Question

1. Estimate the product. Solve using an area model and the standard algorithm. Remember to express your products in standard form. Show your work on paper, enter your final answer. 53 x 1.2 = ____ x ____ + ____ 12 tenths x 53

Answer 1

`53 * 1.2 = 63.6`

Explanation:

Given

53 * 1.2

Required

Solve using the area model and standard algorithm

Using the area model:

53 is represented as: 50 + 3

1.2 is represented as: 1 + 0.2

So, we have:

`\begin{array}{ccc}{} & {1} & {0.2} & {50} & { -} & { -} & {3} & { -} & { -} & {Total } & {-} & {-} \ \end{array}`

Fill in the gaps with row by column multiplication:

`\begin{array}{ccc}{} & {1} & {2\ (tenths)} & {50} & {50 * 1} & {50 * 2} & {3} & {3*1} & {3*2} & {Total } & {-} & {-} \ \end{array}`

`\begin{array}{ccc}{} & {1} & {2\ (tenths)} & {50} & {50} & {100} & {3} & {3} & {6} & {Total } & {-} & {-} \ \end{array}`

Add up each column:

`\begin{array}{ccc}{} & {1} & {2\ (tenths)} & {50} & {50} & {100} & {3} & {3} & {6} & {Total } & {53} & {106} \ \end{array}`

So, the result is:

`53 * 1.2 = 53 + 106\ (tenths)`

`53 * 1.2 = 53 + 10.6`

`53 * 1.2 = 63.6`

Using the standard algorithm

`\begin{array}{cccc}{5} & { } & {3} &{(0\ d.p)} & {*1} & {.} & {2} & {(1\ dp)} \ \end{array}`

Multiply:

`\begin{array}{ccccc} {5} & {} & {3} &{(0\ d.p)} &{}& {1} & {.} & {2} & {(1\ dp)}&{}& {-} & {-} & {-} & {-}&{} & {1 } & {0} & {6} & { }& { } & {5} & {3} & { }\ \end{array}`

Add the results of the multiplication

`\begin{array}{ccccc} {5} & {} & {3} &{(0\ d.p)} &{}& {1} & {.} & {2} & {(1\ dp)}&{}& {-} & {-} & {-} & {-}&{} & {1 } & {0} & {6} & { }& { } & {5} & {3} & { }& { }& { } & {-} & {-} & {- }& {- }& { } & {6} & {3} & {6 }\ \end{array}`

So, the result is:

Add the decimal places together:

`0\ dp + 1\ dp = 1\ dp`

So, the result will be in 1 dp.

i.e.

`53 * 1.2 = 63.6`