(1) Numerical equation- A mathematical statement that contains numbers and equal "=" sign.
For example: \(4+6=10\)
(2) Algebraic equation- A mathematical statement that contains numbers, variables and equal "=" sign.
For example: \(2x+3=13\)
A \(2+3=1+5\)
B \(3x+6\)
C \(36x+2=10\)
D \(5+6\)
1. Keywords for Addition:
Plus
More than
And
Sum
Total
Added to
Combine
Altogether
2. Keywords for Subtraction:
Minus
Less than
Fewer than
Difference
Reduce
3. Keywords for Multiplication:
Times
Product
Double (multiplied by \(2\))
Twice (multiplied by \(2\))
Triple (multiplied by \(3\))
Quadruple (multiplied by \(4\))
4. Keywords for Division:
By
Divided into
Shared
Quotient
Per
Share (equally)
Split (Equally)
Half (divided by \(2\))
For example : Thirteen times a number is twenty-six. Write it as a mathematical equation.
Here,
Thirteen \(\to\;13\)
Times \(\to\;×\) (multiplication)
a number \(\to\;let\;(x)\)
is \(\to\;=\)
Twenty-six \(\to\;26\)
\(13×x=26\;\text{or}\;13x=26\)
Examples:
A \(22\div x=28\)
B \(22x=28\)
C \(22-x=28\)
D \(22+x=28\)
For example:
On his birthday, Aron brought \(100\) candies to school. After distribution, he was left with \(20\) candies. Write an equation to represent the number of candies he distributed.
\(\to\) Let number of candies Aron distributed \(=x\)
\(\to\) Number of candies Aron brought \(=100\)
\(\to\) Number of candies he was left with \(=20\)
Here,
\(\underbrace{\text{(Number of candies Aron brought)}}_{100}-\underbrace{\text{(Number of candies he distributed)}}_{x}=\underbrace{\text{(Number of candies he was left with)}}_{20}\)
So, the equation is, \(100-x=20\)
A \(2x-6=8\)
B \(8-6x=2\)
C \(2x-8=6\)
D \(8x-6=2\)
1. Keywords for Addition:
Plus
More than
And
Sum
Total
Added to
Combine
Altogether
2. Keywords for Subtraction:
Minus
Less than
Fewer than
Difference
Reduce
3. Keywords for Multiplication:
Times
Product
Double (multiplied by \(2\))
Twice (multiplied by \(2\))
Triple (multiplied by \(3\))
Quadruple (multiplied by \(4\))
4. Keywords for Division:
By
Divided into
Shared
Quotient
Per
Share (equally)
Split (Equally)
Half (divided by \(2\))
For example :
Write \(6a=b\) in words.
\(6a=b\;\text{or}\;6×a=b\)
Here,
\('6'\;\to\) Six
Multiplication \((\times)\;\to\) times
\('a'\;\to\) a number
\('='\;\to\) is
\('b'\;\to\) another number
So, the equation is-
Six times a number is another number.
Examples:
A The sum of a number and the quotient of another number by five is twelve
B Five divided by a number plus another number is twelve
C A number and five plus another number is twelve
D five times a number plus another number is twelve
There are \('b'\) number of packets of chocolates in a box. Each packet has \('x'\) chocolates and it is given that a total number of chocolates in the box are \('y'\) . Write an equation which represents the given situation.
\(\to\) In the given situation, three variables are used which are as follows-
\('y'\) represents the total number of chocolates in the box.
\('b'\) represents the total number of packets in the box.
\('x'\) represents the total number of chocolates in each packet.
\(\to\) Since there are \('b'\) number of packets and each has \('x'\) number of chocolates. Thus, the total number of chocolates will be equal to the product of number of packets and number of chocolates in each packet.
\(\therefore\) Total number of chocolates in the box = (Total number of packets in the box) × (Total number of chocolates in each packet)
\(\Rightarrow\;y=b×x\)
or
\(\Rightarrow\;y=bx\)
A \(x=70+y\)
B \(70=x+y\)
C \(y=70+x\)
D \(x+70=70+y\)
\($x=$(2y-50)\)
Here, we will make a real world situation for the given equation.
Cody has \($x\) that is equal to \($50\) less from the two times of money \($y\).
A Cost of a pen is \($x\), then cost of \(y\) pens is \($35\).
B Cost of a black pen and a blue pen is \($x\) and \($y\) respectively. The total cost of both pens is \($35\).
C Cooper had \($x\), after purchasing a pen for \($y\) he was left with \($35\).
D Mr. Gibbons distributed \(x\) pens to \(y\) students so that each student had \(35\) pens.
1. Keywords for Addition:
Plus
More than
And
Sum
Total
Added to
Combine
Altogether
2. Keywords for Subtraction:
Minus
Less than
Fewer than
Difference
Reduce
3. Keywords for Multiplication:
Times
Product
Double (multiplied by \(2\))
Twice (multiplied by \(2\))
Triple (multiplied by \(3\))
Quadruple (multiplied by \(4\))
4. Keywords for Division:
By
Divided into
Shared
Quotient
Per
Share (equally)
Split (Equally)
Half (divided by \(2\))
For example: write the equation, \(9-x=7\) in words.
Here,
\(9\;\to\) Nine
\(-\;\to\) less than
\(x\;\to\) a number
\(=\;\to\) is
\(7\;\to\) Seven
A number less than nine is seven.
Example:
A Five shared equally by a number is eight hundredths
B Five minus a number is eight hundredths
C Five times a number is eight hundredths
D Five and a number is eight hundredths
1. Keywords for Addition:
Plus
More than
And
Sum
Total
Added to
Combine
Altogether
2. Keywords for Subtraction:
Minus
Less than
Fewer than
Difference
Reduce
3. Keywords for Multiplication:
Times
Product
Double (multiplied by \(2\))
Twice (multiplied by \(2\))
Triple (multiplied by \(3\))
Quadruple (multiplied by \(4\))
4. Keywords for Division:
By
Divided into
Shared
Quotient
Per
Share (equally)
Split (Equally)
Half (divided by \(2\))
For example:
'Seven times a number is another number'. Write it as a mathematical equation.
Here,
Seven \(\to\;7\)
Times \(\to\;\times\) (multiplication)
a number \(\to\;let\;(x)\)
is \(\to\;=\)
another number \(\to\;let\;(y)\)
So, the equation is-
\(7×x=y\;\text{or}\;7x=y\)
Examples:
A \(x-2=y\)
B \(x+2=y\)
C \(x×2=y\)
D \(x\div2=y\)