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Ch. 7.4 Equations with Fractions and Decimals

Ch. 7.4 Equations with Fractions and Decimals. To solve an equation with fractions:. Find the least common denominator (LCD) of all fraction terms on both sides of the equation. Multiply each term on both sides of the equation by the LCD. This should remove all fractions from the equation.

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Ch. 7.4 Equations with Fractions and Decimals

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  1. Ch. 7.4 Equations with Fractions and Decimals

  2. To solve an equation with fractions: • Find the least common denominator (LCD) of all fraction terms on both sides of the equation. • Multiply each term on both sides of the equation by the LCD. This should remove all fractions from the equation. • Solve the resulting equation using the methods from earlier sections.

  3. Solve: • LCD = 20, so multiply both sides by 20.

  4. Solve: • LCD = 12, so multiply each term by 12

  5. Solve:

  6. Solving Linear Equations • Tip: Equations containing fractions and decimal numbers can lead to messy computations. To avoid such messy computations, be sure to follow these tips. • When clearing an equation containing fractions, be sure to multiply every term on each side of the equation by the LCD. • When clearing an equation containing decimals, be sure to multiply every term on each side of the equation by an appropriate power of 10. Choose the smallest exponent on 10 needed to eliminate the decimals.

  7. – 10 = + m m m m m m m m m 8 – 10 = + 8 8 – 10 = + 8 8 8 1 5 3 1 5 3 1 3 5 8 4 2 2 2 4 4 8 8 Solving an Equation with Fractions Multiply by LCD: 8. Distribute. 5m – 80 = 6m + 4m Multiply. Now use the four steps to solve this equivalent equation.

  8. – 80 5m = 5 5 5m – 80 = 6m + 4m 5m – 80 = 10m Step 1 Combine terms. Subtract 5m. Step 2 5m – 80 – 5m = 10m– 5m – 80 = 5m Combine terms. Step 3 Divide by 5. – 16 = m

  9. – 10 = + m m m (–16) (–16) (–16) – 10 = + 3 3 1 5 1 5 8 2 4 8 2 4 Step 4 Check by substituting –16 for m in the original equation. ? Let m = –16. –10 – 10 = –12 – 8 ? Multiply. –20 = –20 True The solution to the equation is –16.

  10. 17v – 153 = 17 17 Solving an Equation with Decimals 0.2v – 0.03 ( 11 + v ) = – 0.06 ( 31 ) 20v – 3 ( 11 + v ) = – 6 ( 31 ) Multiply by 100. Step 1 20v – 3 ( 11) – 3 ( v ) = – 186 Distribute. 20v – 33 – 3v = – 186 Multiply. Combine terms. 17v – 33 = – 186 Step 2 17v – 33 + 33 = – 186 + 33 Add 33. 17v = – 153 Combine terms. Divide by 17. Step 3 Check to confirm that – 9 is the solution. v = – 9

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