Layla makes jewellery to sell at a school fair. Each bracelet has 53 beads. She makes 68 bracelets. Each necklace has 105 beads. She makes 34 necklaces. How many beads does Layla use altogether?
In this problem, Layla is making different types of jewellery to sell at a school fair and she’s making two different types: bracelets and necklaces. And our job is to calculate the number of beads that Layla uses altogether. She uses different amounts of beads on the bracelets and the necklaces. We’re told that each bracelet has 53 beads and that she makes 68 bracelets. So how can we find the total number of beads that Layla uses to make bracelets out of?
We just need to multiply the two numbers together. 53 beads on 68 bracelets is the same as 53 multiplied by 68. The numbers are different for the necklaces, but the idea is the same. Each necklace contains 105 beads and Layla makes 34 necklaces. So to calculate the total number of beads that Layla uses on necklaces, we just need to multiply 105 and 34 together. Once we’ve then found the number of beads that she uses on bracelets and then necklaces, we just need to add the two together to find out the overall total. So let’s go through these three steps.
First of all, let’s calculate the number of beads that Layla uses to make bracelets: 53 times 68. We could use a grid method to multiply these two two-digit numbers together. We can start by partitioning 53 into 50 and three and 68 into 60 and eight. Let’s find the product for each part of the grid. We know that five sixes are 30. So 50 sixes must be 300. And 50 60s must be 3000. Three sixes are 18. So three lots of 60 equal 180. Five-eighths are 40. So 50 eights are 10 times this, 400. Finally, three eights are 24.
Now, we just need to add the various parts together: 3000 plus 400 plus 180 plus 24. We have four ones. Eight tens plus two tens equals 10 tens, which is the same as 100. 400 plus 100 equals 500. But then we also exchange 100. That takes us to 600. And then, we only have three in the thousands column. So the total number of beads that Layla uses to make her bracelets out of is 3604.
Now, let’s think about the necklaces. We need to multiply 105 by 34 to find the answer. How can we do this quickly? Well, we can partition 105 into 100 and five. What if we found 100 lots of 34 and five lots of 34 and then added the two together? When we multiply a number by 100, the digits move two places to the left. So 34 becomes 3400. Now, how can we find five lots of 34 quickly? We can calculate 10 lots of 34 then use this to help. 10 lots of 34 is 340. So if we divide this by two, we’ll be able to find five lots of 34. Five is half of 10.
Let’s think of 340 as 300 and also 40. Half of 300 is 150 and half of 40 is 20. 150 plus 20 equals 170. So five lots of 34 equal 170. We know what 13 fours are which is 3400. And we know what five 34s are which is 170. Add the two together. And what’s our total? 3570. So the total number of beads that Layla uses to make necklaces out of is 3570.
Now, we can work out the number of beads she uses altogether. This is simply the number of beads that we found she uses on bracelets, 3604, plus the number of beads that she uses on necklaces, 3570. Four ones plus zero ones equal four ones. Zero tens plus seven tens remain seven tens. Six hundreds plus five hundreds equals 11 hundreds which is the same as 1100. Two lots of 3000 equal 6000. But we’ve also exchanged the 1000 that takes us to 7000, which equals a lot of beads to use on a lot of items of jewellery. The number of beads that Layla uses altogether is 7174.