Question

1. julius and walt are finding the product of 25 and 16.

part a
julius answer is incorrect. what did julius do wrong?
part b
what did walt do wrong?
part c
what is the correct product?

1. a clothing store sells 26 shirts and 22 pairs of jeans. each item of clothing costs $32.

part a
what is a reasonable estimate for the total cost of the clothing?
show or explain how you found your answer.
part b
what is the exact answer for the total cost of the clothing? show or explain how you found your answer.

Explanation:

Problem 20 Part C

Step1: Recall multiplication method

To find the product of \(25\) and \(16\), we can use the distributive property: \(25\times16 = 25\times(10 + 6)\).

Step2: Apply distributive property

First, calculate \(25\times10 = 250\) and \(25\times6 = 150\). Then add these two results: \(250+150 = 400\).
Or, we can also calculate \(25\times16\) as \(25\times4\times4=100\times4 = 400\).

Step1: Estimate the number of items

First, find the total number of clothing items. \(26 + 22\approx30+20 = 50\) (we round \(26\) to \(30\) and \(22\) to \(20\) for estimation).

Step2: Estimate the total cost

Each item costs \(\$32\), and we can round \(32\) to \(30\). Then the estimated total cost is \(50\times30=\$1500\). (Another way: \(26 + 22 = 48\approx50\), \(32\approx30\), so \(50\times30 = 1500\))

Step1: Calculate total number of items

First, find the total number of clothing items: \(26+22 = 48\).

Step2: Calculate total cost

Each item costs \(\$32\), so the total cost is \(48\times32\). We can calculate this as \(48\times(30 + 2)=48\times30+48\times2=1440 + 96 = 1536\).

Answer:

\(400\)

Problem 21 Part A