Given the ratio 3:4::6:8, which operation verifies the proportion?
3 x 8 = 6 x 4
The given ratio problem requires verification of the proportion 3:4::6:8. This type of problem tests understanding of the concept of proportion, which states that two ratios are equal.
The proportion 3:4::6:8 means that the ratio of 3 to 4 is the same as the ratio of 6 to 8. In mathematical terms, this can be understood as:
- If \frac{a}{b} = \frac{c}{d}, then the proportion is true.
- Alternatively, we use the cross-multiplication property, which states that for the ratios to be equal, the cross products must be equal. This means:
Cross-multiplication of the terms gives us:
- 3 x 8 = 24
- 6 x 4 = 24
Since both cross products are equal, the given proportion is verified correctly.
Now, let's evaluate the options:
- 3 \times 8 = 6 \times 4 : This is true, as both sides equal 24.
- 3 - 4 = 6 - 8 : This simplifies to -1 = -2, which is false.
- 3 + 8 = 6 + 4 : This simplifies to 11 = 10, which is false.
- \frac{3}{8} = \frac{6}{4}: This is false because \frac{3}{8} is not equal to \frac{3}{2}.
Thus, the correct option that verifies the proportion is 3 x 8 = 6 x 4.
Conclusion: In verifying proportions, cross-multiplication is a reliable method to determine the equality of two ratios.
Similar Questions
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Important Questions from Ratio and proportion
A’s marks in Mathematics are directly proportional to practice time. In 6 hours of practice, A gets 70 marks. What should be the practice time (approximately) to get 90 marks?
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In a triangle ABC, D and E are two points on sides AB and AC, respectively, such that DE is parallel to BC and AD : DB = 3 : 5. If AC = 5.6 cm, then find the value (in cm) of AE.
In a triangle ABC, P and Q are two points on AB and AC, respectively, such that PQ is parallel to BC. If AC = 5QC, then the ratio PQ : BC is equal to:
Find the mean proportional between 25 and 81.
