Reasoning with Equivalences

Question 1

Lila wants to find 37 × 25 quickly. She decides to first multiply 37 by 100 and then divide the result by 4. Which answer shows the correct product and explains why this method works?

Accepted Answer

925; because multiplying by 100 gives 3700 and dividing by 4 gives the original factor of 25 since 25 = 100 ÷ 4.

Answer

925; because 25 is half of 50, so after multiplying by 100 you should divide by 2.

Answer

740; because 25 equals 100 ÷ 5, so you divide the 100‑times product by 5.

Answer

1850; because after multiplying by 100 you need to divide by 2 to get the product.

Question 2

What is 35% of 240? (Use the ideas: 10% = divide by 10, 5% = half of 10%, then combine them.)

Accepted Answer

84

Answer

76

Answer

90

Answer

70

Question 3

The sequence 52, 47, 42, 37, … is formed by applying the same operation to get each next number. What is the 20th term of this sequence?

Accepted Answer

-43

Answer

-48

Answer

147

Answer

-24

Try three questions

Lila wants to find 37 × 25 quickly. She decides to first multiply 37 by 100 and then divide the result by 4. Which answer shows the correct product and explains why this method works?

What is 35% of 240? (Use the ideas: 10% = divide by 10, 5% = half of 10%, then combine them.)

The sequence 52, 47, 42, 37, … is formed by applying the same operation to get each next number. What is the 20th term of this sequence?

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