Solving Problems (Medium)
Find out what the brown box weighs in question 7.

Solving Problems (Medium)

Solving problems in real life often requires multiplication, so make sure you continue to practise your times tables until you know them off by heart! If you know that one box of pencils holds 12 pencils, how many pencils will 30 boxes hold? It's important to get to grips with this kind of problem.

Let's say you are the caterer for a large wedding. There will be 275 guests. Now, you know how many knives and forks you will need (and if you don't know, you'd better start learning your times tables quickly!), but each guest will be receiving a gift bag. In this bag will be 6 different items. It's up to you to supply these items. How many of each item will you need?

Give this 11-plus Maths quiz a go and see how well you do.

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  1. The French writer Jules Verne wrote the adventure novel 'Twenty Thousand Leagues Under the Sea'. If 1 league = 5.556 km, how many leagues is 2,778 km?
    2,778 km = 2,778 ÷ 5.556 = 500 leagues. You have to divide 2,778 by 5.556 because you want to find out how many 'lots' of 5.556 there are in 2,778 : each 'lot' equals 1 league: this is the same adding 'lots' of 5.556 to itself until you get to 2,778 . By the way, it's a great read!
  2. Some workers are filling up sacks with quality garden soil. If each sack can hold 25 kg, how many sacks can be filled from 1,250 kg of quality soil?
    The number of sacks that can be filled = 1,250 ÷ 25 = 50 sacks. You have to divide 1,250 by 25 because you want to find out how many 'lots' of 25 there are in 1,250: each 'lot' equals 1 sack: this is the same as adding 'lots' of 25 to itself until you get to 1,250
  3. In a certain child's game, pushing a stick into a hole to a depth of 2 cm causes a wheel to turn through half a rotation (turn). How many complete rotations will the wheel turn through if the stick is pushed to a depth of 12 cm?
    12 ÷ 2 = 6. You have to divide 12 by 2 because you want to find out how many 'lots' of 2 there are in 12: each 'lot' equals half a rotation: this is the same as adding 'lots' of 2 to itself until you get to 12. Six 'lots' means 6 × 0.5 = 3 complete rotations. DON'T forget, half a rotation = 180°
  4. If each box holds 12 items, how many boxes are required to hold 96,000 items?
    The number of boxes required = 96,000 ÷ 12 = 8,000. You have to divide 96,000 by 12 because you want to find out how many 'lots' of 12 there are in 96,000 : each 'lot' equals 1 box: this is the same as adding 'lots' of 12 to itself until you get to 96,000
  5. A paperback book has 1,000 pages. If the book weighs 785 g, what is the weight of a single page? (You may ignore the front and back covers of the book.)
    A single page weighs 785 ÷ 1,000 = 0.785 g. You have to divide 785 by 1,000 because you want to find out how many 'lots' of 1,000 there are in 785: each 'lot' equals 1 page
  6. The circumference of a wheel is 24 cm. How many complete revolutions (turns) will it make in travelling 24 m?
    First convert 24 m to centimetres: 24 × 100 = 2,400 cm. The number of revolutions (turns) = 2,400 ÷ 24 = 100. You have to divide by 24 because you want to find out how many 'lots' of 24 there are in 2,400: each 'lot' equals 1 turn: this is the same as adding 'lots' of 24 to itself until you get to 2,400
  7. If a piece of material of length 4 m is folded in half on itself four times, what will the final length of the material be in centimetres?
    First convert 4 m to centimetres: 4 × 100 = 400 cm. Folding in half four times, means that the length of the material decreases by a half four times:
    400 ÷ 2 = 200
    200 ÷ 2 = 100
    100 ÷ 2 = 50
    50 ÷ 2 = 25
    This is the same as calculating 400 ÷ (2 × 2 × 2 × 2) = 400 ÷ 16 = 25 cm
  8. The brown box weighs eight times more than the black box. If the black box weighs 8 kg, what does the brown box weigh?
    The brown box weighs eight times more than the black box which weigh 8 kg ∴ the brown box weighs 8 × 8 = 64 kg
  9. If 12 people are served every two minutes in a fast food shop, how many people will have been served in 1 hour?
    There are 60 minutes in an hour. 60 ÷ 2 = 30. You have to divide 60 by 2 because you want to find out how many 'lots' of 2 there are in 60: each 'lot' equals 12 people: this is the same as adding 'lots' of 2 to itself until you get to 60. Thirty 'lots' means that 30 × 12 = 360 people are served every hour
  10. If the area of a square field is 144 m2, what is the length and width of the field?
    The length and width of the field are the same because the sides of a square are the same. You need to find a number which when multiplied with itself gives 144 because area = length × width: 12 × 12 = 144

Author: Frank Evans

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