Question

Saleem wants to create a table of ratios that are equivalent to 2/3. He includes the ratios 4/5 and 5/6.

Are these ratios equivalent to 2/3? Explain your reasoning,

Answer 1

The ratios 4/5 and 5/6 are not equivalent to 2/3. Equivalency can be tested through cross-multiplication, and in both cases, the products do not match those of 2/3, indicating that the ratios are not equivalent.

Step-by-step explanation:

Saleem wants to determine if the ratios 4/5 and 5/6 are equivalent to 2/3. To be equivalent, two ratios must have the same value when simplified. To check equivalency, one can cross-multiply the ratios or simplify them for comparison.

For 4/5 to be equivalent to 2/3:

• Cross Multiply: (4 × 3) must equal (5 × 2)
• This would give us 12 = 10, which is not true.
• Therefore, 4/5 is not equivalent to 2/3.

For 5/6 to be equivalent to 2/3:

• Cross Multiply: (5 × 3) must equal (6 × 2)
• This would give us 15 = 12, which is also not true.
• Thus, 5/6 is also not equivalent to 2/3.

The ratios Saleem listed (4/5 and 5/6) are not equivalent to the ratio 2/3, as their cross products do not match the cross products of 2/3.

Answer 2

No....if you set them up as proportions and cross multiply the sides do not equal