Question

How do you write and simplify “150 boys to 175 girls” as a ratio?

Answer 1

Hint: We know that mathematical expression and algebraic expression are both the same. we need to convert the given word sentence to mathematical expression. An algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations. An expression is a group of terms. Here algebraic operations are addition, subtraction, division and multiplication etc.

Complete step-by-step answer:
We have “150 boys to 175 girls”.
Since we know that ratio of boys to girls is represented by \[boys:girls\] or \[\dfrac{{boys}}{{girls}}\].
Similarly we can write “150 boys to 175 girls” as \[150:175\] or \[\dfrac{{150}}{{175}}\].
Now for simplification
\[ \Rightarrow \dfrac{{150}}{{175}}\]
Now divide the numerator and the denominator by 25,
\[ \Rightarrow \dfrac{6}{7}\]. This is the exact form.
We can also put it in decimal form
\[ \Rightarrow 0.857\]
The simplest form of \[\dfrac{{150}}{{175}}\] is \[6:7\] or \[\dfrac{6}{7}\]

Note: Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation\[( + )\]. Similarly If we have ‘less’ or ‘difference’ we use subtraction \[( - )\]. If we have ‘quotient’ we use division operation \[( \div )\]. To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.