a landscaper ordered $\frac{5}{6}$ ton of soil and $\frac{2}{3}$ ton of mulch from a nursery. how many tons of material did she order altogether?

a. $\frac{7}{9}$ ton. since the landscaper has $\frac{5}{6}$ tons of soil and $\frac{2}{3}$ tons of mulch to add two fractions we just add the numerator and denominator together to get $\frac{7}{9}$ tons.
b. $\frac{5}{4}$ ton. since the denominators are not the same for both fractions we need to cross multiply to get the total number of tons of material used by the landscapers.
c. $1\frac{1}{2}$ ton. since the denominators are different we first need to get a common denominator. since 3 times 2 is 6 we can multiply the numerator and denominator of $\frac{2}{3}$ by 2 and then add them directly across.
d. 1 ton. since the denominators are not the same for both fractions we need to cross add to get the total number of tons of material used by the landscapers which come to $\frac{8}{8}$ and reduces to 1 ton.

Question

a landscaper ordered $\frac{5}{6}$ ton of soil and $\frac{2}{3}$ ton of mulch from a nursery. how many tons of material did she order altogether?

a. $\frac{7}{9}$ ton. since the landscaper has $\frac{5}{6}$ tons of soil and $\frac{2}{3}$ tons of mulch to add two fractions we just add the numerator and denominator together to get $\frac{7}{9}$ tons.
b. $\frac{5}{4}$ ton. since the denominators are not the same for both fractions we need to cross multiply to get the total number of tons of material used by the landscapers.
c. $1\frac{1}{2}$ ton. since the denominators are different we first need to get a common denominator. since 3 times 2 is 6 we can multiply the numerator and denominator of $\frac{2}{3}$ by 2 and then add them directly across.
d. 1 ton. since the denominators are not the same for both fractions we need to cross add to get the total number of tons of material used by the landscapers which come to $\frac{8}{8}$ and reduces to 1 ton.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Fraction Addition", "Common Denominator" ], "new_concepts": [], "current_concepts": [ "Fraction Addition", "Common Denominator", "Mixed Numbers" ] } ## Identify the operation $$ \text{Total} = \frac{5}{6} + \frac{2}{3} $$ ## Find a common denominator $$ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} $$ ## Add and simplify $$ \frac{5}{6} + \frac{4}{6} = \frac{9}{6} = \frac{3}{2} = 1 \frac{1}{2} $$

a. 7/9 ton. Since the landscaper has 5/6 tons of soil and 2/3 tons of mulch to add two fractions we just add the numerator and denominator together to get 7/9 tons.

b. 5/4 ton. Since the denominators are not the same for both fractions we need to cross multiply to get the total number of tons of material used by the landscapers.

c. 1 1/2 ton. Since the denominators are different we first need to get a common denominator. Since 3 times 2 is 6 we can multiply the numerator and denominator of 2/3 by 2 and then add them directly across.

d. 1 ton. Since the denominators are not the same for both fractions we need to cross add to get the total number of tons of material used by the landscapers which come to 8/8 and reduces to 1 ton.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Fraction Addition" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the operation

Find a common denominator

Add and simplify

Answer: