Question

Nate’s work to solve a math problem is shown below.

Problem: Leona traveled 25 miles in 2/3 of an hour. What was her average speed in miles per hour?

What was Nate’s first error?
A-He used division instead of multiplication to model the problem in step 1.
B-He switched the divisor and the dividend when creating an equation to model the problem in step 1.
C-He replaced the wrong term with its reciprocal in step 2.
D-He should not have changed division to multiplication in step 2.


And
Which question is best modeled with a division expression?
A-How many 3/8's are in 48?
B-What is 3/8 of 48?
C-What is the total of 3/8 and 48?
D-How much more than 3/8g is 48?

Answer 1

1. Leona traveled 25 miles in 2/3 of an hour. What was her average speed in miles per hour?

speed = distance/time

So, her speed will be 25/2/3

So, this becomes : 25*3/2

Nate did the wrong calculation here.

Instead of inversing 2/3 , he inversed 25.

So, answer is C-He replaced the wrong term with its reciprocal in step 2.

2. A is right.

How many 3/8 's are in 48?

B is multiplication, C is addition and D is subtraction.

Answer 2

Answer (C) ⇒ He replaced the wrong term with its reciprocal in step 2

Answer (A) ⇒ How many 3/8 's in 48

Explanation:

∵ The distance = 25 miles

∵ The time = 2/3 hour

∵ Average speed = distance ÷ time

∴ Average speed = 25 ÷ 2/3 ⇒ step 1 (he is √)

= 25 × 3/2 ⇒ step 2 (his 1st error 1/25 × 2/3)

= 75/2 miles/h

∵ How many 3/8 's are in 48 means:

48 ÷ 3/8 = 48 × 8/3 = 128

∴ Answer (A) is best modeled with a division expression