Answer :
Let's solve each part using mental math shortcuts.
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(a) Calculate [tex]\( 99 + 54 \)[/tex]
Notice that [tex]\(99\)[/tex] is just [tex]\(1\)[/tex] less than [tex]\(100\)[/tex]. We can add using [tex]\(100\)[/tex] and then adjust:
1. Compute:
[tex]$$100 + 54 = 154.$$[/tex]
2. Since we added [tex]\(1\)[/tex] extra (because [tex]\(100\)[/tex] is [tex]\(1\)[/tex] more than [tex]\(99\)[/tex]), subtract [tex]\(1\)[/tex]:
[tex]$$154 - 1 = 153.$$[/tex]
So,
[tex]$$ 99 + 54 = 153. $$[/tex]
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(b) Calculate [tex]\( 244 - 99 \)[/tex]
Recognize that subtracting [tex]\(99\)[/tex] is almost subtracting [tex]\(100\)[/tex]. We perform the subtraction with [tex]\(100\)[/tex] first, then add back [tex]\(1\)[/tex]:
1. Compute:
[tex]$$244 - 100 = 144.$$[/tex]
2. Since [tex]\(99\)[/tex] is [tex]\(1\)[/tex] less than [tex]\(100\)[/tex], add [tex]\(1\)[/tex] back:
[tex]$$144 + 1 = 145.$$[/tex]
So,
[tex]$$ 244 - 99 = 145. $$[/tex]
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(c) Calculate [tex]\( 99 \times 6 \)[/tex]
Notice that [tex]\(99\)[/tex] is [tex]\(1\)[/tex] less than [tex]\(100\)[/tex]. Multiply by [tex]\(6\)[/tex] using [tex]\(100 \times 6\)[/tex] then subtract [tex]\(6\)[/tex]:
1. Compute:
[tex]$$100 \times 6 = 600.$$[/tex]
2. Subtract:
[tex]$$600 - 6 = 594.$$[/tex]
Thus,
[tex]$$ 99 \times 6 = 594. $$[/tex]
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(d) Calculate [tex]\( 99 \times 15 \)[/tex]
Similarly, rewrite [tex]\(99\)[/tex] as [tex]\(100-1\)[/tex]:
1. Multiply:
[tex]$$100 \times 15 = 1500.$$[/tex]
2. Then subtract [tex]\(15\)[/tex]:
[tex]$$1500 - 15 = 1485.$$[/tex]
So,
[tex]$$ 99 \times 15 = 1485. $$[/tex]
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Final Answers:
[tex]\[
\begin{array}{ll}
\text{(a)} & 153 \\
\text{(b)} & 145 \\
\text{(c)} & 594 \\
\text{(d)} & 1485 \\
\end{array}
\][/tex]
These are the results of the mental calculations.
–––––––
(a) Calculate [tex]\( 99 + 54 \)[/tex]
Notice that [tex]\(99\)[/tex] is just [tex]\(1\)[/tex] less than [tex]\(100\)[/tex]. We can add using [tex]\(100\)[/tex] and then adjust:
1. Compute:
[tex]$$100 + 54 = 154.$$[/tex]
2. Since we added [tex]\(1\)[/tex] extra (because [tex]\(100\)[/tex] is [tex]\(1\)[/tex] more than [tex]\(99\)[/tex]), subtract [tex]\(1\)[/tex]:
[tex]$$154 - 1 = 153.$$[/tex]
So,
[tex]$$ 99 + 54 = 153. $$[/tex]
–––––––
(b) Calculate [tex]\( 244 - 99 \)[/tex]
Recognize that subtracting [tex]\(99\)[/tex] is almost subtracting [tex]\(100\)[/tex]. We perform the subtraction with [tex]\(100\)[/tex] first, then add back [tex]\(1\)[/tex]:
1. Compute:
[tex]$$244 - 100 = 144.$$[/tex]
2. Since [tex]\(99\)[/tex] is [tex]\(1\)[/tex] less than [tex]\(100\)[/tex], add [tex]\(1\)[/tex] back:
[tex]$$144 + 1 = 145.$$[/tex]
So,
[tex]$$ 244 - 99 = 145. $$[/tex]
–––––––
(c) Calculate [tex]\( 99 \times 6 \)[/tex]
Notice that [tex]\(99\)[/tex] is [tex]\(1\)[/tex] less than [tex]\(100\)[/tex]. Multiply by [tex]\(6\)[/tex] using [tex]\(100 \times 6\)[/tex] then subtract [tex]\(6\)[/tex]:
1. Compute:
[tex]$$100 \times 6 = 600.$$[/tex]
2. Subtract:
[tex]$$600 - 6 = 594.$$[/tex]
Thus,
[tex]$$ 99 \times 6 = 594. $$[/tex]
–––––––
(d) Calculate [tex]\( 99 \times 15 \)[/tex]
Similarly, rewrite [tex]\(99\)[/tex] as [tex]\(100-1\)[/tex]:
1. Multiply:
[tex]$$100 \times 15 = 1500.$$[/tex]
2. Then subtract [tex]\(15\)[/tex]:
[tex]$$1500 - 15 = 1485.$$[/tex]
So,
[tex]$$ 99 \times 15 = 1485. $$[/tex]
–––––––
Final Answers:
[tex]\[
\begin{array}{ll}
\text{(a)} & 153 \\
\text{(b)} & 145 \\
\text{(c)} & 594 \\
\text{(d)} & 1485 \\
\end{array}
\][/tex]
These are the results of the mental calculations.
