## Solving Algebra Word Problems

In algebra a word problem is equivalent to a mathematical story problem. In which we need to decide what information is given, what is to be found and the translation of English sentences to equivalent mathematical sentences with the appropriate operations. So, basically the given problem has to be divided into parts and each part solved.

For solving, first the translation of the English sentences to equivalent equations with variables is important. Then the equations are to be solved using the appropriate operations and finally the solution should be checked if it works for the given problem.

So the key to how to solve algebra word problems is to correctly translate English words to equations with variables. The following are some key words and their respective mathematical translations:

Addition sum of, increased by, more than, combined, together

Total of, added to

Subtraction Minus, difference between, decreased by, less than

Multiplication Times, of, multiplied by, product of

Division Out of, ratio of, quotient of, per, when divide by 100 it is percent

Equals Are, is, was, were, in all, will be, yields, gives

In the above key words some of the words have to be translated with care. For instance, ‘per’ means divided by. If we have something like 80 miles where covered using 2 gallons it means 40 miles per gallon, so division. Also at times ‘a’ is used for division, for example, a person paid $32 for 10 gallons of gas, it would be $3.20 a gallon. ‘less than’ has to be taken backwards, that is, if it is given he makes $2.75 an hour less than me, means you subtract $2.75 from your wage and not your wage from $2.75, so it is constructed backwards. So, translations are to be done carefully as per the given information.

let the number be ‘x’

Half of the number = x/2

Five is added to half of the number = (x/2) + 5

Now, we can translate the given whole sentence and write the mathematical equation as

(x/2)+5= 11

Next step would be to solve for x

Subtracting 5 on both sides

(x/2)+5-5 = 11-5

(x/2)=6

Multiplying on both sides with 2

(x/2)(2) = 6(2)

x=12

Finally checking the answer, 12/2=6+5=11. So the solution x=12 is correct!

For solving, first the translation of the English sentences to equivalent equations with variables is important. Then the equations are to be solved using the appropriate operations and finally the solution should be checked if it works for the given problem.

So the key to how to solve algebra word problems is to correctly translate English words to equations with variables. The following are some key words and their respective mathematical translations:

**Mathematical Operation English words**Addition sum of, increased by, more than, combined, together

Total of, added to

Subtraction Minus, difference between, decreased by, less than

Multiplication Times, of, multiplied by, product of

Division Out of, ratio of, quotient of, per, when divide by 100 it is percent

Equals Are, is, was, were, in all, will be, yields, gives

In the above key words some of the words have to be translated with care. For instance, ‘per’ means divided by. If we have something like 80 miles where covered using 2 gallons it means 40 miles per gallon, so division. Also at times ‘a’ is used for division, for example, a person paid $32 for 10 gallons of gas, it would be $3.20 a gallon. ‘less than’ has to be taken backwards, that is, if it is given he makes $2.75 an hour less than me, means you subtract $2.75 from your wage and not your wage from $2.75, so it is constructed backwards. So, translations are to be done carefully as per the given information.

**Algebra Questions and Answers****Question:**Find the number if when five is added to half of the number gives eleven.**Answer:**First the given sentence is translated into mathematical expression by partslet the number be ‘x’

Half of the number = x/2

Five is added to half of the number = (x/2) + 5

Now, we can translate the given whole sentence and write the mathematical equation as

(x/2)+5= 11

Next step would be to solve for x

Subtracting 5 on both sides

(x/2)+5-5 = 11-5

(x/2)=6

Multiplying on both sides with 2

(x/2)(2) = 6(2)

x=12

Finally checking the answer, 12/2=6+5=11. So the solution x=12 is correct!

**free math problem solver online**helps in checking the solutions.