evaluate the expression $\frac{4}{15} \div x + 0.4$ for $x$ if: $x = 1$; $x = \frac{4}{9}$; $x = 1\frac{1}{3}$.

answer

if $x = 1$, the value of the expression is .

if $x = \frac{4}{9}$, the value of the expression is ,

if $x = 1\frac{1}{3}$, the value of the expression is .

Question

evaluate the expression $\frac{4}{15} \div x + 0.4$ for $x$ if: $x = 1$; $x = \frac{4}{9}$; $x = 1\frac{1}{3}$.

answer

if $x = 1$, the value of the expression is  .

if $x = \frac{4}{9}$, the value of the expression is  ,

if $x = 1\frac{1}{3}$, the value of the expression is  .

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Fraction Division", "Dividing Mixed Numbers" ], "new_concepts": [ "Algebraic Expression Evaluation" ], "current_concepts": [ "Fraction Division", "Dividing Mixed Numbers", "Algebraic Expression Evaluation" ] } ## Substitute $x = 1$ into the expression Using the *Fraction Division* knowledge point $$ \begin{aligned} &\frac{4}{15} \div 1 + 0.4 \ &= \frac{4}{15} + \frac{2}{5} \ &= \frac{4}{15} + \frac{6}{15} \ &= \frac{10}{15} = \frac{2}{3} \end{aligned} $$ ## Substitute $x = \frac{4}{9}$ into the expression Using the *Fraction Division* knowledge point $$ \begin{aligned} &\frac{4}{15} \div \frac{4}{9} + 0.4 \ &= \frac{4}{15} \times \frac{9}{4} + \frac{2}{5} \ &= \frac{9}{15} + \frac{6}{15} \ &= \frac{15}{15} = 1 \end{aligned} $$ ## Substitute $x = 1\frac{1}{3}$ into the expression Using the *Dividing Mixed Numbers* and *Fraction Division* knowledge points $$ \begin{aligned} &1\frac{1}{3} = \frac{4}{3} \ &\frac{4}{15} \div \frac{4}{3} + 0.4 \ &= \frac{4}{15} \times \frac{3}{4} + \frac{2}{5} \ &= \frac{3}{15} + \frac{6}{15} \ &= \frac{9}{15} = \frac{3}{5} \end{aligned} $$ ## Question 1 If $x = 1$, the value of the expression is $\frac{2}{3}$. ## Question 2 If $x = \frac{4}{9}$, the value of the expression is $1$. ## Question 3 If $x = 1\frac{1}{3}$, the value of the expression is $\frac{3}{5}$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Algebraic Expression Evaluation" ] }

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QUESTION IMAGE

Question

Explanation:

Substitute \(x = 1\) into the expression

Substitute \(x = \frac{4}{9}\) into the expression

Substitute \(x = 1\frac{1}{3}\) into the expression

Answer:

Question 1

Question 2

Question 3