Question

Allana used Fraction 3 over 5 yard of fabric to make a scarf. Can she make 2 of these scarves with Fraction 1 and 7 over 10 yards of fabric, and why? No, because the quotient of Fraction 1 and 7 over 10 ÷ Fraction 3 over 5 is 1 and 1 over 50 No, because the quotient of Fraction 3 over 5 ÷ Fraction 1 and 7 over 10 is 1 and 1 over 50 Yes, because the quotient of Fraction 1 and 7 over 10 ÷ Fraction 3 over 5 is 2 and 5 over 6 Yes, because the quotient of Fraction 3 over 5 ÷ Fraction 1 and 7 over 10 is 2 and 5 over 6

Answer 1

Yes, because the quotient of Fraction 1 and 7/10 [division sign]Fraction 3/5 is 2 and 5/6", third choice

Explanation:

Divide 1 7/10 by 3/5 to see if the quotient is greater than 2. If it's not, you can't get 2 scarves out of it. If it is, then you can get 2 scarves out of it and have whatever the remainder is as left-over. Before we divide, let's change that 1 7/10 into an improper fraction since it will be easier to work with.

1 7/10 = 17/10

Now we can divide:

The rule for dividing fractions is that you bring up the lower fraction and flip it to multiply, so that looks like this:

×

To simplify before we multiply, we can reduce between the 5 and the 10 and have smaller numbers to deal with:

×

The product there is

So the answer you want from your choices is

"Yes, because the quotient of Fraction 1 and 7 over 10 [division sign]Fraction 3 over 5 is 2 and 5 over 6", third choice

Answer 2

Explanation:

Divide 1 7/10 by 3/5 to see if the quotient is greater than 2. If it's not, you can't get 2 scarves out of it. If it is, then you can get 2 scarves out of it and have whatever the remainder is as left-over. Before we divide, let's change that 1 7/10 into an improper fraction since it will be easier to work with.

1 7/10 = 17/10

Now we can divide:

`((17)/(10) )/((3)/(5) )`

The rule for dividing fractions is that you bring up the lower fraction and flip it to multiply, so that looks like this:

`(17)/(10)`×
`(5)/(3)`

To simplify before we multiply, we can reduce between the 5 and the 10 and have smaller numbers to deal with:

`(17)/(2)`×
`(1)/(3)`

The product there is
`(17)/(6)=2(5)/(6)`

So the answer you want from your choices is

"Yes, because the quotient of Fraction 1 and 7 over 10 [division sign]Fraction 3 over 5 is 2 and 5 over 6", third choice