[PDF] Equations and Problem Solving with Fractions Variable Expression

View - Download Equations and Problem Solving with Fractions Variable Expression

Previous PDF

Next PDF

MAT 040: Basic Math Learning Unit 6: Handout

Page 1 of 10

Equations and Problem Solving with Fractions

Variable

A variable is a letter used to represent a number.

Expression

An algebraic expression is a combination of variables and/or numbers and symbols.

Equation

An equation is a statement of equality between two expressions.

An equation has an equal sign.

Key words help translate a problem into an equation or an expression.

Key Word Translation

is = (equals) of, product (multiply)

Sum, increase, total + (add)

difference, less, decrease (subtract) quotient (divide) twice half Multiply by 1/2

The following are examples of expressions.

MAT 040: Basic Math Learning Unit 6: Handout

Page 2 of 10

Translating Words into an Expression

You can use any variable to represent a number.

Common letters used as variables are x, y, z, and n.

Words Expression

five times a number 5n or the sum of 1/3 and a number 1/3 + x seven less than a number x twice a number 2y or a number divided by 4 x or four fifths of a number y or

Translating Words into an Equation

Represent the unknown number with any variable.

Use symbols to represent key words.

Words Equation

Three times a number is 21. or

The product of a number and 8 is 40. or

The difference between a number and ½ is 6. x

Twice a number equals ¼. or

Five more than a number is 20.

One fourth less than a number is one third.

The quotient of a number and 5 is ½.

The sum of a number and 1/5 is 10.

MAT 040: Basic Math Learning Unit 6: Handout

Page 3 of 10

Solving Equations

You can use properties of equality to solve equations.

Addition Property of Equality

The addition property of equality allows you to add the same number to each side of an equation.

Subtraction Property of Equality

The subtraction property of equality allows you to subtract the same number from each side of an equation.

Multiplication Property of Equality

The multiplication property of equality allows you to multiply by the same non-zero number on each side of an equation.

Division Property of Equality

The division property of equality allows you to divide by the same non-zero number on each side of an

equation.

Basic Operations

The four basic operations are addition, subtraction, multiplication and division. Inverse operations are

used when solving equations. An inverse operation will undo the result of a previous operation.

Example 1

The following illustrates an inverse operation.

Start with 4.

Add six to four to get 10. 4 + 6 = 10

MAT 040: Basic Math Learning Unit 6: Handout

Page 4 of 10

To undo this operation subtract 6 from 10. 10 - 6 = 4 Now you are back to the number you started with which is 4.

We were able to undo adding 6 by subtracting 6.

Inverse Operations

Addition and subtraction are inverse operations. Multiplication and division are also inverse operations.

Operation Inverse Operation

Addition Subtraction

Subtraction Addition

Multiplication Division

Division Subtraction

To solve an equation you must get the variable alone on one side of the equation. You can do this by performing the inverse operation on each side of the equation.

Example 2

Solve the following equation for x.

The inverse of adding 9 is subtracting 9.

Subtract 9 from each side of the equation.

Example 3

Solve the following equation for n.

The inverse of subtracting 5 is adding 5.

Add 5 to each side of the equation.

Example 4

Solve the following equation for x.

5x means 5 times x.

The inverse of multiplying by 5 is dividing by 5.

Divide each side by 5.

MAT 040: Basic Math Learning Unit 6: Handout

Page 5 of 10

Example 5

Solve the following equation for x.

means

The inverse of dividing by 9 is multiplying by 9.

Multiply each side by 9.

The following examples show how to translate word problems into equations and solve for a variable.

Example 6

Solve. A number increased by is . Replace ͞a number" with

Replace "increased" with +.

Replace "is" with =."

The inverse of adding is to subtract .

Subtract from each side of the equation.

MAT 040: Basic Math Learning Unit 6: Handout

Page 6 of 10

Example 7

Solve. less than a number is . To find less, subtract from the unknown number. Let the unknown number be n.

Order is important in subtraction.

would be wrong.

The inverse of subtracting is adding .

Add to each side of the equation.

Notice:

Example 8

The quotient of a number and 4 is . A number divided by 4 is represented as .

Replace ͞is" with the с sign.

The inverse of dividing by 4 is multiplying by 4.

Multiply each side of the equation by 4.

MAT 040: Basic Math Learning Unit 6: Handout

Page 7 of 10

Example 9

of what number is 16? The word ͞of" represents multiplication.

Replace ͞is" with the с sign.

The inverse of multiplying by is dividing by .

Divide each side of the equation by

When dividing by invert and multiply by .

Example 10

What fraction of is ? Replace ͞what fraction" with

Replace "of" with times.

Replace "is" with =."

Inverse of multiplying by is dividing by 3 .

Divide each side of the equation by .

When dividing by , invert and multiply by

Divide 2 and 4 by 2.

MAT 040: Basic Math Learning Unit 6: Handout

Page 8 of 10

Example 11

Find a number such that ¾ of it is . The word ͞of" represents multiplication.

Replace ͞is" with the = sign.

The unknown number is represented by

The inverse of multiplying by is dividing by .

Divide each side of the equation by .

When dividing by invert and multiply by .

Divide 8 and 4 by 4.

Example 12

Half of a number is . To find half of a number, multiply by .

Replace ͞is" with the с sign.

The unknown number is represented by

The inverse of multiplying by is dividing by .

Divide each side of the equation by .

When dividing by invert and multiply by .

Divide 8 and 4 by 2.

MAT 040: Basic Math Learning Unit 6: Handout

Page 9 of 10

Example 13

of what number is 5? The word ͞of" represents multiplication.

Replace ͞is" with the с sign.

The unknown number is represented by

Change each mixed number to an

improper fraction.

The inverse of multiplying by is dividing by .

Divide each side of the equation by .

When dividing by invert and multiply by .

Divide 16 and 8 by 8. Divide 3 and 3 by 3.

Example 14

What fraction of is ? Replace ͞what fraction" with n.

Replace "of " with times.

Replace ͞is" with the с sign.

The inverse of multiplying by is

dividing by .

Divide each side of the equation by .

When dividing by , invert and multiply by .

MAT 040: Basic Math Learning Unit 6: Handout

Page 10 of 10

Example 15

Find of . Replace "of " with times.

Let the unknown number be represented by

© Brenda Moore and Indian Hills Community Collegequotesdbs_dbs47.pdfusesText_47

[PDF] maths fractions

[PDF] Maths Fractions 3 ème

[PDF] maths fractions college

[PDF] maths fractions priorité operatoires

[PDF] Maths Fréquence valeurs

[PDF] maths full form

[PDF] Maths Géographie

[PDF] Maths géometrie

[PDF] maths geometrie 4 eme

[PDF] Maths géométrie dur

[PDF] Maths geometrie pyramides

[PDF] maths graphique fonction

[PDF] MATHS IMPORTAANT !!

[PDF] Maths in english

[PDF] maths informatique metier