# Determine whether the given problem is an equation or an expression. If it is an

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. $$\displaystyle\frac{y}{{4}}+\frac{{{2}{y}}}{{5}}-\frac{{{3}{y}}}{{10}}$$

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Velsenw
Step 1
Given that:
$$\displaystyle{\frac{{{y}}}{{{4}}}}+{\frac{{{2}{y}}}{{{5}}}}-{\frac{{{3}{y}}}{{{10}}}}$$
It is an expression.
To determine whether the given problem is an equation or expression,
Expression:
An expression is a number, a variable, or a combination of numbers and variables and operation symbols
Equation:
An equation is made up of two expressions connected by an equal (=) sign.
Therefore the given problem is an expression.
Step 2
To solve the given expressions,
L.C.M of 4, 5 and 10 is 20
$$\displaystyle{\frac{{{y}}}{{{4}}}}+{\frac{{{2}{y}}}{{{5}}}}-{\frac{{{3}{y}}}{{{10}}}}={\frac{{{5}{y}+{4}{\left({2}{y}\right)}-{2}{\left({3}{y}\right)}}}{{{20}}}}$$
$$\displaystyle={\frac{{{5}{y}+{8}{y}-{6}{y}}}{{{20}}}}$$
$$\displaystyle={\frac{{{7}{y}}}{{{20}}}}$$