Question 1
A fruit salad recipe uses 4 cups of mango and 2 cups of pineapple. What is the ratio of mango to pineapple in simplest form?No clue? Show me the answer
Correct answerCorrect!
IncorrectStep-by-step walkthrough
Choose a solution method
Method #1Direct ApproachStep 1: Write the ratio in the correct order
The question asks for mango to pineapple, so we write mango first. The ratio is 4 : 2.
Step 2: Find the HCF of 4 and 2
Factors of 4: 1, 2, 4. Factors of 2: 1, 2. The HCF = 2.
Step 3: Divide both parts by the HCF
Step 4: State the answer
The ratio of mango to pineapple in simplest form is 2 : 1.
Method #2Process of EliminationStep 1: Identify what is being asked
We need the ratio of mango to pineapple in simplest form. The original ratio is 4 : 2.
Step 2: Eliminate '4 : 2'
4 : 2 is the original ratio but it is not in simplest form because both numbers share a common factor of 2.
Step 3: Eliminate '1 : 2' and '2 : 4'
1 : 2 reverses the order, comparing pineapple to mango instead. 2 : 4 is also reversed and not simplified.
Step 4: Select the correct answer
2 : 1 is the simplified form of 4 : 2 (dividing both by 2), with mango listed first. This is correct.
Question 2
Which of the following correctly describes a rate (not a ratio)?No clue? Show me the answer
Correct answerCorrect!IncorrectStep-by-step walkthrough
Choose a solution method
Method #1Direct ApproachStep 1: Recall the definition of a rate
A rate compares two quantities with different units, such as distance and time. A ratio compares quantities of the same type.
Step 2: Check each option for different units
60 km per hour compares kilometres (distance) and hours (time) — two different units. This fits the definition of a rate.
Step 3: Classify the other options
Boys to girls, flour to sugar, and a simplified ratio all compare quantities of the same type — these are ratios, not rates.
Step 4: Select the answer
60 km per hour is the only rate because it compares two different types of measurement.
Method #2Process of EliminationStep 1: Identify what a rate requires
A rate must compare two quantities with different units (e.g., distance and time, or cost and weight).
Step 2: Eliminate '3 boys for every 2 girls'
Both boys and girls are people — same type of quantity. This is a ratio, not a rate.
Step 3: Eliminate '12 : 8 simplified' and '5 cups of flour to 2 cups of sugar'
12 : 8 simplified is just a ratio with no units. Flour to sugar compares two ingredients measured in the same unit (cups) — still a ratio.
Step 4: Select the correct answer
60 km per hour compares kilometres and hours — different units — making it a rate.
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