 # Determine whether the given problem is an equation or an expression. If it is an Dolly Robinson 2021-09-30 Answered

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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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
$$\displaystyle{\frac{{{y}}}{{{4}}}}+{\frac{{{2}{y}}}{{{5}}}}-{\frac{{{3}{y}}}{{{10}}}}={\frac{{{5}{y}+{4}{\left({2}{y}\right)}-{2}{\left({3}{y}\right)}}}{{{20}}}}$$
$$\displaystyle={\frac{{{5}{y}+{8}{y}-{6}{y}}}{{{20}}}}$$
$$\displaystyle={\frac{{{7}{y}}}{{{20}}}}$$