 × −4 = −12

Dividing uses exactly the same rule.

Same signs: positive. Different signs: negative.

Have a go

  1. 4 × −3 =
  2. −5 × −2 =
  3. −7 × 3 =
  4. −24 ÷ 6 =
  5. −18 ÷ −3 =
  6. Challenge: −2 × −2 × −2 =
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  1. −12
  2. 10
  3. −21
  4. −4
  5. 6
  6. −8 (−2 × −2 = 4, then 4 × −2 = −8)
3 HCF: Highest Common FactorPrime factor trees and a Venn diagram 1:56

The HCF is the biggest number that goes into both numbers.

  1. Split each number into primes with a factor tree. Start with the smallest prime, 2.
  2. Write each number as primes multiplied: 12 = 2 × 2 × 3, 18 = 2 × 3 × 3
  3. Put the primes in a Venn diagram. Primes they share go in the middle.
  4. Multiply the middle: 2 × 3 = 6. The HCF of 12 and 18 is 6.

Middle for HCF. Everything for LCM.

Have a go

  1. Write 20 as a product of primes.
  2. Find the HCF of 8 and 12.
  3. Find the HCF of 15 and 25.
  4. Find the HCF of 18 and 24.
  5. Find the HCF of 36 and 48.
  6. Challenge: find the HCF of 30 and 42.
Show answersHide answers
  1. 20 = 2 × 2 × 5 = 2² × 5
  2. 4
  3. 5
  4. 6
  5. 12
  6. 6 (30 = 2 × 3 × 5, 42 = 2 × 3 × 7, middle is 2 × 3)
4 LCM: Lowest Common MultipleThe first number in both times tables 1:21

Multiples are the numbers in a times table.

To find the LCM, list the multiples of both numbers and find the smallest one that is in both lists.

4: 4, 8, 12, 16, 20, 24…
6: 6, 12, 18, 24…

24 is in both lists too, but 12 comes first. So the LCM of 4 and 6 is 12.

We need the LCM to add and subtract fractions with different bottoms.

LCM = the smallest number in both times tables.

Have a go

  1. Find the LCM of 3 and 4.
  2. Find the LCM of 5 and 10.
  3. Find the LCM of 6 and 8.
  4. Find the LCM of 4 and 10.
  5. Find the LCM of 9 and 12.
  6. One bus leaves every 6 minutes. Another leaves every 9 minutes. They both leave at 9:00. When do they next leave together?
Show answersHide answers
  1. 12
  2. 10
  3. 24
  4. 20
  5. 36
  6. 9:18 (the LCM of 6 and 9 is 18)
5 What is a fraction?Equal parts, equivalent fractions and simplifying 2:00

A fraction is part of a whole. The parts must be equal.

  • The bottom number: how many equal parts in total.
  • The top number: how many parts we colour in.

Equivalent fractions are the same amount with different names: 1 over 2 = 2 over 4 = 4 over 8

To make one, multiply the top and the bottom by the same number. To simplify, divide the top and bottom by their HCF: 6 over 8 → 3 over 4

Whatever you do to the top, do to the bottom.

Have a go

  1. A bar is cut into 5 equal parts. 2 parts are coloured. What fraction is coloured?
  2. Fill the gap: 1 over 2 = ? over 8
  3. Fill the gap: 2 over 3 = ? over 12
  4. Simplify 4 over 8
  5. Simplify 9 over 12
  6. Simplify 10 over 15
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  1. 2 over 5
  2. 4 (× 4 on top and bottom)
  3. 8 (× 4 on top and bottom)
  4. 1 over 2 (÷ 4)
  5. 3 over 4 (÷ 3)
  6. 2 over 3 (÷ 5)
6 Adding fractionsMake the bottoms match, then add the tops 1:14

If the bottoms are the same, add the tops. The bottom stays the same: 1 over 5 + 2 over 5 = 3 over 5

Never add the bottoms. The size of the parts does not change.

If the bottoms are different, the parts are different sizes:

  1. Find the LCM of the bottoms (3 and 4 → 12).
  2. Change both fractions: 1 over 3 = 4 over 12, 1 over 4 = 3 over 12
  3. Add the tops: 4 over 12 + 3 over 12 = 7 over 12

Make the bottoms match, then add the tops.

Have a go

  1. 1 over 7 + 3 over 7 =
  2. 2 over 9 + 5 over 9 =
  3. 1 over 2 + 1 over 4 =
  4. 1 over 3 + 1 over 2 =
  5. 1 over 4 + 1 over 6 =
  6. 2 over 5 + 1 over 3 =
Show answersHide answers
  1. 4 over 7
  2. 7 over 9
  3. 2 over 4 + 1 over 4 = 3 over 4
  4. 2 over 6 + 3 over 6 = 5 over 6
  5. 3 over 12 + 2 over 12 = 5 over 12
  6. 6 over 15 + 5 over 15 = 11 over 15
7 Subtracting fractionsMake the bottoms match, then take away the tops 1:10

Subtracting works just like adding.

