Answer:
[tex]53 * 1.2 = 63.6[/tex]
Step-by-step 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:
[tex]\begin{array}{ccc}{} & {1} & {0.2} & {50} & { -} & { -} & {3} & { -} & { -} & {Total } & {-} & {-} \ \end{array}[/tex]
Fill in the gaps with row by column multiplication:
[tex]\begin{array}{ccc}{} & {1} & {2\ (tenths)} & {50} & {50 * 1} & {50 * 2} & {3} & {3*1} & {3*2} & {Total } & {-} & {-} \ \end{array}[/tex]
[tex]\begin{array}{ccc}{} & {1} & {2\ (tenths)} & {50} & {50} & {100} & {3} & {3} & {6} & {Total } & {-} & {-} \ \end{array}[/tex]
Add up each column:
[tex]\begin{array}{ccc}{} & {1} & {2\ (tenths)} & {50} & {50} & {100} & {3} & {3} & {6} & {Total } & {53} & {106} \ \end{array}[/tex]
So, the result is:
[tex]53 * 1.2 = 53 + 106\ (tenths)[/tex]
[tex]53 * 1.2 = 53 + 10.6[/tex]
[tex]53 * 1.2 = 63.6[/tex]
Using the standard algorithm
[tex]\begin{array}{cccc}{5} & { } & {3} &{(0\ d.p)} & {*1} & {.} & {2} & {(1\ dp)} \ \end{array}[/tex]
Multiply:
[tex]\begin{array}{ccccc} {5} & {} & {3} &{(0\ d.p)} &{}& {1} & {.} & {2} & {(1\ dp)}&{}& {-} & {-} & {-} & {-}&{} & {1 } & {0} & {6} & { }& { } & {5} & {3} & { }\ \end{array}[/tex]
Add the results of the multiplication
[tex]\begin{array}{ccccc} {5} & {} & {3} &{(0\ d.p)} &{}& {1} & {.} & {2} & {(1\ dp)}&{}& {-} & {-} & {-} & {-}&{} & {1 } & {0} & {6} & { }& { } & {5} & {3} & { }& { }& { } & {-} & {-} & {- }& {- }& { } & {6} & {3} & {6 }\ \end{array}[/tex]
So, the result is:
Add the decimal places together:
[tex]0\ dp + 1\ dp = 1\ dp[/tex]
So, the result will be in 1 dp.
i.e.
[tex]53 * 1.2 = 63.6[/tex]
