Equations with Decimal and Fractional Terms
description
Transcript of Equations with Decimal and Fractional Terms
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Equations with Decimal and
Fractional Terms
Slideshow 22, Mathematics
Mr Richard SasakiRoom 307
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Objectives• Solve equations with non-integer
terms (decimal)• Review how to add and subtract
fractions• Solve equations with fractions
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DecimalsMultiplying decimal numbers by , , (or some ), can create integers!
10
72
100
2158
10
413
1000
32402
100
−300 593
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Decimal NumbersDecimal numbers make questions look harder than they actually are.ExampleSolve .What can we do to make this equation look easier?Multiply both sides
by !0.4 𝑥=0.5 𝑥−0.6×10 ×104 𝑥=5 𝑥−6−5 𝑥 −5 𝑥−𝑥=−6×(−1) ×(−1)𝑥=6
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Decimal NumbersWe should multiply both sides of the expression by the smallest value to make all terms have integers.ExampleSolve .The term on the right has hundredths, so let’s multiply both sides by .100
5.6 𝑥−0.1=0.05𝑥×100 ×100560 𝑥−10=5 𝑥−560 𝑥 −560 𝑥−10=−555𝑥÷(−555) ÷(−555)𝑥=
10555¿
2111
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Answers
𝑥=3 𝑥=5 𝑥=310
𝑥=2 𝑥=2 𝑥=27𝑥=7 𝑥=5 𝑥=±3𝑥=±5 𝑥=0.6 𝑥=±3𝑥=
5324
𝑥=±110
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FractionsLet’s have some practice working with fractions.
1 1 2 −1
2 𝑥 𝑥 𝑥2 2 𝑥34
−1612
2935
05𝑥6
3𝑥10
3𝑥14
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Fractional TermsLet’s try some equations with fractions.ExampleSolve .
−𝑥3
−𝑥36 𝑥
3=4
2 𝑥=4𝑥=2
Equations are simple to solve when denominators of fractions are the same.
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Fractional TermsExampleSolve .
−𝑥3 −
𝑥32𝑥
5−𝑥3=2
We need to calculate .6 𝑥15−5 𝑥15
=2
If you are low on vertical space, you can calculate horizontally by using the symbol. This means implies that.
⇒𝑥15
=2⇒𝑥=30
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Answers
𝑥=4 𝑥=7 𝑥=8
𝑥=6 𝑥=12 𝑥=21
𝑥=16 𝑥=36 𝑥=−353
𝑥=307 𝑥=282 𝑥=
74