QuestionComplete the area model and then calculate $24 \times 35$ using the standard algorithm.

Studdy Solution

STEP 1

Assumptions1. We are given two numbers,24 and35, to multiply. . We are to use the area model and standard algorithm for multiplication.

STEP 2

First, let's break down the numbers24 and35 into their place values.24 can be broken down as $20 +4$ and35 can be broken down as $30 +5$ .

STEP 3

Now, let's create the area model. The area model is a visual representation of the multiplication process.We draw a rectangle and divide it into four smaller rectangles. The length of the larger rectangle is24 (broken down into20 and) and the width is35 (broken down into30 and5).

STEP 4

Now, we calculate the area of each smaller rectangle. The area of a rectangle is calculated by multiplying the length by the width.
The area of the first rectangle is $20 \times30$ .

STEP 5

Calculate the area of the first rectangle.
$Area_{1} =20 \times30 =600$

STEP 6

The area of the second rectangle is $20 \times5$ .

STEP 7

Calculate the area of the second rectangle.
$Area_{2} =20 \times5 =100$

STEP 8

The area of the third rectangle is $4 \times30$ .

STEP 9

Calculate the area of the third rectangle.
$Area_{3} =4 \times30 =120$

STEP 10

The area of the fourth rectangle is $4 \times5$ .

STEP 11

Calculate the area of the fourth rectangle.
$Area_{4} =4 \times5 =20$

STEP 12

Now, we add up the areas of all four rectangles to get the total area, which is the product of24 and35.
$Total\, area = Area_{} + Area_{2} + Area_{} + Area_{4}$

STEP 13

Plug in the values for the areas of the rectangles to calculate the total area.
$Total\, area =600 +100 +120 +20$

STEP 14

Calculate the total area.
$Total\, area =600 +100 +120 +20 =840$ So, $24 \times35 =840$ .

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