Same bottoms: take away the tops. 4 over 5 − 1 over 5 = 3 over 5

Different bottoms:

  1. Find the LCM of the bottoms (4 and 3 → 12).
  2. Change both fractions: 3 over 4 = 9 over 12, 1 over 3 = 4 over 12
  3. Take away the tops: 9 over 12 − 4 over 12 = 5 over 12

Make the bottoms match, then take away the tops.

Have a go

  1. 6 over 7 − 2 over 7 =
  2. 5 over 8 − 2 over 8 =
  3. 3 over 4 − 1 over 2 =
  4. 4 over 5 − 1 over 2 =
  5. 2 over 3 − 1 over 4 =
  6. 5 over 6 − 1 over 4 =
Show answersHide answers
  1. 4 over 7
  2. 3 over 8
  3. 3 over 4 − 2 over 4 = 1 over 4
  4. 8 over 10 − 5 over 10 = 3 over 10
  5. 8 over 12 − 3 over 12 = 5 over 12
  6. 10 over 12 − 3 over 12 = 7 over 12
8 Multiplying fractionsTops times tops, bottoms times bottoms 1:09

With fractions, times means "of". 2 over 3 × 3 over 4 means 2 over 3 of 3 over 4.

In the video, the answer is where the coloured parts overlap: 6 boxes out of 12.

The quick way:

  • Multiply the tops: 2 × 3 = 6
  • Multiply the bottoms: 3 × 4 = 12

2 over 3 × 3 over 4 = 6 over 12

You do not need the bottoms to match when multiplying.

Tops times tops. Bottoms times bottoms.

Have a go

  1. 1 over 2 × 1 over 3 =
  2. 2 over 5 × 1 over 3 =
  3. 3 over 4 × 1 over 2 =
  4. 2 over 3 × 4 over 5 =
  5. What is 1 over 2 of 3 over 5?
  6. 3 over 4 × 2 over 3 = (then simplify)
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  1. 1 over 6
  2. 2 over 15
  3. 3 over 8
  4. 8 over 15
  5. 3 over 10
  6. 6 over 12 = 1 over 2
9 Dividing fractionsKeep, Change, Flip 1:15

Dividing asks: how many fit in? How many quarters fit into 3 wholes? 12.

The quick method is Keep, Change, Flip:

  1. Keep the first fraction.
  2. Change ÷ into ×.
  3. Flip the second fraction upside down.

Then multiply: 1 over 2 ÷ 1 over 4 = 1 over 2 × 4 over 1 = 4 over 2 = 2

Keep, Change, Flip. Then multiply.

Have a go

  1. How many halves fit into 4 wholes?
  2. 3 ÷ 1 over 3 =
  3. 1 over 2 ÷ 1 over 6 =
  4. 3 over 4 ÷ 3 over 8 =
  5. 2 over 3 ÷ 1 over 2 =
  6. 2 over 5 ÷ 1 over 3 =
Show answersHide answers
  1. 8
  2. 9
  3. 1 over 2 × 6 over 1 = 6 over 2 = 3
  4. 3 over 4 × 8 over 3 = 24 over 12 = 2
  5. 2 over 3 × 2 over 1 = 4 over 3 = 11 over 3
  6. 2 over 5 × 3 over 1 = 6 over 5 = 11 over 5
10 Percentage increase and decreaseFind 10% first 2:18

Per cent means "out of 100".

The key trick: find 10% first by dividing by 10. 10% of £80 = £8, so 20% = £16.

  • Increase: find the percentage, then add it on. £80 + 20% = £80 + £16 = £96
  • Decrease: find the percentage, then take it away. £50 − 30% = £50 − £15 = £35

With a calculator: increase by 20% → × 1.2. Decrease by 30% → × 0.7.

Find the percentage. Then add it or take it away.

Have a go

  1. Find 10% of £60.
  2. Find 20% of £40.
  3. Find 30% of £90.
  4. Increase £50 by 10%.
  5. Increase £70 by 20%.
  6. Decrease £60 by 30%.
  7. Calculator: what do you multiply by to increase by 15%?
Show answersHide answers
  1. £6
  2. £8
  3. £27
  4. £50 + £5 = £55
  5. £70 + £14 = £84
  6. £60 − £18 = £42
  7. 1.15 (you end up with 115%)
11 Solving equationsKeep it balanced: do the same to both sides 2:36

An equation has a mystery number, x. The = sign means both sides are balanced.

Golden rule: do the same thing to both sides.

Undo each step with the inverse:

  • + is undone by −, and − by +
  • × is undone by ÷, and ÷ by ×

Two-step: 2x + 1 = 11
− 1 from both sides: 2x = 10
÷ 2 both sides: x = 5

Check: 2 × 5 + 1 = 11 ✓

Undo the + or − first, then the × or ÷. Always check.

Have a go

Solve each equation, then check your answer by putting it back in.

  1. x + 5 = 9
  2. x − 3 = 10
  3. 4x = 20
  4. 2x + 3 = 11
  5. 5x − 4 = 21
  6. Challenge: 3x + 7 = 1
Show answersHide answers
  1. x = 4
  2. x = 13
  3. x = 5
  4. x = 4 (2x = 8)
  5. x = 5 (5x = 25)
  6. x = −2 (3x = −6)