The amount of gold (in terms of inches) that the considered jewelry maker is left with from the considered gold chain is 12.5 inches
How can we interpret the division?
When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.
Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.
Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.
Thus, [tex]a \div b[/tex] = a divided in b equal parts.
Also, we can write: [tex]a \div b = a \times \dfrac{1}{b}[/tex]
(it is since a = a times 1 so [tex]a/b = 1 \times (a/b) = (1/b) \times a[/tex] )
What does 'a/b' of a quantity means?
'a/b' of a quantity means that quantity is first divided in 'b' parts, and then mutiplied by 'a', or,
[tex]\text{3/8 of a quantity} = \dfrac{\text{That quantity}}{b} \times a = \dfrac{a}{b} \times \text{that quantity}[/tex]
If a < b, then we say that a/b of that quantity is a parts out of 'b' equal parts of that thing.
Given that:
- Gold chain is 20 inches in length.
- 3/8 of that chain is used (assuminly, it is used in terms of its length)
- To find: How much of the chain is left (in terms of inches)
So, 3/8 of 20 inches is used, that means:
[tex]\dfrac{20}{8} \times 3 = \dfrac{15}{2} = 7.5 \: \rm in.[/tex] is used.
Inches of gold left = 20 - inches of gold used
Inches of gold left = 20 - 7.5 = 12.5 inches
Thus, the amount of gold (in terms of inches) that the considered jewelry maker is left with from the considered gold chain is 12.5 inches
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