Equations with Decimal and

Fractional Terms

Slideshow 22, Mathematics

Mr Richard SasakiRoom 307

Objectives• Solve equations with non-integer

terms (decimal)• Review how to add and subtract

fractions• Solve equations with fractions

DecimalsMultiplying decimal numbers by , , (or some ), can create integers!

10

72

100

2158

10

413

1000

32402

100

−300 593

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

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

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

FractionsLet’s have some practice working with fractions.

1 1 2 −1

2 𝑥 𝑥 𝑥2 2 𝑥34

−1612

2935

05𝑥6

3𝑥10

3𝑥14

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.

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

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