Question

Harlan used 3 1/2 kg of sand to make a large hourglass. To make a smaller hourglass, he only used 1 3/7 kg of sand. How much more sand did it take to make the large hourglass than the smaller one?

Answer 1

2
`(1)/(14)` kg more sand need to make large hourglass than the smaller one

Explanation:

given data

large house sand = 3
`(1)/(2)` kg

small house sand = 1
`(3)/(7)` kg

to find out

How much more sand did it take to make the large hourglass than the smaller one

solution

we know sand used for small house is 1
`(3)/(7)` kg and for large is 3
`(1)/(2)` kg

so we need more extra sand is = sand used for large - sand used for small ..........1

put here value

more extra sand is = 3
`(1)/(2)` - 1
`(3)/(7)`

more extra sand is = 3
`(1)/(2)` - 1
`(3)/(7)`

more extra sand is = 2
`(1)/(14)`

so 2
`(1)/(14)` kg more sand need to make large hourglass than the smaller one

Answer 2

Answer:
`2(1)/(14)\ kg`

Explanation:

We can make the conversion from mixed numbers to improper fractions:

• Multiply the whole number part by the denominator of the fraction.
• Add the numerator of the fraction and the product obtained (This sum will be the new numerator).
• The denominator is the same.

Then:

`3(1)/(2)=((3*2)+1)/(2)=(7)/(2)\\\\1(3)/(7)=((1*7)+3)/(7)=(10)/(7)`

We need to subtract the fractions how much more sand it took to make the large hourglass than the smaller one.

Notice that the denominators are differente, then we must find the Least Common Denominator (LCD):

`2=2\\\\7=7\\\\\\LCD=2*7=14`

Then, subtracting the fractions, we get:

`(7)/(2)-(10)/(7)=(49-20)/(14)=(29)/(14)\ kg`

To convert this improper fraction to a mixed number:

• When you divide 29 by 14 you get a quotient of 2. This will be the whole number.
• The remainder obtained is 1. This will be the numerator of the fraction.
• The denominator does not change.

Then:

`(29)/(14)\ kg=2(1)/(14)\ kg`

Therefore, it took
`2(1)/(14)\ kg` more sand to make the large hourglass than the smaller one.